| Tuesday, Jun 9 (17-18, Paris-Madrid-Berlin Time)
|| Miroslav Krstic (University of California, San Diego)
|| Control of PDEs with Boundaries Governed by ODEs
|| In this talk, which is based on my 2019 SIAM Reid Lecture, I will draw attention to PDE control problems with moving boundaries, in which the dynamics of the boundaries are governed by (nonlinear) ODEs. The main emphasis will be on parabolic problems, represented by the Stefan model of phase change (in solids and liquids), with the remainder of the time spent on hyperbolic models of congested traffic. All the feedback designs presented are based on the PDE backstepping approach, with explicit expressions for the gain kernels.
| Tuesday, Jun 23 (17-18, Paris-Madrid-Berlin Time)
|| Christophe Prieur (Univ. Grenoble Alpes, CNRS, Gipsa-lab, France)
|| From traffic control to Covid-19 pandemic simulation: the effect of transport dynamics
||This presentation will review some recent results on traffic control and Covid-19 pandemic simulation. The focus will be first done on the traffic congestion of linearized Aw-Rascle Zhang model with disturbances. Backstepping method will be used to compute a boundary feedback control for the linearized model, with two opposite transport dynamics. The second part of the talk will be on the Covid-19 pandemic where multiple-scale transport dynamics could be observed on simulations. For this ill-posed problem, a preliminary work has been done to obtain parametrized dynamical model, and numerical simulations have been performed to illustrate the transport dynamics.
| Tuesday, Jul 7 (17-18, Paris-Madrid-Berlin Time)
|| Iasson Karafyllis (National Technical University of Athens)
|| Global Stabilization of 1-D Reaction-Diffusion PDEs by Means of Boundary Feedback
|| Very few results are available in the literature for global stabilization of 1-D semilinear Reaction-Diffusion (R-D) PDEs by means of boundary feedback. The talk will focus on the obstacles for the construction of globally stabilizing boundary feedback laws for R-D PDEs with arbitrary nonlinearities in the reaction terms and will show that necessarily we have to restrict our attention to two classes of reaction terms: (i) reaction terms with linear growth, and (ii) reaction terms with stabilizing higher order terms. Two different approaches for the construction of boundary feedback laws for R-D PDEs will be presented: (i) the small-gain methodology, and (ii) the Control Lyapunov Functional (CLF) methodology. Methodologies for the construction of simple CLFs for R-D PDEs will also be given. Finally, the talk will also point out significant open problems which will require novel mathematical tools for their solution.
| Tuesday, Jul 21 (17-18, Paris-Madrid-Berlin Time)
|| Emilia Fridman (Tel Aviv University)
|| Robust delayed and sampled-data control of parabolic PDEs
|| The talk (based on my plenary on CPDE 2019)
will start with distributed static output-feedback control of semilinear 1D heat equations in the presence of input/output delays (which may include sampling in time). I will present sampling in space or spatial decomposition method, where the domain is divided into N subdomains. It is assumed that N sensors located in each subdomain provide delayed in time point or averaged measurements of the state, whereas the delayed control is applied through distributed in space shape functions. Given upper bounds on the delays, sufficient conditions ensuring the stability and performance (exponential decay rate or L2-gain) are established in terms of linear matrix inequalities using appropriate Lyapunov–Krasovskii functionals. As an application of results, a network-based deployment of multi-agent systems via PDEs will be considered.
Extension to N-D heat , Kuramoto-Sivashiskii, damped wave and other PDEs will be discussed.
If I have time, I will mention input delay compensation for heat equation by using observers of the future state.
| Tuesday, Jul 28 (17-18, Paris-Madrid-Berlin Time)
|| Alexander Keimer (University of California, Berkeley)
|| Controllability of nonlocal conservation laws
|| In recent years, nonlocal conservation laws have drawn a lot of attention for the capability of modelling the dynamics of traffic flow, supply chains, chemical ripening processes and more. Nonlocal refer s to the fact that the velocity of the conservation law depends on a spatial integration of the solution (and not -- as for classical conservation laws -- point-wise in space time on the solution). Questions of controllability and long time behavior for nonlocal conservation laws have rarely been addressed. This is why we will introduce in this talk scalar nonlocal conservation laws on a bounded domain, define the proper boundary values, and present applications in traffic flow modelling. We will discuss recent results on controllability, when the control is located at the boundaries and investigate the long-time behavior of the solution. Several challenging and interesting open problems will conclude the talk.
