 
Last updated on July 11, 2021. This conference program is tentative and subject to change
Technical Program for Tuesday September 14, 2021

WSA1 
Room 1 
Optimal Control and Differential Games: Constructive Approximate Solutions
and Learning Strategies 
Tutorial Workshop Session 
Organizer: Sassano, Mario  University of Rome, Tor Vergata 
Organizer: Mylvaganam, Thulasi  Imperial College London 
Organizer: Astolfi, Alessandro  Imperial Col. London & Univ. of Rome Tor Vergata 

08:0008:30, Paper WSA1.1  
An Introduction to Dynamic Optimisation Problems 

Astolfi, Alessandro  Imperial Col. London & Univ. of Rome Tor Vergata 
Keywords: Control of Nonlinear Systems
Abstract: Problems involving dynamic (multiobjective) optimisation are ubiquitous in modern applications and are therefore of paramount interest. In addition, such problems have a rich mathematical structure, hence have been extensively studying in mathematical systems theory. Such problems entail the minimization of one or more cost functionals, while satisfying a dynamic constraint. The latter captures the behaviour of the environment that is influenced by the actions of the decisionmaking agents. Arising in various guises, such as optimal control, differential games and meanfield games, problems involving dynamic optimisation are notoriously difficult to solve, particularly in the presence of nonlinear cost functionals and/or nonlinear dynamics. Consequently, significant effort has been dedicated to develop methods to efficiently tackle such problems. Existing methods are diverse and can roughly be divided into two classes, namely offline methods, aimed at obtaining solutions (or approximations thereof), and online methods, aimed at learning solutions in realtime. In the context of optimal control, the latter include iterative learning control and reinforcement learning. The aim of this talk is to provide a brief overview on the formulation of the problem as well as a few results available within the frameworks of Dynamic Programming and Pontryagin’s Minimum Principle.


08:3009:10, Paper WSA1.2  
An Introduction to Dynamic Optimisation Problems: Part II 

Astolfi, Alessandro  Imperial Col. London & Univ. of Rome Tor Vergata 
Keywords: Control of Nonlinear Systems
Abstract: Problems involving dynamic (multiobjective) optimisation are ubiquitous in modern applications and are therefore of paramount interest. In addition, such problems have a rich mathematical structure, hence have been extensively studying in mathematical systems theory. Such problems entail the minimization of one or more cost functionals, while satisfying a dynamic constraint. The latter captures the behaviour of the environment that is influenced by the actions of the decisionmaking agents. Arising in various guises, such as optimal control, differential games and meanfield games, problems involving dynamic optimisation are notoriously difficult to solve, particularly in the presence of nonlinear cost functionals and/or nonlinear dynamics. Consequently, signicant effort has been dedicated to develop methods to efficiently tackle such problems. Existing methods are diverse and can roughly be divided into two classes, namely offline methods, aimed at obtaining solutions (or approximations thereof), and online methods, aimed at learning solutions in realtime. In the context of optimal control, the latter include iterative learning control and reinforcement learning. The aim of this talk is to provide a brief overview on the formulation of the problem as well as a few results available within the frameworks of Dynamic Programming and Pontryagin's Minimum Principle.


09:1010:00, Paper WSA1.3  
OffLine Solutions of Dynamic Optimisation Problems Via Immersion and Algebraic Conditions 

Mylvaganam, Thulasi  Imperial College London 
Keywords: Control of Nonlinear Systems
Abstract: Considering three classes of control problems, namely optimal control, L2disturbance attenuation and differential games, we present a design framework which enables the systematic construction of (approximate) solutions offline. Differently from the classic offline strategies, typically based on Taylor expansion of the underlying value function or the solution of the HJB equation pointwise with respect to x, the proposed design framework hinges upon the immersion of the nonlinear dynamics into an extended system and certain algebraic conditions that are much milder to satisfy than the corresponding HJB PDE. As a consequence, the strategy yields a dynamic control law, in which the behaviour over time of the auxiliary (extended) variable, driven by measurements of the current values of the state x, is autonomously adjusted to compensate for the mismatch in the solutions of the algebraic conditions and the actual HJB PDE.


