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Classical and Fuzzy-System Guidance Laws In Homing Missiles Systems1,2

Georgi M. Dimirovski1 & 2, Stoyce M. Deskovski3, and Zoran M. Gacovski3

1 Dogus University, Faculty of Engineering Acibadem, Kadikoy, 34722 Istanbul, Turkey

e-mail: gdimirovski@dogus.edu.tr 2 SS Cyril and Methodius University, Faculty of Electrical Engineering

Skopje, Macedonia 3 Military Academy “General M. Apostolski”, Skopje, Macedonia

e-mail: stodes@mt.net.mk

1 0-7803-8155-6/04/$17.00© 2004 IEEE 2 IEEEAC paper #1025

Abstract—In this paper we present developed models of homing guidance missile systems (surface-to-air and air-to-surface) and of the seeker, which is suitable for research, development and testing of different guidance and control laws, obtained from different synthesis techniques. In homing-guidance missile systems the so called proportional navigation is commonly employed, and various improved solutions and optimal guidance laws are also used. All system models for guidance and control of missiles are rather complex and typically non-linear. Guidance laws are often designed and synthesized by using linearized models, which are obtained from general laws for flying objects (missile and aircrafts) under some assumptions. In homing missile technology, the requirement for missiles to neutralize targets in the presence of widely changing range of variables in different shooting regimes is of paramount importance. To ensure a quality guidance process and small guidance error some self-adaptation property is needed, and we applied fuzzy logic to achieve it in parameters of the guidance law. We have investigated classical proportional navigation, augmented proportional navigation, and optimal guidance laws for different shooting conditions. Simulation programs were realized by using Fortran and Fuzzy Tool Box of Matlab as appropriate, and they constitute a PC training simulator platform. The results on fuzzy guidance laws combined with proportional navigation have been found more effective yet sufficiently simple for practical implementation. All simulation experiments have confirmed these findings. Index Terms— Autonomous guidance and control, fuzzy inference systems, guidance laws, homing guidance missiles.

TABLE OF CONTENTS

........................................................................... ... 1. INTRODUCTION 1 2. ON MATHEMATICAL MODELS OF HOMING … 3 3. ON GUIDANCE LAWS IN HOMING MISSILE … 6 4. A FUZZY INFERENCE SYSTEM IN SURFACE-TO-… 6 5. A FUZZY INFERENCE SYSTEM IN AIR-TO- … 9 6. COMMENTS ON APPLICATONS OF FUZZY … 12 7. CONCLUSIONS 13 REFERENCES 14

1. INTRODUCTION

By its very concept homing-guidance represents an autonomous missile guidance operating upon received target information only, i.e. detection and processing of the information based on target energy that is performed by missile’s devices [16], [40], [41]. This energy can be radio wave, light or IR ray – reflected or emitted by the target [31] – which is being captured by the missile system. The system devices for this guidance concept are completely mounted on the missile and they consist of: seeker sensor (playing a coordinator’s role), guidance computer, autopilot and missile, the latter being the controlled flying object (see Figures 1.1 and 2.1; all symbols become clear in the text). In the missile guidance computer, the classic proportional navigation (PN) is most commonly used in terms of the guidance law. However, various modified solutions of PN and optimal guidance laws based on modern control theory [5], [7], [38], [44], [51] are also employed. These laws are synthesized on the grounds of certain assumptions that allow for general models of the missile and target motions

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to be linearized and simplified.

Figure 1.1 - Illustration of missile’s kinematics variables (flying towards a target) of the mass center relative to standard fixed ),,;0( 0000 zyxG and moving ),,;( ggg zyxPG Earth’s as well as body-axis ),,;( zyxPB and aero-ballistic ),,;( bbb

b zyxPB

coordinate systems. More recently the use of fuzzy-system based computational intelligence techniques became a topic of extensive research in missile technology [11], [26], [51] too, as in many other areas of technological applications for quite some time, e.g. see [20], [23], [35]. It is the purpose of this paper to report on a couple of research results on application of the concepts of fuzzy inference (FI) and fuzzy control (FC) [36], [44], [47] in PN homing missiles to endow the seeker [51] (also see Figures 1.2 and 1.3) with additional performance capacity, It is believed to bring some novelty on application of fuzzy-logic inference systems (FIS) in conjunction with classical proportional navigation (PN) albeit our access on worldwide available literature was and is rather limited (see list of references). Also this research involved a comparative study on homing missiles with classical PN guidance and with FIS-PN guidance laws designed.

Figure 1.2 – Overall architecture of missile control and guidance

system employing seeker with structured fuzzy logic inference

system; the missile dynamics block encompasses the functional model of missile control systems

Figure 1.3 – Architecture of fuzzy-logic inference system in

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conjunction with the seeker, employing a decision unit (inference) to perform fuzzy inference based proportional navigation.

Figure 2.1 - Illustration of the geometry of guidance in the vertical plane [5] It is well known that systems for guidance and control of homing missiles are rather complex and typically non-linear. On the other hand, the need for intercepting and disabling targets with wide range of variable changes (i.e. acceleration, velocity and height) in different shooting regimes (incoming, outgoing, etc.) has to be observed. In order to achieve a quality controlled process and small guidance error we have explored the use of fuzzy logic to obtain some parameters for the guidance law by means of relatively simple affordable and reliable fuzzy inference systems (FIS) designs; one is for surface-to-air missiles and the other for air-to-surface missiles. The purpose for employing fuzzy-system inference in missile control and guidance systems stems from the fact that these can decrease the number of sensors needed in the system compared to the conventional design. And secondly, a higher manoeuvring potential of the homing guidance missile may well be achieved. The obtained results are comparable or slightly better to those known to the authors from the available literature, though this does not preclude other existing results that may even be better than ours are. The paper is written as follows. In Section 2 of this paper, we present a general simulation model of the homing-guidance system as well as simulation model for guidance in the vertical plane in sufficient details. An outline discussion on the classic guidance laws of the homing-guidance missiles is given in Section 3. In Section 4 thereafter, in two subsections, we describe our results on applying the concepts of fuzzy-logic inference and control to homing-

guidance missiles for surface-to-air shooting in two operating regimes (incoming and outgoing target). In Section 5, we present our results on the use of embedded fuzzy logic in the seeker of traditional missile control system architecture for air-to-surface shooting, along with an appropriate analysis. Section 6 provides an additional but relevant discussion on applications of fuzzy systems to missile control and guidance. And conclusions and references are given thereafter.

