fusing predictive control and machine learning towards

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Stufen der Verkehrsoptimierung

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4 Einleitung Maximilian Merkert // Die intelligente Ampelkreuzung

System

DATA System

Model based control

Data

Model

Laboratory for Systems Theory and Automatic ControlOtto-von-Guericke University Magdeburg

wind

Fusing Predictive Control and Machine Learning Towards Safe Autonomous SystemsRolf Findeisen, J. Matscheck, M. Maiworm, J. Bethge, H.H. Nguyen, T. Zieger, H. Rewald, A. Savchenko

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Autonomous systems

Challenge: standard adaptive/disturbance rejection control/planning approaches often fail►Exploit / fuse machine learning approaches with control & estimation

• Should operate autonomously ►involves many tasks• Perception/estimation• Planning• Control• Communication• …

wind

• Autonomous systems are increasingly important• Robotics, autonomous cars, drones, …• Industrial production, …• Chemical/bio-chemical plants, …• Energy systems, …

• Should be able to adapt/react to even large changes in environment• Disturbances• Changes in operation modes• Tasks & objectives• …

H2O

H2

CO2

SynGas

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+

Machine learning for safe autonomous systems?

How can one fuse control and machine learning approaches to achieve• Safety and reliability ►satisfaction of constraints (collisions, ….)• Stability, performance, transparency, …• Exploit pre-knowledge (models, physical insight, …)

• Significant advancements in the field of machine learning/AI• Deep-networks, re-enforcement learning, Gaussian processes, …

• Mainly driven by• Availability of data for training due to digitalization• (Cloud) computing resources for learning• Big companies like Amazon, Google, …• Freely available software tools/environments (tensorflow, PyTorch, …)

• Widely used for• (Image-)classification, image processing• Learning customer demands and wishes• Autonomous driving• …

So far only limited use in control/planning• Challenging to provide guarantees/safety certificates for machine learning approaches• Real-time learning

System

DATA

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Mainly used “tool”: model predictive control

1. Obtain state

2. Predict system behavior and optimize input

3. Apply optimal input signal

Predictive control = repeated optimal control

prediction horizon

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Model predictive control?

• direct consideration of constraints ►safety • nonlinear systems with multiple inputs ►flexibility• use of preview information and model knowledge ►trustability, adaptation • possibility to “optimize” a cost ►performance • many stability & robustness results available ►stability & robustness• efficient embedded optimization strategies

3. Apply optimal input

2. Calculate optimal input

1. Obtain system state

s.t.

How can we handle highly uncertain systems / systems with limited model knowledge?

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Pure learning-based control

+ Exploits available data + No physical model needed- Lot’s of data needed- Physical insight?- Retraining required- Guarantees?

System+ Uncertainty

DATA

Pure model-based control

+ Exploits physical knowledge+ Provides physical insight+ Exploits model and data+ Guarantees possible- challenging to handle large changes

System+ Uncertainty

MPC

Data

Dynamical Model

Fusing learning and control

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Pure learning-based control

System+ Uncertainty

DATA

Learning supported model-based control

+ Exploits physical knowledge+ Provides physical insight+ Exploits model and data+ Guarantees possible+ Allows adaptation

System+ Uncertainty

MPC

Data

Dynamical Model

Fusing learning and control

SystemMPC

references, disturbances

Here: focus on learning supported control (MPC) with safety and stability “guarantees“

SystemMPC

model

SystemMPC

controller

+ Exploits available data + No physical model needed- Lots of data needed- Physical insight?- Retraining required- Guarantees?

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Existing works MPC and learning with guarantees (incomplete!)Learning references/disturbances and predictive control• GPs as reference/disturbance model in MPC [Klenske ´16,Ortmann ´17], ...• NN as reference model in MPC [Ling´18], ...Exploiting Gaussian process models in robust/stochastic MPC• Variance in cost function [Ažman ´08, Cao´17, Murray-Smith ´03,Yang ´15], ...• Constraint tightening/chance constraints [Grancharova ´08, Ostafew´16,Hewing ´19, Likar ´07, Wang ´16, Soloperto 18]Learning models in predictive control with guarantess• Learning dynamic models via Gaussian processes with Guarantees [Berkenkamp ´16, ´17], …• Deep learning for dynamic models in MPC [Terzi ´19], …• Support vector machine to learn part of the model and input-to-state stability guaranteed [Yoo ´17], ...• Invariant safe sets & layer control frame [Akametalu´14, Gilluala´12, Koller´18, Fisac´18, Wabersich´18, Aswani´ 13], ...• Lipschitz constant for constructing upper and lower bounds (LACKI) [Limon ´17]Learning MPC controllers• Explicit learning of an linear MPC controller [Chen ´18], [Karg ’18, ´19], …• Learning an Approximate MPC with Guarantees [Hertneck ´18], ...• Safe and Fast Tracking on a Robot Manipulator [Nubert ´20], ...Verification of learned controllers• Use Robust Control Theory approach [Wang ´19, Jin ´18], ...• Exploit the characteristics of specific type of nonlinear activation function [Ivanov ´18], ...and many, many more!

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Fusing Predictive Control and Machine Learning Towards Safe Autonomous Systems

MPC and learned references & disturbances• Support controller with learned reference/disturbance previews• Use reachable sets ► Safety / constraint satisfaction and repeated feasibility

Key message: fusion of model based predictive control and learning verypromising for the control of autonomous systems with guarantees

MPC subject to learned system dynamics• Learning input-output models with Gaussian processes• Guarantee safety and feasibility under learned switching dynamics► Enforcing stability despite learning and multiple modes

Learned baseline controllers• Neural network-based learning of a baseline controller► Validation of closed loop stability of learned controller

SystemMPC

SystemMPC

SystemMPC

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Challenges• Complete ablation despite uncertainties• Avoid thermal overheating of spinal cord• Avoid injury of spinal cord/sensible areas

Robot supported intervention

Remove tumor by heating via electrodes

• Precise needle positioning & stabilization• Precise control of applied forces

Motivation - robot supported spine radio frequency tumor ablation

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Cont

rol T

asksForce controlConstrained path following

control

Many sub-tasks • Tracking• Registration• Human-Robot-Interface• Minimize tooltip errors• Collision free & optimal path planning• Optimal robot configurations

Towards precise & safe robot supported intervention

Force limitation

& compensation

Access path constraints

Predictive force feedback control

Exp. Design Optimal Control

Therapyplanning

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Predictive force feedback path following control

Predictive force feedback path following control

Under suitable conditions one can guarantee feasibility & stability & safety

Basic idea• add controllable dynamics by a virtual system for reference evolution• cost penalizes path-following error

[Faulwasser & Findeisen`09, '12, ‘16; Matschek et.al. 2017]

Cost functional path following error

constraints on forces

error with force &position components

reference speed = additional degree

of freedom

• small error• real-time capable

(22nd order model,3ms sampling time)

Experimental validation

path

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Cont

rol T

asksForce controlConstrained path following

controlLearning / adaptation

Many sub-tasks • Tracking• Registration• Human-Robot-Interface• Minimize tooltip errors• Collision free & optimal path planning• Optimal robot configurations

Towards precise & safe robot supported intervention

Movementcompensation

Force limitation

& compensation

Access path constraints

Combine predictive control & learning. Safety and performance guarantees?

Exp. Design Optimal Control

Therapyplanning

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Basic idea: identify reference model for prediction

Gaussian processes

Patient movement MPC

Measure-ments Reference /

DisturbancePrediction

Robot

Tool position

Approach should• Be able to handle noisy measurements• Loss of information• Allows inclusion of prior knowledge• Self-adapting• Safety-guarantees

Past observation

Future prediction

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Gaussian processes-based learning

Advantages of Gaussian Processes• Non-parametric, data-based modelling

o No explicit physical model neededo Adapts to current situation (e.g. via online data update)

• Robust against overfitting despite noisy measurements• Provides estimate of uncertainty • Inclusion of prior knowledge via mean and covariance functions

Gaussian Process

• Generalisation of Gaussian distribution to function space• Mean function• Covariance function

GP as reference generator:Use posterior mean as reference

Past observation Future prediction

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GP learning for movement compensation

GP setup• 6 independent GPs (position, orientation of goal structure)

• GP regressor is time • GP prior mean is constant with known parameter

prior data

posterior

Prior knowledge: Selection of covariance - motion includes quasi-periodic effects

Squared exponentialcovariance function

Periodiccovariance function

Learning

MPC

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Learning and MPC based movement compensation - results

Learning supported MPC for motion control allows precise tracking

Closed loop maximum errors 0.3 mm, 0.03°

Can we provide safety and stability guarantees despite learning?• Enforce reasonable/feasible references?• Stability of the closed loop?

• Moving horizon of training data• Mean value used in controller• Variance: additional safety layer for warnings

GP error is very small

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Safety of MPC reference trackingRequirements on learned reference

Performance• Reference known over prediction horizon• Smooth, i.e. no overfitting of noisy signal

Safety• Reference known for prediction horizon• Trackable under constraints

Idea: Use Gaussian process with constrained learning algorithm

Learning of references should• Provide predictions

(extrapolation)• Take constraints (=safety)

into account • Filter noisy data

GP

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Posterior mean and variance

Gaussian processes-based learning

►Include constraints in hyperparameter optimization

Training &prediction via

hyperparameteroptimization and

conditionalprobabilities(Bayes rule)

Hyper-parameters

+

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Constrained hyperparameter optimization

With negative logarithmic marginal likelihood

Constrained Gaussian-processes learning

Reachable tube with input constraints & dynamics ►stability

State constraints►safety

Theorem (Matschek et al. ‘20): under reasonable conditions we can guarantee tracktability & safety & stability.

How do we guarantee safety in the states? ► consider reachable points are inside of safe set

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Example constraint learning and safety

• standard learned reference not trackable

• Constrained GP provides a trackable reference

• Constrained GP learning allows to model, filter and predict references • Can achieve safety & stability in the sense of perfect tracking

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Key message: fusion of model predictive control and learning verypromising for the control of safe autonomous systems with guarantees



SystemMPC

SystemMPC

SystemMPC


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Learning input-output dynamics with Gaussian-processes

SystemMPC• Gaussian process learns NARX prediction model

• Optimal control problem formulation: nominal formulation, does not exploit uncertainty of GP

Stability, inherent robustness/performance despite ”learning”?

Past observation Future prediction

Theorem (ISS of MPC with a Gaussian process model) [Maiworm et al. (2018,2020)]The closed loop system is input-to-state stable under reasonable assumptions

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Simple example

• Hard input constraints:

• Soft output constraints:

Maiworm ET AL 11

FIGURE 5 Comparison of the three MPC schemes for thecase of initial training dataDref. Thin lines represent individualsimulations, thick lines represent mean values.

FIGURE 6 Comparison of the three MPC schemes for the caseof initial training data Dcomb. Thin lines represent individualsimulations, thick lines represent mean values.

This lack of knowledge leads even to a violation of the con-straints. The rGP however performs significantly better due tothe added data points, especially at the beginning of operation.

These simulations suggest that one should in general pre-fer the Dref case over the other cases, which is convenient forthe used MPC scheme because knowledge at the reference isrequired anyway to determine the terminal cost and controller.

In the second set of simulations we investigate the influenceof di�erent thresholds for the data inclusion approach, i.e.,

di�erent values for the maximum prediction error Ñep and the

maximum prediction variance Ñ�2. To this end, Fig. 7 combines

the rGP results of the previous figures for the three trainingdata cases, together with the evolution of the prediction errore

p and the prediction variance �2. In particular the latter illus-

trates nicely the di�erence between the three cases. In the caseof D0, the variance is small at the beginning and increasesaround t = 8min when the system leaves the neighborhoodof the initial condition and moves towards the reference. Thesame holds, but the other way round, for the case withDref. Theinitial high variance is caused by its computation before thefirst data point is added to the training set. In the case of Dcomb,the variance is almost always small, except at t = 5min andaround t = 9min, probably because the combinations of therespective output values and the relatively large input valuesare not present in Dcomb (see the input evolution in Fig. 6).

FIGURE 7 rGP simulation results for the di�erent train-ing data cases together with the prediction error e

p and theprediction variance �

2.

These findings suggest that Ñ�2 is particularly suited to

include points into D during exploration and that Ñep should

be preferred to refine prediction quality during interpolation.This is verified in Fig. 8 and Fig. 9, where we focus for the

► Proofable “stability and safety“ of the closed loop►“Bounded model plant mismatch“ leads to “bounded error “ in the output

Seborg et al. (1989)

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Uncertain environment – multiple possible modes

Challenge: Often “discrete uncertainties” due to the environment• Other systems / objects are unknown (grabbing)• Decisions of other participants are unknow a priory

F

Changes in material

properties

Uncertainsystem

behavior

Handling of such uncertain modes• Safety guarantees?• Limited performance decrease?

Trafficcrossing

Grasping ofDifferent Objects

Stufen der Verkehrsoptimierung

zentral gesteuertvolle Information

dezentral gesteuertzentrale (volle)

Information

dezentral gesteuertlokale Information

dezentral gesteuertunsichere

Information

4 Einleitung Maximilian Merkert // Die intelligente Ampelkreuzung

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Motivation: optimization of traffic flow

• Can we avoid congestion by intelligent coordination and control?• Influence of autonomous vehicles on the traffic flow• Local decision making

Macroscopic (“global“ perspective)

Microscopic(single vehicle planning and local decisions)

?

• Behavior of single (autonomous) vehicles?•What is the optimal path (path, stop, ...)

• How should drive when?• Global or local decisions?

Cooperation: S. Sorgatz, H. Rewald (VW), S. Sager, M. Markert, H. Duc OvGU

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Safety and performance despite uncertain behaviorsIdea• Keep all modes that are possible in the prediction, guarantee for all constraints = safety• Learn and optimize performance with respect to most probable mode• Remove impossible modes

min Cost(𝛴1, 𝛴2, 𝛴3)

𝛴1(t)∊ 𝓧1

𝛴2(t)∊ 𝓧1

𝛴3(t)∊ 𝓧1

STOP

used for performance optimization

t1 t2 t3

70%

20%

10%

80%

20%

Classification and estimation phase 1



used for performance optimization

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Overall MPC formulationCore idea: consider all modes, improve performance by learning

Differnt possibilitiesrobust constraint

satisfactionfor all modes

(safety)

Learned partimprove performance

Cost functionoptimize performance

STOP

Theorem (Bethge et al. 2018, safety and feasibility)If all nominal models satisfy tightened constraints, then the real system satisfies the constraints = safety and the problem is repeatedly feasible

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Toy simulation results: quadcopter

With learning and multiple modes• Constraint satisfaction guaranteed• Learning improves performance

No learning• Standard MPC violates the constraints• Multi-Mode MPC ensures

robust constraint satisfaction

MPC with one model

Multi-mode MPC

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Key message: fusion of model predictive control and learning verypromising for the control of safe autonomous systems with guarantees



SystemMPC

SystemMPC

SystemMPC


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Towards nominal stability certification of deep learning-based control

Objectives

• Learning from an existing baseline controller (mathematical description does not need to be known to)

• Decrease computational load

• Learn and adapt unknown controller

• Improve robustness, ...

• Data collected from measurements or simulations

• Baseline controller may or may not provide guarantees

Application scenario: learn behavior of human-based driver for autonomous driving

baseline controller

learned controller Σ!

plant Σ"

data

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• Plant Σ!:

• Baseline controller

Key idea• Exploit classical Lyapunov stability conditions• Specific type of deep neural network:

NAIS-Net (Non-Autonomous Input-output Stable Network)• Special type of residual neural network • Share weights of matrices within one block

Question: Can we provide performance and safety guarantees for nominal system with learning-based controller?

baseline controller

learnedcontroller Σ!

plant Σ"

data

Towards nominal stability certification of deep learning based controller

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Basic Idea: stability of the closed-loop system with NAIS-Net based controller

NAIS-Net basedcontroller with

finite number oflayer

plant Σ"

NAIS-Net basedcontroller with

infinite number oflayer

plant Σ"

Disturbance 𝜹(𝒙)

When NAIS-Net is suitably trained, the closed-loop system is equivalent to an auxiliary system with bounded disturbances

• Auxiliary system is asymptotically stable• Disturbance bound depends on # of hidden layers• The plant can be unstable

Theorem: If

Then the closed-loop system is practically asymptotically stable

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Simple simulation example: continuously stirred tank reactor

• Baseline Controller:MPC without provable asymptotic stability properties

• NAIS-Net based controller• 30 nodes in each layer• 512 layers

MPC controller

DNN controller

Learned controller is stable, even so that the baseline NMPC controller has no stability guarantees!

Open question: How can we integrate the stability conditions in the learning?

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Many possible applications• energy systems, batteries, …• cooperative robotics, medical robotics, …• autonomous vehicles, UAVs, aircrafts

Outlook:• Enforcing safety of NN-based controllers using the last layer• Embedded learning: can we perform the learning also online?• …

Fusion of predictive control and learning for autonomous systems• Allows to handle uncertainty and provides adaptation• One can learn many things: model, reference, cost, constraints• Stability and performance guarantees possible

Key message: fusion of model predictive control and learning verypromising for the control of autonomous systems with guarantees

wind

Summary:Fusing Predictive Control and Machine Learning Towards Safe Autonomous Systems

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Thanks

Janine Matschek Johanna Bethge

Hannes Rewald

Hoang Hai Nguyen

All collaborators:• S. Sorgatz (VW), S. Sager (OvGU), Limon group (U. Sevilla), Braatz group (MIT), Mesbah group (UC Berkley), Colin group

(EPFL), Wagener/Tautz group (FZ Jülich), Diehl group (U Freiburg), Borrelli group (UC Berkley), di Cairano group(MERL), Limo group (U Sevilla), S. Waldherr (KU Leuven), J. How group (MIT), M. Zeilinger (ETH)

• Siemens CRT, Bosch, Volkswagen, IAV, Airbus, Baker Hughes, ....

Michael Maiworm Former group members• Prof. Timm Faulwasser (TU Dortmund)• Prof. Sergio Lucia (TU Berlin)• Prof. Stefan Streif (TU Chemnitz)• Prof. Masako Kishida (NII Tokio)• Prof. Steffen Borchers (HTW Berlin)

Tim Zieger

Anton Savchenko

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Selected References• J. Matschek and R. Findeisen. Learning supported Model Predictive Control for Tracking of Periodic References. In Proceedings of Machine Learning

Research, volume 120, pages 511-520, 2020.• M. Maiworm, D. Limón, and R. Findeisen. Online learning-based model predictive control with Gaussian process models and stability guarantees.

International Journal of Robust and Nonlinear Control, 2020.• M. Maiworm, D. Limón, J. M. Manzano, and R. Findeisen. Stability of Gaussian process learning based output feedback model predictive control. In 6th IFAC

Conference on Nonlinear Model Predictive Control (NMPC), pages 551-557, Madison, USA, 2018.• J. Matschek, T. Gonschorek, M. Hanses, N. Elkmann, F. Ortmeier, and R. Findeisen. Learning references with Gaussian processes in model predictive control

applied to robot assisted surgery. In Proceedings of European Control Conference (ECC), pages 362-367, 2020.• J. Matschek and R. Findeisen. Learning supported Model Predictive Control for Tracking of Periodic References. In Proceedings of Machine Learning

Research, volume 120, pages 511-520, 2020.• J. Matschek, A. Himmel, K. Sundmacher, and R. Findeisen. Constrained Gaussian process learning for model predictive control. In Proceedings of 20th IFAC

World Congress Berlin, 2020, to appear.• J. Matschek, R. Jordanowa, and R. Findeisen. Direct Robotic Force Control with Learning Supported Model Predictive Control. 2020. Conference on Control

technology and Applications(CCTA), to appear.• J. Bethge, B. Morabito, J. Matschek, and R. Findeisen. Multi-mode learning supported model predictive control with guarantees. In Proceedings of 6th

Nonlinear Model Predictive Control Conference (NMPC), pages 616-621, Madison, United States, 2018.• J. Matschek and R. Findeisen. Learning supported Model Predictive Control for Tracking of Periodic References. In Proceedings of Machine Learning

Research, volume 120, pages 511-520, 2020.• T. Zieger, J. Matschek, H. Nguyen, T. Oehlschlägel, A. Savchenko and R. Findeisen. Towards Neural Network Based Control with Guarantees - Application to a

Chemical Reactor. In Proceedings of FOPAM, 2019• H. Nguyen, J. Matschek, T. Zieger, A. Savchenko, N. Noroozi, R. Findeisen. Towards Nominal Stability Certification of Deep Learning-based Controllers, In

Proceedings of 2020 American Control Conference , pages 3886-3891, 2020.• T. Zieger, A. Savchenko, T. Oehlschleagel, R. Findeisen. Towards Safe Neural Network Supported Model Predictive Control. In Proceedings of IFAC World

Congress, 2020.• M. Pfefferkorn, M. Maiworm, C. Wagner, F. S. Tautz, and R. Findeisen. Fusing online Gaussian process-based learning and control for scanning quantum dot

microscopy. In 59th Conference on Decision and Control (CDC), 2020, to appear.• T. Zieger, A. Savchenko, T. Oehlschlaegel, R. Findeisen. Safe Neural Network Control and the Potential of the Output Layer, 2020. (submitted)• H. Nguyen, T. Zieger, R. Braatz, R. Findeisen. Stability Certificates for Neural Network Learning-based Controllers using Robust Control Theory, 2020.

(submitted)

fusing predictive control and machine learning towards

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