10:0010:40, Paper WSA1.4  
MultiAgent Collision Avoidance: A Case Study 

Mylvaganam, Thulasi  Imperial College London 
Keywords: Control of Nonlinear Systems
Abstract: Within the framework of continuoustime differential games, the design framework based on immersion and dynamic extension discussed in the previous talk has proved effective in the context of navigation and control of multiagent systems. In this talk, we present a game theoretic approach to multiagent collision avoidance as a practical case study, including theoretical and experimental results via the use of a team of wheeled mobile robots. Moreover, the practical implementation of the theoretical claims revolve around steps which enable a shift from offline to online implementation of control strategies.


10:4011:20, Paper WSA1.5  
A FixedPoint Characterization of Optimal Control Laws 

Sassano, Mario  University of Rome, Tor Vergata 
Keywords: Control of Nonlinear Systems
Abstract: In the context of infinitehorizon problems, Dynamic Programming and Pontryagin's Minimum Principle provide two alternative strategies to solve optimal control problems and disturbance attenuation problems. We then present a method to solve these control problems via the simultaneous consideration of the strategies mentioned above. Such alternative characterizations are in particular merged together to provide a description of the optimal control law in terms the fixed point of a certain mapping defined by a suitable composition of flows. The latter conditions suggest interesting insights on the linear as well as the nonlinear settings. In the former, it is shown that the fixedpoint description leads to a (pseudo) Algebraic Riccati Equation, the quadratic term of which is always sign definite also in the case of Hinfinity control problems. In the nonlinear setting, the result yields a control design strategy which requires the solution of algebraic equations that permit the construction of the optimal feedback by considering the behavior of the closedloop dynamics at a single point in the state space. Interestingly, a similar intuition can be further extended to tackle several problems, including the construction of the optimal costate variable in finitehorizon optimal control problems or to circumvent the need for solving the (asymmetric) AREs arising in the characterization of openloop Nash equilibrium strategies.


11:2011:40, Paper WSA1.6  
A FiniteDimensional Characterisation of Optimal Control Laws 

Sassano, Mario  University of Rome, Tor Vergata 
Keywords: Control of Nonlinear Systems
Abstract: Exploiting properties of the Hamiltonian system associated with a generic optimal control problem, we demonstrate that the solution of the optimal control problem can be recast as a (static) finitedimensional optimisation problem. In particular, the latter involve a cost function based on the forward and backward propagation of the Hamiltonian dynamics from a point lying on the surface of a hypersphere of sufficiently small radius. The exact characterisation can be relaxed to yield a strategy that allows to determine an arbitrarily accurate approximate solution. The resulting strategy can be implemented in a recedinghorizon fashion to improve the performance (in terms of robustness) of the strategy. Therefore, the method is also put into perspective and compared with existing recedinghorizon strategies.


11:4012:00, Paper WSA1.7  
ModelBased Reinforcement Learning for Nonlinear Systems Via Controlled Hamiltonian Dynamics 

Sassano, Mario  University of Rome, Tor Vergata 
Keywords: Control of Nonlinear Systems
Abstract: Within the framework defined by the Pontryagin's Minimum Principle to tackle optimal control problems over an infinite horizon, we demonstrate that the the dynamics of the underlying costate variable in the Hamiltonian dynamics can be steered by means of a (virtual) control input in such a way that the stable invariant manifold (which characterises the exact solution of the optimal control problem) becomes externally attractive. The quality of approximate solutions can then be measured by considering the corresponding distance from invariance of the manifold and approximate solutions can be improved to minimise this measure. Therefore, it is shown that the external stabilization of the (stable) invariant manifold constitutes the key enabling ingredient to employ the above distancefrominvariance as the temporal difference error in a modelbased reinforcement learning architecture.


WSA2 
Room 2 
Nonlinear Modeling and Control of IndustryRelated Systems 
Tutorial Workshop Session 
Organizer: Tsubakino, Daisuke  Nagoya University 

08:0009:05, Paper WSA2.1  
Modeling and Identification of Hydraulic Cylinder Dynamics 

Sakai, Satoru  Shinshu University 
Keywords: Mechatronics and Robotics, Modeling and Identification of Nonlinear Systems, Nonlinear Model Predictive Control
Abstract: A new generation of modeling, identification and control of hydraulic systems is coming. In this presentation, some new results on modeling and identification of hydraulic cylinder dynamics are focused. First, the basics of hydraulic cylinder dynamics are reviewed and the structural properties are revealed. Second, based on the properties, several new modeling and identification methods are introduced without losing their links to nonlinear control. Finally, the numerical and experimental validations of the methods are discussed in the application to a construction machinery. "Nonlinear modeling and control of industryrelated systems"


09:0510:05, Paper WSA2.2  
Control, State Estimation, and Model Identification of Batteries 

Wada, Toshihiro  Mitsubishi Electric Corporation 
Keywords: Modeling and Identification of Nonlinear Systems, Power and Energy Control, Chemical Technology
Abstract: Importance of batteries is unquestionable in modern electronics, and is increasing because of the popularization of electric vehicles, aircraft, and wider utilization of renewable energy in the next decade. However, modeling and control of batteries are still challenging due to the nonlinearity derived from mutual dependence of chemical reactions and thermal responses, as well as limited observability for a lot of internal states and unknown model parameters. In this talk, we introduce fundamental equations for batteries, typical motivations to control battery systems, and industrial applications with our contributions to this research area. Tutorial workshop: Nonlinear modeling and control of industryrelated systems


10:0511:05, Paper WSA2.3  
TheoryBased Design and Control of Biomolecular Systems 

Hori, Yutaka  Keio University 
Keywords: Systems Biology, Control of Networks, Chemical Technology
Abstract: Recent advancements in synthetic biology have enabled the bottomup design of biomolecular reaction networks. This has opened up an opportunity to build chemicallydriven circuits and systems that perform sensing, actuation, and information processing based on programmed biomolecular reactions, which could potentially lead to chemicallydriven celllike robots. In this talk, we first review the basic concept of biomolecular circuits and introduce a modeling framework for analysis and design. Examples of engineered circuit components such as biomolecular oscillators are then demonstrated. In particular, we show how one can develop/use tools in feedback control to help accelerate the tedious design and tuning process. Finally, applications of engineered biomolecular systems are discussed along with remaining challenges and opportunities.


11:0512:00, Paper WSA2.4  
Approximate Modeling and Controller Design for Fluid Flows 

Tsubakino, Daisuke  Nagoya University 
Keywords: Control of Nonlinear Systems, Nonlinear Model Predictive Control, Machine Learning
Abstract: Fluid flow exists ubiquitously and it sometimes causes practical problems. Recent development of actuator devices enables us to realize feedback control of fluid flows to some extent. It is wellknown that a reliable model of dynamics of fluid flows is the NavierStokes equations. Unfortunately, the NavierStokes equations are nonlinear partial differential equations. It is generally difficult to design feedback control laws theoretically based on the model. Hence, incorporating approximation into modeling or design of control laws seems to be necessary. In this talk, we first review the NavierStokes equations and their variations. Then, we introduce approximation of models, control laws, and state estimator based on physical observation and datadriven approaches.


WSB1 
Room 1 
The Koopman Operator in Systems and Control: Concepts, Methodologies, and
Applications 
Tutorial Workshop Session 
Organizer: Susuki, Yoshihiko  Osaka Prefecture University 
Organizer: Mauroy, Alexandre  University of Namur 
Organizer: Mezic, Igor  Univ of California, Santa Barbara 

12:3013:10, Paper WSB1.1  
Koopman Operator in Systems and Control: Concepts and Methodologies 

Mauroy, Alexandre  University of Namur 
Keywords: Control of Nonlinear Systems, Modeling and Identification of Nonlinear Systems
Abstract: The socalled Koopman operator framework provides a global description of nonlinear dynamical systems in terms of observablefunctions. This framework turns nonlinear systems into a linear (but infinitedimensional) systems, an approach which yields systematic and efficient linear techniques to solve nonlinear problems, in particular in the specific context of control theory. In the first part of this talk, basic concepts in Koopman operator theory will be reviewed. The second part will focus on numerical (datadriven) methods that provide finitedimensional approximations of the Koopman operator. Finally, recent developments in control theory will be presented in the third part of the talk.


13:1014:00, Paper WSB1.2  
Koopman Operator in Systems and Control: Concepts and Methodologies Part 2 

Mauroy, Alexandre  University of Namur 
Keywords: Control of Nonlinear Systems, Modeling and Identification of Nonlinear Systems
Abstract: The socalled Koopman operator framework provides a global description of nonlinear dynamical systems in terms of observablefunctions. This viewpoint turns nonlinear systems into linear (but infinitedimensional) systems, an approach which yields systematic and efficient linear techniques to solve nonlinear problems, in particular in the specific context of control theory. In the first part of this talk, basic concepts related to Koopman operator theory will be reviewed. The second part will focus on numerical (datadriven) methods that provide finitedimensional approximations of the Koopman operator. Finally, recent developments in control theory will be presented in the third part of the talk. Title of workshop: The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications


14:0014:40, Paper WSB1.3  
Koopman Operator in Systems and Control: Applications, Part 1 

Susuki, Yoshihiko  Osaka Prefecture University 
Keywords: Control of Nonlinear Systems, Modeling and Identification of Nonlinear Systems, Power and Energy Control
Abstract: The socalled Koopman operator framework provides a global description of nonlinear dynamical systems in terms of the evolution of "observable functions" defined on the state space. The framework enables us to turn nonlinear systems into linear (but infinitedimensional) systems. This yields systematic and efficient linear techniques to solve problems on analysis and control of systems with nonlinear dynamics. In the first part of this talk, based on our recent book (A. Mauroy, I. Mezic, and Y. Susuki (editors), The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications, Springer Nature, 2020) and the preceding talk on concepts and methodologies, I will provide an overview of applications of the Koopman operator framework in the specific context of systems and control. Applications here can be taken from both engineering and science such as mechatronics, thermal engineering, power grids, and synthetic biology. The second part will describe concrete and detailed introduction to (some of) the applications in order to discuss their effectiveness. Finally, recent progresses in applications will be presented in the third part of the talk.


14:4015:30, Paper WSB1.4  
Koopman Operator in Systems and Control: Applications, Part 2 

Susuki, Yoshihiko  Osaka Prefecture University 
Keywords: Control of Nonlinear Systems, Modeling and Identification of Nonlinear Systems, Power and Energy Control
Abstract: The socalled Koopman operator framework provides a global description of nonlinear dynamical systems in terms of the evolution of ``observable functions'' defined on the state space. The framework enables us to turn nonlinear systems into linear (but infinitedimensional) systems. This yields systematic and efficient linear techniques to solve problems on analysis and control of systems with nonlinear dynamics. In the first part of this talk, based on our recent book (A. Mauroy, I. Mezic, and Y. Susuki (editors), The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications, Springer Nature, 2020) and the preceding talk on concepts and methodologies, I will provide an overview of applications of the Koopman operator framework in the specific context of systems and control. Applications here can be taken from both engineering and science such as mechatronics, thermal engineering, power grids, and synthetic biology. The second part will describe concrete and detailed introduction to (some of) the applications in order to discuss their effectiveness. Finally, recent progresses in applications will be presented in the third part of the talk.


15:3016:30, Paper WSB1.5  
Koopman Operator, Geometry, and Machine Learning 

Mezic, Igor  Univ of California, Santa Barbara 
Keywords: Machine Learning, Control of Nonlinear Systems
Abstract: A tutorial is provided for learning of dynamical and control systems rooted in the concept of representations and Koopman operators. The use of neural networks in this context is discussed. Examples are given.

 