| Tuesday, Sep 8 (17-18, Paris-Madrid-Berlin Time)
|| John Baras (University of Maryland)
|| From Copernicus-Bachy-Kepler to Swarms: Learning Composable Laws from Observed Trajectories
|| A novel approach is described, rooted in the port-Hamiltonian formalism on multi-layered graphs, for modeling, learning and analysis of governing laws of physical systems. The problem is inspired by the discovery by Kepler of the laws governing planetary motion from the data collected by Copernicus. We focus on learning the coordination laws of ensembles of autonomous multi-agent systems from empirical indexed trajectories data (position, velocity, etc.). Natural collectives like flocking birds, insects, and fish are included. We describe our results on validation of the applicability of universal port-Hamiltonian models (single and multi-agent) for an efficient learning framework to physics and biology related processes. We employ methods and techniques from mathematical physics for efficient and scalable learning (symmetries, invariants, conservation laws, Noether’s theorems, sparse learning, model reduction). We describe the modeling and software implementation of the methodology via deep learning platforms and efficient numerical schemes. We validate the performance on simulated ensemble data, generated by multiple potentials (various forms of Cucker-Smale models) and Boids models, with complex behaviors and maneuvers of autonomous swarms. We investigate the identification of leaders and sub-swarm motions. We apply mean-field theory to derive macroscopic (PDE) models of the ensemble that lead to explanations of certain coordination laws observed in bird flocks. Finally, we apply these methods to the control of several DPS physics-based systems described by PDEs.`
| Tuesday, Sep 22 (17-18, Paris-Madrid-Berlin Time)
|| Swann Marx (LS2N - Laboratoire des Sciences du Numerique de Nantes)
|| Forwarding approach for the stabilization of coupled PDE-ODE system
|| This talk will be about a stabilization technique for a class of coupled PDE/ODE system. This technique relies mainly on the forwarding method, popularized in the 90's in the finite-dimensional nonlinear control community. Our technique is thus an extension of some finite-dimensional technique to the infinite-dimensional world. We will discuss on the structural properties needed to apply such a technique and on the introduction of mathematical objects, such as the infinite-dimensional Sylvester equation, which are essential for our analysis. Our technique will be illustrated on some systems of transport equations coupled with ODEs. It is a joint work with Lucas Brivadis (LAGEPP) and Daniele Astolfi (LAGEPP)"
| Tuesday, Oct 6 (17-18, Paris-Madrid-Berlin Time)
|| Nicolas Espitia (Univ. Lille, CNRS, Centrale Lille, UMR 9189 - CRIStAL)
|| Event-triggered boundary control and event-triggered gain scheduling of reaction-diffusion PDEs
|| This talk will focus on some recent results on event-triggered boundary control and event-triggered gain scheduling of some classes of reaction-diffusion PDEs. The presentation will start by discussing what event-triggered control is about while highlighting some motivating examples of real application for which event-triggered control can play a fundamental role (e.g. a more realistic way for the actuation on the PDE system). Then, the presentation will deal with an event-triggered boundary control of reaction-diffusion with constant parameters. The approach relies on the emulation of backstepping control, small-gain arguments, and on a suitable state-dependent triggering condition which establishes the time instants at which the control value needs to be sampled/updated. The stability result and the issue of Zeno phenomenon will be discussed.
Finally, a brief introduction and some preliminary results on event-triggered gain scheduling for reaction-diffusion systems with time- and space- varying reaction coefficients will also be presented.
| Tuesday, Oct 20 (17-18, Paris-Madrid-Berlin Time)
|| Kirsten Morris (University of Waterloo)
|| Estimation of partial differential equations with disturbances
|| Often only some aspect of the state needs to be estimated, not the whole state. Also, there may be disturbances other than Gaussian noise. In such situations a Kalman filter may not be the most appropriate estimator. One alternative approach is to reduce the worst error over all disturbances. A derivation of this type of estimator for linear infinite-dimensional systems is described. The connection to a Kalman filter is discussed. A practical framework for constructing finite-dimensional estimators that provide performance arbitrarily close to optimal is then developed. Some work on the related issue of sensor location will be described.
| Tuesday, Nov 3 (17-18, Paris-Madrid-Berlin Time)
|| Yann Le Gorrec (FEMTO-ST, Univ. Bourgogne Franche-Comte, CNRS)
|| Control of Distributed Parameter Systems : The port Hamiltonian approach
|| In this talk we give an overview on some basic and more recent results on control of distributed parameter systems using the port Hamiltonian framework. After a short reminder on port Hamiltonian formulations for 1D boundary controlled linear systems, we recall the main results on asymptotic or exponential stabilization of these BCS using static or dynamic feedbacks. We show how these results and the intrinsic structural properties of these systems can be used for control design purposes using energy shaping, even in the case the DPS is connected at one of its boundary to an anti-damping element and controlled at the other side of the spatial domain. We also show how the passivity properties can be efficiently used for robust output tracking control. This talk will end with some extensions and perspectives in the non-linear and multidimensional cases.
| Tuesday, Nov 17 (17-18, Paris-Madrid-Berlin Time)
|| Thomas Meurer (Kiel University)
|| Multi-agent systems – continuum models and PDE-based control
|| Multi-agent systems consist of dynamical subsystems (agents) that exchange information so that the agent collective is enabled to solve complex tasks. Applications address robotic actuator and sensor networks, intelligent traffic control and monitoring systems, coupled micro-mechanical oscillators, load balancing in processor clusters, distributed energy systems, or networks of micro-satellites. For the mathematical description of multi-agent systems it is typically distinguished between the discrete and the continuous approach. While the discrete setting makes use of ordinary differential equations to model each agent and graph theoretical concepts to address the agent coupling in the continuous setting partial differential equations (PDEs) are considered to represent an agent continuum. The latter is particularly suited for systems involving a large number of agents but still allows to recover the individual agent dynamics and interconnection.
This presentation addresses recent developments for modeling and control of multi-agent systems by exploiting the continuous setting using PDEs. It is shown that this set-up enables us to develop an inverse approach, where the collective dynamics of the agent continuum is a priori imposed and serves as a degree-of-freedom to be exploited for the control design. This implies a design that is in principle independent of the actual communication topology, i.e., the inter-agent communication network, that is naturally obtained by discretizing the PDE model and the determined controller. With this, distributed and decentralized control strategies can be efficiently deduced independently of the agent number and the topology. Theoretical developments are supported by simulation and experimental results taking into account linear and nonlinear PDE models to solve problems of synchronization and formation control in large scale multi-agent systems.
| Tuesday, Dec 1 (17-18, Paris-Madrid-Berlin Time)
|| Nikolaos Bekiaris-Liberis (Technical University of Crete)
|| PDE-based traffic flow control: Delay-compensating, coordinated, and adaptive cruise control designs
|| Delay compensation, coordination, and adaptive cruise control are, potentially, effective means for achievement of safe, efficient, and "green" traffic systems, combining both advanced control design methodologies and technologies. Towards this end, various PDE-based traffic flow control designs will be reviewed in this seminar. As regards delay compensation, predictor-feedback control designs will be presented, at both macroscopic (via introduction of a predictor-feedback ramp metering strategy for quasilinear transport PDE-ODE interconnections) and microscopic (via design of a predictor-based adaptive cruise control law) levels. With respect to coordinated designs, a fault-tolerant ramp metering (or variable speed limits) feedback controller will be presented (via introduction of bilateral boundary control laws for viscous Hamilton-Jacobi PDEs, which interlace PDE feedback linearization with PDE backstepping), as well as an inverse optimal, predictor-feedback controller, for traffic systems with multiple actuators, under unknown traffic demand flows. Capitalizing on the capabilities of adaptive cruise control-equipped vehicles, a feedback control strategy will be presented, aiming at homogenization of traffic speed profile (via considering an Aw-Rascle-Zhang-type traffic flow model with distributed actuation, arising from the presence of connected/automated vehicles).
| Tuesday, