Abstract
Distributed parameter systems arising from different physical domains share an underlying geometric structure. This has been exploited for formulating an overarching port-Hamiltonian theory of multiphysics distributed parameter systems. From a control engineering point of view the interaction of distributed parameter systems with their surroundings (including controller systems) is either distributed over their spatial domain, and/or via the boundary of this spatial domain (boundary control systems).

The first part of this talk will concentrate on the identification of proper boundary variables. From a geometric point of view there are two structures that determine the boundary variables. The first one is the Stokes-Dirac structure (and its generalizations) defining the power-conserving interconnection structure of the system. In this case the boundary variables arise in the remainders in integration by parts of a skew-adjoint differential operator (Stokes’ theorem). This corresponds to the well-known Dirichlet and Von Neumann boundary conditions. The second one, less prominent, is the Lagrangian subspace corresponding to (quadratic) energy storage relations. The resulting boundary variables arise from integration by parts of the self-adjoint differential operator underlying ths Lagrangian subspace.

The second part of the talk will concentrate on the use of the natural boundary variables for control purposes, e.g., set-point regulation. In particular, a methodology for ‘control by interconnection’ will be discussed, aimed at shaping the physical characteristics of the system. This will be illustrated on a number of examples from different areas of application.

Third part of the talk will take a closer look at it energy conversion of multiphysics systems. To what extent, and how, can energy flowing into the system from one (boundary) port be converted into energy flowing out of the system at a second port? From thermodynamics it is well known that there are limitations to the energy transfer from the thermal to the mechanical port, dictated by the Second law of thermodynamics. It turns out that similar limitations can be present in a general port-Hamiltonian system, depending on the structural properties of its Dirac structure.

Bio sketch
Arjan van der Schaft received the undergraduate and PhD degrees in mathematics from the University of Groningen, the Netherlands. In 1982 he joined the Department of Applied Mathematics, University of Twente. In 2005 he returned to his Alma Mater as professor in Mathematics. Arjan van der Schaft is Fellow of IEEE, Fellow of IFAC, and was the 2013 recipient of the 3-yearly awarded Certificate of Excellent Achievements of the IFAC Technical Committee on Nonlinear Systems. He was Invited Speaker at the International Congress of Mathematicians, Madrid, 2006. Books authored by him include Variational and Hamiltonian Control Systems (1987, with P.E. Crouch), Nonlinear Dynamical Control Systems (1990, 2016, with H. Nijmeijer), L2-Gain and Passivity Techniques in Nonlinear Control (1996, 2000, 2017), An Introduction to Hybrid Dynamical Systems (2000, with J.M. Schumacher), and Port-Hamiltonian Systems: An Introductory Overview (2014, with D. Jeltsema).

Abstract
Studies on transportation management systems have undergone several waves of advancement in both theory and practice, led by revolutions taking place in parallel, including automation, machine learning electrification, and sharing economy. My research focuses on a combination of two of these revolutions, control and learning methodologies and their applications in intelligent traffic systems. In this talk, I will discuss traffic state estimation problem of freeway stop-and-go traffic, also known as phantom traffic jam, a common phenomenon that has drawn a lot of research interests over the years. The congestion leads to acceleration-deceleration traffic oscillations on freeway, causing increased fuel consumption, and driving risk. Traffic state estimation problem refers to a process of inferring traffic state variables from partially observed traffic data. I will first show a methodological Partial Differential Equation model-based solution to obtain traffic state values from boundary sensing data in real-time. Inspired by physics-informed machine learning, we develop observer-informed deep learning which integrates the PDE observer with deep learning paradigm. The observer-informed neural network forms a novel class of data-efficient function approximators that encode PDE observer as theoretical guarantee and improves the accuracy and convergence speed of spatial-temporal traffic state estimation.

Bio sketch
Dr. Huan Yu is an Assistant Professor in the Intelligent Transportation Thrust of the Systems Hub at the Hong Kong University of Science and Technology (Guangzhou), an affiliated Assistant Professor in the Department of Civil and Environmental Engineering at the Hong Kong University of Science and Technology (HKUST). Yu received her B.Eng. degree in Aerospace Engineering from the Honor School (Elite program in engineering) of Northwestern Polytechnical University, and the M.Sc. and Ph.D. degrees in Aerospace Engineering from the Department of Mechanical and Aerospace Engineering, University of California, San Diego. She was a visiting scholar at University of California, Berkeley in 2018 and Massachusetts Institute of Technology in 2019. She was a postdoc researcher at University of California, San Diego before joining the HKUST(GZ) in 2021. Dr. Yu is broadly interested in control, optimization, and learning methodologies and their applications in intelligent transportation systems.

Abstract
The objective of this talk is to present a few key aspects pertaining to the implementation of advanced backstepping-based control designs for coupled ODEs and Hyperbolic PDEs. The talk will be centered in practical aspects including verifying the assumptions required for recent control designs to work, solving the kernel PDEs for the backstepping design and approximating and implementing the resulting controllers using Matlab/Simulink. The overarching goal is to demonstrate that infinite-dimensional based controllers do not necessarily give rise to insurmountable difficulties for implementation. Due to time constraints, we will focus on full-state feedback design instead of output-feedback designs that also require an observer to be implemented.

Bio sketch
Federico Bribiesca-Argomedo (Member, IEEE) received a B.Sc. degree in mechatronics engineering from the Tecnologico de Monterrey, Monterrey, Mexico, in 2009, a M.Sc. degree in control systems from Grenoble INP, Grenoble, France, in 2009, and a Ph.D. degree in control systems from the Grenoble University, Grenoble, France.
He held a postdoctoral position with the Department of Mechanical and Aerospace Engineering, University of California at San Diego, San Diego, CA, USA. He is currently an Associate Professor with the Ampère Laboratory Department of Mechanical Engineering, INSA Lyon, Villeurbanne, France. Past and current applications of his research interests include tokamak safety factor profiles, electrochemical models of Li-ion batteries, and energy distribution networks. His research interests include control of hyperbolic and parabolic partial differential equations and nonlinear control theory.

Jean Auriol (Member, IEEE) received the master’s degree in civil engineering (major: applied mathematics) from the MINES ParisTech, part of PSL Research University, in 2015, and the Ph.D. degree in control theory and applied mathematics from the Centre Automatique et Systèmes, MINES ParisTech, in 2018. His Ph.D. thesis, titled Robust Design of Backstepping Controllers for Systems of Linear Hyperbolic PDEs, has been nominated for the Best Thesis Award given by the GDR MACS
and the Section Automatique du Club EEA in France. From 2018 to 2019, he was a Postdoctoral Researcher at the Department of Petroleum Engineering, University of Calgary, Calgary, AB, Canada, where he was working on the implementation of backstepping control laws for the attenuation of mechanical vibrations in drilling systems. Since December 2019, he has been a Researcher (Chargé de Recherches) at the Laboratoire des Signaux et Systèmes (L2S), CNRS, Centrale Supelec, Université Paris-Saclay, Gif-sur-Yvette, France. His research interests include robust control of hyperbolic systems, neutral systems, networks, and interconnected systems.

Abstract

This talk describes advances in the design of model predictive control (MPC) algorithms that are implementable in real time for distributed parameter systems (DPS), and their application to the control of lithium-ion battery systems.

The presentation begins with a review of methods that have been developed and demonstrated for large-scale manufacturing systems that explicitly include the effects of model uncertainties while retaining low on-line computational costs. The specific techniques underlying various methods are described, including the use of input-output formulations, the replacing of optimization- with simulation-based uncertainty analysis, and the moving most of the computations from on-line to off-line.

After that review, a recently developed approach is described for the design of MPC algorithms for nonlinear DPS in which the on-line computational cost is reduced to a single mixed continuous-discrete (aka hybrid) simulation at each sampling instance. While not applicable to all nonlinear optimal control problems, the approach is shown to be effective in some real applications including for the minimization of the charging time for energy storage systems. The approach is generalized to explicitly incorporate time-invariant probabilistic uncertainties into the optimal control problem at each time instance, while retaining low online computational cost. The specific techniques underlying the approach are described, which includes the main idea of translating the optimization in the optimal control problem into logic-based calculations that are embedded into the hybrid simulation.

In the lithium-ion application case study, the online computational time is reduced to ~10 ms per sampling instance — fast enough for real-time implementation of nonlinear MPC that directly incorporates a sophisticated porous electrode theory-based battery model, without use of any model reduction. The computational time is shown to solvable in ~10 ms when chance constraints are including in the optimal control problem, by making use of existing multicore hardware in modern microprocessors and proper structuring of the calculations in and communications between the cores. The approach is demonstrated for a wide range of practical operating constraints, including explicit constraints are unmeasured states associated with battery degradation that evolve on very long time scales. For the battery application, it is also shown that, for some sets of practical operating constraints, the real-time nonlinear MPC calculations can be converted into an explicit control law. The resulting computational cost drops to less than 0.1 ms on a single core.

The results in this talk draw from research collaborations with students and faculty at multiple universities.

Bio sketch

Richard D. Braatz is the Edwin R. Gilliland Professor at the Massachusetts Institute of Technology (MIT) where he does research in applied mathematics and robust optimal control theory and its application to advanced manufacturing systems. He received an MS and PhD from the California Institute of Technology and was Professor and Millennium Chair at the University of Illinois at Urbana-Champaign and a Visiting Scholar at Harvard University before moving to MIT.

His past professional service includes the Editor-in-Chief of IEEE Control Systems Magazine, the President of the American Automatic Control Council, General Chair of the IEEE Conference on Decision and Control and of the American Control Conference, and Vice-Chair of the IFAC Conference Board. Honors include the AACC Donald P. Eckman Award, the Antonio Ruberti Young Researcher Prize, and best paper awards from IEEE- and IFAC-sponsored control journals. He is a Fellow of IEEE and IFAC and a member of the U.S. National Academy of Engineering.

Abstract

In many applications there exists the necessity to model the separation among different physical processes. These moving interfaces can be described by the level set of the solution of Hamilton-Jacobi partial differential equations such as the normal flow and mean curvature flow equations. The motion of dynamic surfaces (in two and three dimensions) is fundamental in a number of research fields, including combustion, computational fluid dynamics, and image processing. Theory and practice of this modeling paradigm is part of the wide research area of the so-called level set methods. Such methods are based on the idea to deal with moving interfaces according to an Eulerian approach, which turns out to be more easily tractable as compared with particle or Lagrangian approaches. Despite the vast literature on the control of distributed parameter systems, up to now very little has been proposed on the control of level sets. Starting with a short introduction on level set methods, the talk will concern the presentation of some first attempts to attack such problems from the point of view of the control theory, by focusing on the existing stability results and the prospect of future investigations.

Bio sketch

Angelo Alessandri received the “Laurea” degree degree in Electronics Engineering and the Ph.D. degree in Electronics and Computer Engineering from the University of Genoa, Genoa, Italy, in 1992 and 1996, respectively. From 1996 to 2005, he was a research scientist with the National Research Council of Italy, Genoa. In 2005, he joined the University of Genoa, where he is currently a full professor in the Department of Mechanical, Energetics, Management, and Transportation Engineering. His main research interests include estimation, fault diagnosis, and optimal control. He was an associate editor of the IFAC Journal of Engineering Applications of Artificial Intelligence, the IEEE Transactions on Neural Networks, and the IEEE Transactions on Control Systems Technology. He serves as an editor of the International Journal of Adaptive Control and Signal Processing and as an associate editor of the EUCA European Journal of Control and of the IFAC journal Automatica.

Abstract

The presentation will address concepts for the control and observer design for PDE systems by making use of dissipativity and small-gain arguments.

First, Riesz spectral systems in terms of coupled linear diffusion-reaction systems are considered. Based on a suitable decomposition of the system operator into a slow and a fast subsystem the finite-dimensional (modal) state feedback control with state observer is considered. Closed-loop stability is addressed using a small-gain approach that allows us to capture the well-know observer spillover, which is analyzed for in-domain / boundary actuation and sensing. This includes an approach for the computation of the required dimension of the slow subsystem used for controller and observer design.

Secondly, the combination of the backstepping methodology with dissipativity concepts in the framework of observer design are presented for coupled semilinear diffusion-reaction systems. For this purpose, sufficient conditions for the convergence of the observer are derived with the help of the intrinsic connection between dissipativity and Lyapunov’s direct method. The design is divided into two steps: (I) the exponential stabilization of the observer error dynamics for a decoupled linear subsystem and (II) the consideration of linear and nonlinear couplings between the PDEs by assuming certain dissipativity properties.

The theoretical developments are supported by numerical simulations that illustrate the performance of the developed control and observer concepts.

Bio sketch

Thomas Meurer received the diploma in Process Systems Engineering from the University of Stuttgart, Germany in 2001, the M.Sc. in Engineering Science and Mechanics from the Georgia Institute of Technology, Atlanta, USA in 2000, and the Ph.D. degree from the University of Stuttgart in 2005. From 2005 to 2007 he was a Postdoctoral Fellow at the Saarland University, Germany. In 2007 he joined the Automation and Control Institute at the TU Vienna, Austria as a Senior Researcher, where he was appointed Associate Professor (Privatdozent) in 2012. Since 2012 he has been Full Professor and head of the Automation and Control Group at Kiel University, Germany. He is Associate Editor for the journals Automatica, IEEE Control Systems Letters, and Mathematical Control and Related Fields. He was chair of the IFAC TC 2.6 on Distributed Parameter Systems from 2011 to 2017 and has been chair of the IEEE-CSS TC Distributed Parameter Systems since 2019. He received the VDI/GMA Eugen Hartmann Award in 2009, the Cardinal Innitzer Award in 2012, the IFAC Congress Best Interactive Paper Prize at the 2017 IFAC World Congress, and the Control Engineering Practice Paper Prize Award in 2020. His research interests include control of distributed parameter systems, nonlinear control theory, observer design, and optimal control with applications in robotics, production processes, mechatronics, marine systems, and process systems engineering.