2. ON MATHEMATICAL MODELS FOR HOMING GUIDANCE MISSILE SYSTEMS

System models for guidance and control of surface-to-air and air-to-surface missiles are rather complex and non-linear time-varying in nature because these all emanate from general models of motion dynamics and kinematics (e.g., see [13], [25], [39]) of missiles and targets (attacked aircrafts or missiles). However, technological developments have led to a typical structure of a homing-guidance missile system [5], [39] (e.g. an anti-aircraft missile] as depicted in Figure 2.2, which has been observed in our research too along with the relevant standards [14], [21]. For actually operating homing guided missile technology the geometry relationships and the analysis of the motion in the vertical plane are of primary importance. In Figure 2.1 (also see Figure 2.2) there is depicted the geometry interpretation of guidance in the vertical plane along with all relevant kinematics variables for the model,

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following 3D representation in Figure 1.1. Technology of the system for missile guidance and control include the main devices such as target sensors, playing the role of guidance coordinator called seeker, and guidance computing configuration, which comprises the homing-guidance head and the autopilot. The block diagram model (Figure 2.3) presents the overall system for guidance and control as well as the missile as a controlled object. It also has a kinematics block that emulates the relative motion of the target relative to the missile. The main control loop is closed with this block and the output variables of missile dynamics that is amenable to real-time measurements or estimation.

Figure 2.2 - Additional geometry of related variables in the vertical plane for a missile approaching to a target, useful in

choosing and defining the respective fuzzy subsets in fuzzy-rule knowledge bases [33]

Let us observe variables that describe the state of system at any instant of time by using Figures 2.1 and 2.3. In doing so, observe the respective velocity vectors of missile and target, and relative distance r from the missile (Pursuer –

P ) to the target (Evader – E ) with PE being the Line-of-Sight (LOS). Then we have: =r ],,[ λϕr ,

Trr ],,[ λϕ &&&& = , and [ ]ϕξη &,,=∆ where ϕ , λ (or Λ )are the LOS angles measured in the vertical and the horizontal planes, respectively, and dtd /ϕϕ =& and

dtd /λλ =& (or dtd /Λ=Λ& ) are the respective rates;

look η and ξ lead angles can be measured with sensors in order to realize the chosen guidance method. The target motion is also presented with a block to whose output the motion variable of target’s center of mass (CM; point P in Figure 1.1) in the real-world space are obtained; these are: position T

oeoeoeeG zyx ],,[=R , velocity T

ezeyexeG gggVVV ],,[=V , and acceleration

TezeyexeG ggg

aaa ],,[=a .

The missile motion, given by a separate block, is represented by dynamic and kinematics equations of the flight that have been obtained via neglecting Earth’s rotation and its curvy shape. These assumptions are valid for missiles with small range and short flying time. The obtained model is non-linear and system parameters are changing in time (non-stationary). The input vector of the 6DOF model of the missile is determined by the deflection of missile control surfaces Bδ , expressed in body-axis coordinate system. The output variables of the 6DOF missile model are: the position of the missile’s CM T

opopopG zyx ],,[=R ; TB rqp ],,[=ω -

body absolute angular rates; body orientation S is determined by the angles φ - roll, θ - pitch, and ψ -

yaw; specific force TzyxB fff ],,[=f ; acceleration

TzyxG ggg

aaa ],,[=a ; velocity TzyxG ggg

VVV ],,[=V of

CM, etc. All acting vectors are represented in adequate coordinate systems as defined by ISO [21]: Normal-fixed-Earth axis ),,;( oooo zyxPG , Normal-airborne-Earth

(moving) axis ),,;( ggg zyxPG , and Body axis

),,;( zyxPB systems (also see Figures 1.1 and 2.1). A more detailed description of simulation models of homing-guidance systems is given in previous works [6], [7], [10]. For the purpose of our present investigations, system representation model of the motion in the vertical plane is of primary importance [25], [51] because it enables a thorough analysis of homing-guidance missile operations. Thus this system representation is given in Figure 2.4, depicted and described in full detail. The target motion (block 1) is defined by tangential )(taex

and normal )(taez accelerations as input variables, which determine the target maneuvering, and the initial conditions

0)0( ee VV = , 0)0( ee γγ = , 0)0( oeoe xx = ,

0)0( oeoe zz = . The equations describing target motion in the vertical plane (see Fig. 2.1) are as follows:

)()( tatV exe =& , 0)0( ee VV = , (2.1a)

)(/)()( tVtat eeze −=γ& , 0)0( ee γγ = , (2.1b)

)(cos)()( ttVtx eeoe γ=& , 0)0( oeoe xx = , (2.1c)

)(sin)()( ttVtz eeoe γ−=& , 0)0( oeoe zz = . (2.1d) The missile motion (block 2) can be described by simplified differential equations and in order to solve them the dynamic coefficients ,, δα ZZ qMMM ,, δα as well as

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the law of velocity )(tVV = have to be known. Also the

initial conditions should be defined 0)0( αα = ,

0)0( qq = , 0)0( γγ = , 0)0( opop xx = , 0)0( opop zz = ;

usually it is taken that 00 =α , 00 =q , 00 =opx ,

00 =opz . Thus only the missile launching angle

)0(0 γγ = remains to be specified. The set of equations describing missile motion, constituting our representation model, have the following form:

αγθ += , (2.2 a)

mmz ZZfk

δα δα += , (2.2 b)

Figure 2.3 - Overall architecture of a homing-guidance missile

system [6]

γcosgfakk zz += , (2.2 c)

0)0(,/ ααα =+= Vaqkz& , (2.2 d)

0)0(, qqMqMMq mbmq =++= δαα& , (2.2 e)

0)0(,/ γγγ =−= Vakz& , (2.2 f)

0)0(,cos opopop xxVx == γ& , (2.2 g)

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0)0(,sin opopop zzVz =−= γ& . (2.2 h)

Figure 2.4 - Model of homing-guidance system in the vertical

plane with the FIS turned on to operate. The so called relative motion (block 3) of the target relative to the missile and the current failure )(th function are described with the following equations:

γϕξ −= , (2.3 a)

ee γϕξ −= , (2.3 b)

ξξ coscos VVr ee −=& , )0()0()0( 22oeec zxr += , (2.3 c)

ξξϕ sinsin VV ee +−=& ,)0()0()0(

oe

oe

xzarctg −=ϕ , (2.3 d)

22

2

)( ϕϕ&&

&

rrrh+

= . (2.3 e)

The proportional navigation is technically realized due to

the sensor (block 4) that measures the LOS rate ϕ& . Its dynamics may be modeled with a first-order transfer function ))1/(( +sTK GG or the corresponding linear differential equation. Homing guidance laws (block 5) are discussed in more detail in the subsequent sections, which are believed to bring some of the novel contributions of this paper. At this point here it is sufficient to note that the respective model(s) is part of the overall system representation. The autopilot (block 6) has a structure typical for SA homing guidance missiles, which includes: an actuator with first- order dynamics represented by transfer function

))1/(( +sTK aa or the corresponding linear differential

equation; the feedback for the pitch angle velocity realized by speed gyroscope having gain

dgK ; and the feedback for

the normal load zf realized with an accelerometer having gain daK . It should be also noted that the autopilot has inbuilt limitation of the guidance signal for the specified maximum of normal missile load.

3. ON GUIDANCE LAWS IN HOMING MISSILE SYSTEMS

Guidance laws for homing-guidance missiles by and large are based on classically known guidance methods. An outline of these methods (see Figures 2.1 and 2.4) would be: direct or attitude pursuit guidance method, when the look angle should be zero 0=−= θϕη ; pure pursuit guidance method when the lead angle should be zero

0=−= γϕξ ; method of parallel navigation which requires LOS rate to zero 0=ϕ& ; and proportional navigation guidance method where the turn rate of the missile velocity follows the LOS rate changes strictly

ϕγ && K= . Full detail on these methods is found elsewhere [25], [39], [51]. It should be pointed out that the method of proportional navigation is most frequently used. Our investigation of homing-guidance systems (Fig. 2.3) is focused on the applied proportional navigation (PN). The realization of PN method requires direct measurement of the LOS rate ϕ& or its indirect estimation. On the other hand, it

is well known that the closing velocity r& is normally used for the definition of guidance commands. Hence, the PN guidance law has the forms:

ϕγ &&

&V

rN ||= (3.1 a)

or

λγ &&& || rNVakz == . (3.1 b)

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In there, the variables denote: N is the kinematics gain of closed homing-guidance loop (effective navigation constant) having a value in the range 3 to 5 [39]; V is missile velocity; and || r& is absolute value of the closing velocity. The classic law of PN (3.1) technically is realized so that the signal U that is generated on the grounds of the

measured value ϕϕ && U≈ˆ of LOS rate and the estimated

value r)& closing velocity, which depends essentially on

shooting conditions too. It is represented by means of the formulae:

ϕ̂&fKU = , oeG

f KKrNK

ξcos|ˆ| &= . (3.2)

Here GK is the sensor gain, eK is the gain of the system

“autopilot-missile”, and 0ξ is the lead angle. In simulation models as well as in reality, an improved proportional navigation and optimal laws based on modern control theory [39], [51] can be and have been used, e.g. [38]. We have studied the homing-guidance process using the classical proportional navigation laws (3.1), (3.2) and in doing so explored the alternatives for its further enhancement. It may well be inferred from Figures 2.1 and 2.2 that the closing velocity and the lead angle depend on the shooting regime (incoming/ outgoing target) as well as on the parameters of target motion (target’s position and velocity), which generically are two different categories of information indeed. And so, we decided to explore the application of fuzzy logic to proportional navigation law in order to provide on-line settings of all necessary values for the variables in (3.2) following both shooting regimes. The conceptualization of using fuzzy logic is discussed in the next section. Choosing a good guidance law enables quality guidance process (small dynamic error, good transient response behavior, steady-state accuracy, etc.) as well as enlargement of the launching zones and still making certain target hitting. The latter are very important for every missile system operation. 4. A FUZZY INFERENCE SYSTEM IN SURFACE-TO-

AIR HOMING MISSILES Models that are based on employing fuzzy logic can be used in different kinds of applied information processing for control and decision [36], [43], [47] such as traditional and adaptive control systems, process identification, signal estimation, planning, etc. The main reasons are found in their compatibility with the human expert’s knowledge, the potential to imitate human conceptual reasoning [49], [50] and sometime in the relatively simple development of control applications [27], [28]. These aspects are particularly important when the controlled process is

represented by means of non-well defined or much too complex models. The common feature of fuzzy systems (see Figure 1.3) are the structure and homogeneity of their rule knowledge bases, consisted of imprecise conditional clauses, without or with connections, that manipulate the same state (from the ‘cause’ part) and control or decision variables (from the ‘consequence’ part) of rule based models. It should be noted that the choice of Mamdani type of fuzzy system models have been found rather appropriate (see Section 6). A. Design and Implementation of FIS Based Seeker We have applied fuzzy-rule knowledge base and fuzzy inference (see also Section 6) in the seeker for evaluation of decision process on the grounds of two possible shooting regimes: incoming and outgoing target. These were implemented by making use of Fuzzy Logic Toolbox and Matlab environment [22], [29], [30]. In the FIS, computation of the shooting based reasoning process is performed, and in turn the needed output variable values obtained. The obtained fuzzy variables characterizing missile-target relationship are then defuzzyfied and transferred onto the system as an executive command. There are two options for the system operation: first, an informative option that indicates (audio-visually) to the operator the information on the launching moment; and second, an automatically performed launching when all conditions for successful shot are satisfied. Given the above analysis of navigation laws, the constructed knowledge base (see Figure 1.3) is of Mamdani type with fuzzy rules of the form

If eV = LN and 0ϕ = SP Then r& = LP and 0ξ = ZO. (4.1)

Input variables to FIS are target velocity eV and LOS angle

0ϕ , while output variables closing velocity r& and lead

angle 0ξ . For each of these variables, five fuzzy linguistic values have been chosen – denoted LN (large negative), SN (small negative), ZO (zero), SP (small positive), LP(large positive) – thus five fuzzy segments defined by means of respective membership function grades. The simulation experiments have demonstrated that increasing fuzzy granularity to more fuzzy segments does not contribute particularly to better performance in this design, on one hand, and make the FIS computations more complex, on the other. In this class of FIS applications we believe that the simpler knowledge base is the better it is, and opted for simple solutions. The Matlab based Fuzzy Inference System editor, which is presented in Figure 4.1, shows higher-level information on the simplified inference mechanism based on the fuzzy rules of the knowledge base.

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Figure 4.1 - Computational fuzzy-rule knowledge base of the FIS In principle, both bell-shaped, Gaussian and triangular-shaped membership functions describing the fuzzy subsets can be employed; the respective fuzzy terms should slightly overlap. Similarly, various inference principles can be used, and Mamdani inference performed rather well. However, the crisp sets of values for each of variables ought to be observed from the real-world data via the fuzzification interface (Figure 1.3). Therefore, for instance, in our simulation experiments these were chosen as given below:

eV (m/s) = [-250, 250], 0ϕ (rad) = [0, 1.07],

r& (m/s) = [250, 750], 0ξ (rad) = [-0.45, 0.45].

On the grounds of the determined defuzzified values for r& and 0ξ it is straightforward to calculate the constant

)cos/(|ˆ|)ˆ,ˆ,ˆ( oeGfo KKrNKrf ξξϕ &&& == (4.2)

for the PN guidance law. And this way the entire missile guidance process is being continuously updated in an adaptive manner. It is the application of fuzzy logic inference for the calculating fK that builds in into the fire control system an adaptation property. Computations are performed automatically for any shooting regime (incoming/outgoing target), which is more flexible than in many weapons employing fixed parameter specifications. As seen from Figure 4.1, it is a simple inference system design with a fairly simple knowledge base indeed. It should be noted, however, that the actually performed FIS-PN algorithm is a hybrid one employing both math-analytically modeled knowledge as well as computationally expressed knowledge on the proportional navigation method. It represents an application case where math-analytical and fuzzy-system computational representation

models are combined in compatible synergetic mode. Next the typical simulation results are discussed. B. Simulation Experiments, Results, and Performance Analysis In order to test performance of the models and developed simulation technique we have used a hypothetic situation of an anti-aircraft missile with known geometric, mechanic and aerodynamic characteristics [5], [6]. The missile has the following constructive parameters: length l =2m, diameter d =0.125m, surface 4/2πdS = =0.01227m2; the mass, the engine pressure, the inertial moments, the position of the mass center, and the derivatives of the aerodynamic coefficients are time-varying, i.e. depend on time t and mach number Ma , are given by means of a table. The values of the mass and the inertial moments at the start are: m =40 kg, xI =0.08 kgm2, zy III == =12 kgm2.

Simulation of the missile launching for incoming and outgoing target operating regimes was performed whit the initial value of the LOS angle set to o

o 45=ϕ , and the target height set to 2000 m while the velocity set to 250 m/s. The simulation results for the guidance process in the vertical plane, obtained via using Matlab-Simulink support, are given in Figures 4.2 to 4.5. These simulation results are obtained from the general simulation model of the homing guidance system, computing implementation of which was elaborated in Fortran by using its library routines too.

Figure 4.2 - Homing-guidance trajectories for incoming (a) and

outgoing (b) targets

There are shown in Figures 4.2 and 4.3 the computer trajectories of homing-guidance misses in the vertical plane for both cases of an incoming (a) and an outgoing (b) target. The target is assumed to be maneuvering with acceleration

cza = 4g. In Figure 4.2, there are shown the flight trajectories for incoming/outgoing target that flies with a

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speed of 250m/s on a height of 2000 m, but it does not maneuver gacz 4= . The trajectory intersection represents the point of interception. Figure 4.3 show the evolutions of total homing-guidance misses in both shooting regimes for incoming and outgoing targets.

Figure 4.3 - Total homing-guidance misses for incoming (a) and

outgoing (b) targets

a)

b)

Figure 4.4 - Trajectories of the missile and the target – a) incoming and b) outgoing regime

In Figure 4.4, there is shown the evolution of homing-guidance error only for the shooting regime of an outgoing target, which is more indicative for the actual performance

of homing missile systems in surface-to-air operation. Figure 4.4 (a) corresponds to the case when fuzzy logic is not employed and Figure 4.4 (b) when it is employed in the automatic guidance system. It is apparent from these results that the second case, when the fuzzy-logic block is operational, provides more suitable parameters for the shooting regime and the error with respect to its convergence to zero which demonstrates faster reduction of the error variable; the initial values are the same in both cases. The subsequent set of Figures 4.5 a, b show the results on the evolution of the respective errors for missile operation on outgoing target when (a) no fuzzy logic is employed (i.e. classical proportional navigation), and (b) when fuzzy logic employed in the system. These results clearly demonstrate the effectiveness of the proposed fuzzy-proportional navigation law.

a)

b)

Figure 4.5 - Errors in the shooting regime of an outgoing target without (a) and with (b) fuzzy logic employed in the system

It should be noted that the diverging of the homing-guidance process in the meeting point region is a natural one and well known in the theory of the homing-guidance systems [39], [51]. In the real-world missile homing guidance systems there may take place the so-called blinding effect of the coordinator in the target region close to the target, when the guidance loop is interrupted and the flight becomes no more guided. Our investigations have shown that by employing fuzzy logic inference we avoided this kind of error increasing close to the target. Furthermore, we point out that there is no possibility for parameter change in the guidance law in the system without a fuzzy-logic block unless some kind of dedicated adaptive control

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and guidance system has been implemented.

5. A FUZZY INFERENCE SYSTEM IN AIR-TO-SURFACE HOMING MISSILES

Again the design f fuzzy inference systems can be carried out by using Matlab’s Fuzzy Logic Toolbox [44]. And again a thorough information-theoretic analysis of information carrying real-time measurable or estimable physical variables involve in missile technology is needed in order to conceptualize the adequate use of fuzzy logic [9]. Again we found in our investigations that it is rather convenient to choose Mamdani fuzzy system based inference and Guassian membership functions for the fuzzy subsets. In addition, we found that a practical choice is to make use of “product” for AND and of “max” for Or connectives in conjunction with “min” for the fuzzy implication, “max” for the fuzzy aggregation, and “centroid” for the defuzzification (also see Figure 1.3 and Section 6). In this case, the actual homing missile operation is somehow converse in the sense that the evader target is located and moving on the ground surface and the missile is launched from an aircraft in the air, hence the overall system architecture as depicted in Figure 5.1 is being used. Therefore again a thorough information-theoretic analysis available signals on the significance for the automatic homing guidance process, which may be easily made available at missiles, was carried out.

Figure 5.1 - Architecture of missile control and guidance system employing local error acceleration PI+StateFB control and FIS-PN This signal significance analysis involved the following signals: total velocity, V ; line-of-sight angle Λ (or λ ) and line-of-sight angle rate Λ& (or λ& ); normal acceleration,

za ; and also angle of attack α ; flight path angle γ ; and pitch rate q . It has been found that enough rich information contents are provided jointly by line-of-sight angle (LOS) and line-of-sight angle rate (LOSdot). Consequently, the FIS sub-system can be designed as a two-dimensional fuzzy system with these input variables should the normal acceleration is to be the output applied as command to the missile system. Thus it is readily seen that there will be no more need for measurement signals V , za , α , γ , and q . Nonetheless, it appeared that there are no essential

differences and the same line of analysis and design as before can be followed. It should be noted, however, for the class of air-to-surface homing missile technology two FIS-based PN designs could not be made as simple as in the previous case presented in Section 4. Secondly, it should be noted, in this case of applied FIS-PN designs it was found that a higher fuzzy granulation of system variables was needed involving seven Gaussian fuzzy terms: LN (large negative), MN (medium negative), SN (small negative), ZO (zero), SP (small positive), MP (medium positive), LP (large positive). It will be seen in the sequel that this due to the actual information processing being based on different information carrying signals. A. Design and Implementation of FIS Based Seeker First we have considered missile technology that employs Proportional-Integral-plus-State-Feedback (PI+ StatFB) control designs for automatic control of missile motion, which is illustrated by meant of Figure 5.1, and thereafter the case with the conventional autopilot (Figure 1.2 can serve as illustration in this case). Then a possible fuzzy-system based design is found again in replacing the proportional navigation algorithm with FIS–based PN navigation sub-system (see Figure 5.1) for obvious reasons of operating such homing missiles. The other possibility would be to replace both the proportional navigation and the acceleration feedback information processing with a fuzzy inference system with and adequate capacity (Figure 1.2 can illustrate the overall system architecture in this case). This is to say, the potential of fuzzy inference systems can be well exploited in conjunction with the seeker sub-system. In this type of missile control and guidance system design, the FIS is a two-dimensional fuzzy system having as its inputs the LOS-angle and the LOS-angle rate (fuzified) with the output carrying information on the normal acceleration (defuzzified). In this design, since the information of total velocity is no longer needed, therefore needs no longer measuring or estimation. Upon carrying out a refined post-synthesis design analysis and simulations for improvements and simplification, still it was possible to obtain a fairly simple FIS design. The final design of a fuzzy logic based inference system whose was carried out recently [8], [9]. Its condensed knowledge base in a linguistic If-Then form may be given as follows:

:1R If LOSdot is LN and LOS is LN Then NormACC is LN

:2R If LOSdot is LN Then NormACC is LN

:3R If LOSdot is MN Then NormACC is MN

:4R IF LOSdot is SN Then NormACC is SN

:5R IF LOSdot is ZO Then NormACC is ZO (5.1)

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:6R IF LOSdot is SP Then NormACC is SP

:7R IF LOSdot is MP Then NormACC is MP

:8R IF LOSdot is LP Then NormACC is LP

:9R IF LOSdot is LP and LOS is LP Then NormACC is LP

The respective value intervals of the physical quantities have been defined according to the above seven linguistic value levels into seven equal sub-interval fuzzy terms, represented by the respective Gaussian fuzzy subsets based on real data. We have explored another design of FIS-PN control and guidance system for air-to-surface missiles (also see Figure 1.2) based on conventional control designs in missile technology when the command to missile system is given directly in terms of fin deflection Bδ . For this purpose, again a significance information-theoretic analysis of the respective input signals to the two sub-systems of conventional systems has been carried out involving signals on total velocity, line-of-sight angle and line-of-sight angle rate, normal acceleration, angle of attack, flight path angle, and pitch rate. In this design, however, we have found that yet a higher resolution of linguistic models is to be employed, and we made use of the linguistic value ‘very’ and its implementation by means of powers (2, 4, 8) of membership grades of fuzzy terms as appropriate. Albeit it may not seem much realistic, should a FIS is designed to produce deflection Bδ as output on the grounds of fuzzified information of LOS-angle and LOS-angle rate, there may be no more need for real-time measuring or estimation of other variables. Hence, no longer need for acceleration, angle-of-attack, pitch-rate, and attitude sensors, hence reduced computation time and greatly simplified missile sensory sub-system. This second type of FIS was designed via similar synthesis and design analysis as in the previous case, including the usage of human operator’s knowledge. And again computer simulation experiments for improvements were carried out. Its condensed fuzzy-rule knowledge base in If-Then linguistic form may be summarized as presented bellow:

:1R If LOSdot is Neg.Large Then Bδ is Neg.Large

:2R If LOSdot is Neg.Medium Then Bδ is Neg.Medium

:3R If LOSdot is Neg.Small Then Bδ is Neg.Small

:4R If LOSdot is Very.Small Then Bδ is Zero

:5R If LOSdot is Zero Then Bδ is Zero

:6R If LOSdot is Pos.Small Then Bδ is Pos.Small

:7R If LOSdot is Pos.Medium Then Bδ is Pos.Medium

:8R If LOSdot is Pos.Large Then Bδ is Pos.Large (5.2)

:9R If LOS is Neg.Large Then Bδ is Neg.Large

:10R If LOS is Neg.Medium Then Bδ is Neg.Medium

:11R If LOS is Neg.Small Then Bδ is Neg.Small

:12R If LOS is Zero Then Bδ is Zero

:13R If LOS is Pos.Small Then Bδ is Pos.Small

:14R If LOS is Pos.Medium Then Bδ is Pos.Medium

:15R If LOS is Pos.Large Then Bδ is Pos.Large

As seen, it is still a reasonably simple knowledge base although the complexity of this FIS design is approximately double than the previous one. And this completes the outline presentations of the fuzzy-rule knowledge bases for these two types of FIS designs. Next the typical simulation results are discussed. B. Simulation Experiments, Results, and Performance Analysis Below, Figure 5.2 depicts an evaluation showing the resulting nonlinear surface that can be obtained in the proposed FIS design. The additionally pointed peaks indicate the effects of some expert-knowledge based improvements built in during simulation experiments.

Figure 5.2 - Typical nonlinear surface of the proposed FIS design;

the peaks indicate some expert knowledge built in during improvement simulations.

It is well known in air-to-surface shooting [39], [51] that the satisfactory hit capacity can be taken to be within a radius of either 5m or of 10m. Upon carrying out computing simulations, the typical results that can be obtained are as

12

the ones shown in Figure 5.3, for the first case of fuzzy-system based design, and in Figure 5.4, for this second design. Simulation experiments for air-to-ground shouting have been carried out with the hit points on the ground specified as follows: XHP(thit) = {10000; 15000; 20000}. In simulations, the relevant values of basic physical quantities were chosen the same in order to have clear comparison of the results with both FIS-PN designs, namely: LOS [rad] =[0.22, 0.55]; LOSdot [rad/sec] = [-0.001, 0.005]; values for the respective third physical variables in the two FIS-PN designs have been chosen as presented below.

Figure 5.3 - Attainable missile trajectories targets (at three different distances) with the FIS design for missles with full

PI+StateFB controls

Figure 5.4 - Attainable missile trajectories targets (at three

different distances) with the FIS based navigation for missiles with conventional controls

In the first case of FIS-PN design (see linguistic model (5.1)), the respective value intervals of the physical quantities have been defined according to the above adopted seven linguistic value levels into seven equal sub-interval

fuzzy terms, represented by the respective Gaussian fuzzy subsets. For the normal acceleration, its quantification was chosen as follows: NormalACC ( za ) [m/sec2] = [-2.0, 8.0]. It should be pointed out, all the state variables as well as the control command remained within physically accepted bounds, and no saturation level is reached for missile fin deflection. In this case this FIS-PN system, the obtained trajectories to the hit points on the ground are shown in Figure 5.3. In the second case of FIS-PN design (see linguistic model (5.2)), the respective value intervals of the physical quantities have been again defined into seven equal sub-intervals according to the seven linguistic value levels, and represented by the respective Gaussian fuzzy subsets. The interval value of deflection angle was quantified as follows:

Bδ [rad] = [-0,236, 0.0]. It is pointed out that all the state variables as well as the control command remained within physically accepted bounds, and no saturation level is reached for the fin deflection. With the second FIS-PN systems, the resulting trajectories to the hit points on the ground are shown in Figure 5. 4. Although these trajectories show a small deviation, these demonstrate that similar performance can be achieved with this type of homing guidance missiles. Lastly but not lest, it should be noted both designs are in their experimental stage, and were validated solely through simulation experiments because physical experiments cannot be afforded in our small country. These simulation results are not sufficient for complete validation, of course, because it is likely that the respective missile trajectories in real-world experiments will differ from those in Figures 5.3 and 5.4. On the other hand, however, these results confirm that employing FIS-PN navigation subsystem can be not only feasible but effective too and may considerably simplify the necessary instrumentation on board.

6. COMMENTS ON APPLICATIONS OF FUZZY SYSTEMS IN MISSILE CONTROL AND GUIDANCE

In here we present some points of personal opinion on perspectives regarding the usefulness of fuzzy control as a technology with a promising potential in missile control and guidance applications. Also, we discuss the related issue on syntehsizing simple FIS rule base with regard to the recent theoretical findings on the complexity problem. For this purpose we refer to both semanic-driven FIS designs (e.g. Mamdani) and data-driven ones (e.g., Sugeno), the latter being one of future research topics pointed in the conclusions. It may well be seen some of these are primarely practical ones, while the others may be percieved in conjunction with theoterical issues in fuzzy rule knowldge bases and approximate reasoning. In the first place, there can be no successful control, guidance and supervision systems engineering via totally

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“model-free” approaches, in general, let alone in homing missile technology. The current status of fuzzy control field and its applications, as characterized by the limitations coupled with the importance of non-linear analysis of fuzzy control systems, make it an open area for investigation in establishing the necessary foundations bridging the methodologies of fuzzy-systems based control and of non-linear analysis as well as the so-called conventional and modern control approaches. As a matter of fact, that is precisely what we had to do in our reserach reported here. Some kind of modelling of controlled plants and processes ought to be performed in the course of design, one way or another, and above presented case studies of interest have clearly demonstrated this. Indeed, our entire experience demonstrates that the control engineer, developing a fuzzy control and supervision system, most often either have or must develope a mathematical model. While it may not be used directly in control design, it is often used in simulation to evaluate the performance of the fuzzy design, and by and large this is the case for rule-base re-design. For, in applications like these, there is a need for a high level of confidence in the reliability of the fuzzy system based control design before its implementation may be attempted. Next, it seems rather important to note that in choosing control design tools, there is a need for the control engineer to assess what (if any) advantages fuzzy control methods have over traditional math-analytical methods in the given application domain of concern. This is precisely what we did in our case studies on developing the application designs in homing missile control and guidance, reported here, as well as in multi-target combat simulator before [10]. Moreover, in addition to possible advantages in using fuzzy control, it makes sense to take a critical look at what possible disadvantages too there may occur. For instance, due to the fact that a fuzzy control system attempts to manipulate a human’s knowledge on how to control a plant system, one might ask if the behaviours observed by a human expert include all situations that can occur due to disturbances, noise, variations of plant parameters, or events in a mission scenario. Hence, in homing missile technology the re-design of guidance laws seems to be the only application domain to be explored for fuzzy system applications in a fruitful mode because the knowledge of human expert operator can be involved [43], [47]. In fuzzy system based designs the expert’s a-priori knowledge results in improved knowledge base of fuzzy logic controls as Figure 5.2 shows. With respect to the complexity of fuzzy-rule knowledge base, if T is the average (or maximum) number of fuzzy terms in each dimension and k is the number of dimensions, then the number of rules is of order )( kTO . Thus in every FIS execution when searching the knowledge base for the relevant rules for a given input (observation),

an exhaustive search among all rules should be performed, and hence the exponential complexity. Therefore in real-time applications there is a considerable need for reducing the computational effort as much as possible, which can be achieved by reducing either numbers of fuzzy terms or dimensions, or by combined reduction of both. It is well known that fuzzy system models describe systems by determining the relationship between the prospective inputs and the respective outputs in the form of If-Then rules. In general, one methodology for designing fuzzy models is the so-called semantic-driven modelling, the original idea of which is due to Zadeh [48], and the other is the data-driven modelling. We have used the semantic-driven modelling, hence information-theoretic analyses on significance of available missile signals had to be carried out; data-driven modelling would require gathering rather costly data collections from experiments. In this regard, Mamdani’s version of fuzzy system models and inference [27], [28], i.e. with fuzzy subsets in the consequents

:iR If 1x is 1iA and … and nx is inA Then y is iB , (6.1) which are worked out in projection fuzzy spaces rather than on multidimensional product space. In turn these yield much less computational effort, hence became rather popular in applications to physical system where inputs have to be fuzzified first and then used in FIS structures (e.g. see [1], [20], [21], [33], [35]). It may seem more attractive at a first glance to make use of the alternative Sugeno modelling for FIS models due to the available math-analytical modelling techniques for missiles. It is known as Takagi-Sugeno-Kang modelling [40], [42]. This alternative, albeit exploiting math-analytical function in the consequent part of fuzzy system models, is a data-driven modelling search for feasible yet sufficiently good approximation models. And because of the needed data-driven identification it leads to more complex fuzzy inference systems. Namely, in Sugeno class of models the rule consequents are linear functions of the inputs:

:iR If 1x is 1iA and … and nx is inA Then

iii bxay += rr. (6.2)

In here [ ]iniii aaaa ...,,, 21=r is a vector of parameters to

be determined, and [ ]iniii xxxx ...,,, 21=r is the input

vector. Easier computational handling of this model by numerical methods owes to the fact that consequents are essentially non-fuzzy. Hence the overall output can be written as

∑ =

== Mi

i ii yxwy1

)(r (6.3) weighted sum of outputs of local models pertinent to individual fuzzy rules in the knowledge base, where )(xwi

r

represents the normalized firing strength of the i-th rule. It

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is this equation which enables the way of handling the problem as a linear regression by means of classical numerical methods. The question arises: would it be possible at all by physical experiments to gather enough costly data collections in the first place? Besides it is well known that fuzzy models often contain redundant rules, and furthermore it has been shown [17] that all FIS fuzzy models have exponential computational complexity originally. Should Takagi-Sugeno-Kang modelling be adopted as departure point in FIS design for proportional navigation, then the recent theoretical findings in [34], [37], [47] must be observed and simplification of fuzzy-rule knowledge is to be carried out with respect to this line of arguments. In our research for FIS based navigation designs, presented in Sections 4 and 5, we arrived at minimum number of rules without using hierarchical re-structuring [41] or fuzzy-rule interpolation [19]. Rather we used Mamdani modelling and expert operator’s knowledge and exploited the proposition of Dubois and Prade on gradual semantic interpretation [12]: “The more similar is the observation to an antecendent the more similar the conclusion should be to the corresponding consequent of the given antecendent”. Moreover, due to linguistic-driven synthesis, conclusive fuzzy terms produced retain interpretability as fuzzy set (abnormal fuzzy sets are avoided), which justifies further the proposed designs. Nonetheless, it should be noted that only physical experiments, which are beyond our possibilities, can provide full-scale justification. Our work is confined to building as realistic as possible training simulators [10], [15], [33] in object-oriented design and implementation [2], [3], [45]. 7. CONCLUSIONS In this paper we presented full-scale simulation model development of guidance and control systems for short-range homing missiles employing a fuzzy navigation component. We presented a simulation model for homing-guidance system in the vertical plane, and its implementation was realized by using Matlab/Simulink platform. These are suitable for investigating the dynamics of the system and its sub-systems as well as for exploring and testing the guidance and control laws. We have investigated the well-known guidance law – proportional navigation – with and without employing fuzzy-logic inference in the rule knowledge base, and proposed one solution for surface-to-air and two solutions for air-to-surface missiles. These three solutions are feasible and may well find relevant applications for fire control systems in homing guidance missile technology. Still, it is important to investigate the FIS-PN design using Sugeno class of models and find out how that performance would

compare with the one based on Mamdani class of models, reported in here. In this work, the use of a fuzzy-rule based system that is based on input parameters such as signals on the current position of the target and the states of surrounding environment and system itself, obtained from the system sensors, has been explored. With the use of fuzzy logic inference it is possible to provide necessary parameters for the guidance law that depend on shooting conditions. Also it enables estimation of the launching zone, providing information when the most suitable moment for launching occurs. The use of fuzzy logic for calculation of the guidance law parameters enables an adaptation property of missile guidance system making it functionally dependent on both target motion and on shooting regime, e.g. surface-to-air of an incoming/outgoing target and air-to-surface. The essential prerequisite that the system be equipped with necessary sensors to capture essential information on the target motion, however, remains no matter what technological simplification can enable the design of FIS based navigation laws. Though the use of fuzzy-navigation laws can contribute to simplifying the sensor sub-system to one with less sensors employed, which may contribute to reliability as well. We have shown in these three cases of applied fuzzy system based designs for homing missile systems employing fuzzy inference decision that hybrid or combined math-analytical plus fuzzy soft-computing techniques had to be used. This has to be done in a way ensuring their consistent compatibility, of course. Secondly, we have shown in all three applications that there is a limited benefit on performance of these system engineering designs according to the real-world facts that to some tasks fuzzy system techniques are better suited while to others math-analytical techniques are more fruitful. And thirdly, it is important to note that indeed employing some soft-computing formalism and technique, such as fuzzy inference systems in here, leads to creating technological systems with higher quotient of machine intelligence [43], [47], [50] and simultaneously improving or simplifying engineering structure of the designed system [4], [8], [9]. The latter may well be cost-effective in several respects. It is believed therefore that this line of systems engineering developments in missile technology will continue to advance and expand, in particular towards using adaptive fuzzy laws [23], [25], [52] and exploiting fuzzy-neural synergism. ACKNOWLEDGEMENT

The authors would like to express their thanks to the authorities of Ministry of Defense and Army of the Republic of Macedonia (ARM) for the permission to

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publish in part their recent results as well as to make use of some previous research material.

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BIOGRAPHIES Dr. Georgi M. Dimirovski (IEEE M’86, SM’97) was born in 1941 in Greece, in v. Nestram, Aegean Macedonia. He moved to academia in 1969 after having spent three years in industry. Currently he is Life-time Professor of Automation & Systems Engineering at SS Cyril & Methodius University, Skopje, and Professor of Computer Science & Information Technologies at Dogus University, Istanbul. He has obtained his degrees Dipl.-Ing. in EE from SS Cyril & Methodius University of Skopje, Rep. of Macedonia, and M.Sc. in EEE from University of Belgrade, Rep. of Serbia – both in S.F.R. of Yugoslavia the, in 1966 and 1974, respectively. He obtained his Ph.D. degree in ACC from University of Bradford, Bradford, United Kingdom, in and 1977. Subsequently, he had his postdoctoral research and Visiting Professor positions at University of Bradford in 1979 and 1984, respectively. Also he held positions of Visiting Professor at University of Bradford in 1988, and of a Senior Fellow & Visiting Professor at Free University of Brussels, Belgium, in 1994, and at Johannes Kepler University of Linz, Austria, in 2000. He a number of academic visits to universities in Bradford, Brussels, Coimbra, Duisburg, Istanbul, Linz, Lisbon, Hannover, Valencia, Wien, Wolverhampton and Zagreb during the last two decades. He participated to the European Science Foundation Scientific Programme on Control of Complex Systems (COSY 1995-99; Prof. K. J. Astroem, the leader). He has been awarded grants by Ministry of Education and Science of Macedonia for 5 national projects in automation and control of industrial systems and 2 in complex decision and control processes. He was editor of three volumes of the IFAC and one of the IEEE series, authored several contributed chapters in monographs, and a number of journal articles and conference papers (in IFAC and IEEE proceedings). He supervised successfully 2 postdoctoral, 14 PhD and 25 MSc as well as more than 250 graduation students’ projects. He served on the Editorial Board of Proceedings Instn. Mech. Engrs. J. of Systems & Control Engineering (UK) and was Editor-in-Chief of Journal of Engineering (MK), and currently is serving on Editorial Boards of: Facta Universitatis J. of Electronics & Energetics (University of Nis, Serbia), IU J. of Electrical & Electronics Engineering (University of Istanbul, Turkey), and Information Technologies & Control J. (Association of Automation and Informatics, Sofia, Bulgaria). In 1985 he founded the Institute of Automation & Systems Engineering at Faculty of Electrical Engineering of SS Cyril & Methodius University (now employing 6 full-time academic staff). He was one of the founders of the ETAI Society, Macedonian IFAC NMO, in 1981, and the IEEE Republic of Macedonia Section, in 1996. He has developed a number of undergraduate and/or graduate courses in various areas of control and automation, and others in robotics, applied numerical, fuzzy-system and neural-network computing, and

operations research at his home university and at universities in Bradford, Istanbul, Linz, and Zagreb. During 1988-1993 he served to European Science Foundation on the Executive Council and in other capacities, and during 1996-2002 he was Vice-Chair of the TC on Developing Countries of International Federation of Automatic Control. He has served on IPC’s for many IFAC, IEEE and ECC conferences. He served in capacities of Technical Program Chair of 2003 IEEE CCA and Co-Chairman of 2000 IFAC SWIIS, 2001 IFAC DECOM-TT, and 2003 IFAC DECOM-TT conferences, and of 1993 and 2003 International ETAI AAS symposia. Currently he is serving as the Chairman of IFAC TC on Developing Countries (triennium 2002-05).

Colonel Stoyce M. Deskovski, Ph.D. (Member of AIAA, 2000) was born in 1947 in v. Sopotnica, Republic of Macedonia. He obtained in 1969 his First and Second Degrees from Military Technical Academy (the former YNA of S.F.R. of Yugoslavia) in Zagreb, Rep. of Croatia, specializing in the field of Rocket Technology, and earned the level of command and staff officer in military education and training. For his research in Automatic Control and Missile Guidance Systems, he obtained his M.Sc. and Ph.D. degrees in EE from University of Zagreb in 1980 and 1990, respectively. In the military, he was promoted the rank of 2nd lieutenant in 1969, to lieutenant in 1972, to captain in 1975, and subsequently was awarded the ranks of captain 1st class and major, in 1977 and 1981, respectively. Thereafter in 1985 he was promoted to rank of lieutenant colonel (in the former YNA) and in 1993 to rank of colonel (in the ARM). He was selected and appointed as Research & Teaching Assistant at the Department of Rocket Technology at the Military Technical Academy in Zagreb in 1976, and thereafter promoted to Lecturer, in 1980. In the academic year 1979-1980 he was on assignment and has taught at the Military Academy in Algeria. In 1990 he was promoted to Assistant Professor of Anti-Tank & Air Defense Missile Systems, Guidance & Control, and Synthesis of Guidance Systems, and in 1991 he became an associate of the Electrical Engineering Faculty of the University of Zagreb in the same academic rank. Since 1992 he worked on establishing the ARM military education system and on the foundation of the Military Academy, first as Deputy Head for Education and Training and then as Head of the Institution since 1993. In 1995 upon the foundation of Military Academy “General Mihailo Apostolski” by law passed in the Parliament of the R.M., he was appointed to Dean of the Academy and served in this capacity until year 2003. Dr. Deskovski was promoted to Associate Professor of Military Technology in 1995, and to Full Professor in 2000. He has contributed to the Military Academy professionally by developing courses in: Mechanics of Flight, Missile Technology, Missile Guidance and Control

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Systems, External Ballistics, and Fire Control Systems. Also, Dr. Deskovski was invited to teach the graduate courses in Flight Dynamics & Control at the Faculty of Electrical Engineering, and in Mechanics of Flight at Faculty of Mechanical Engineering of SS Cyril and Methodius University of Skopje, as well as the undergraduate course in Mechanics of Flight at the Technical Faculty of St Clement University of Bitola, the R.M. He has published a number of teaching materials at both Military Academy in Zagreb and at Military Academy in Skopje. In the course of his career, he has been involved in several longer-term research projects and has published more than 10 articles in national and foreign periodicals and magazines, and more than 50 papers in conferences proceedings. In 2000 he became a member of the American Institute of Aeronautics and Astronautics (AIAA).

Dr. Zoran M. Gacovski (IEEE M’96) was born in 1972 in Radovis, Republic of Macedonia. He is a graduate from SS Cyril and Methodius University of Skopje, Macedonia, where from he took his Dipl.-Ing. and M.Sc. in EE degrees with outstanding evaluations in 1995 and 1997, respectively, and also his Ph.D. degree in 2002. He has won the prize 1995 Best Engineering Student of SS Cyril and Methodius University for his highest overall marks to both the study curriculum and his graduation project. Also he has won the 2002 First Prize of the 10th Baltic Olympiad for student research papers. Since 1996 he has been working as chief-engineer in the IT Department of the Ministry of Defense and also as a teaching assistant at Military Academy “General Mihailo Apostolski” in Skopje. In year 2003 he was promoted to Assistant Professor of Control and Information Systems at the Military Academy. He has published more than 25 scientific research papers, mainly in edited proceedings of the well-known international conferences such as of IEEE, IFAC, ETAI and WAC. During the year 2003 he has hold a position of postdoctoral research associate with CAIP Center at Rutgers University, Piscataway, NJ, USA. There he completed his postdoctoral project in agent based fusion of sensory inputs in multimodal communications for human-computer systems. BiSv.P!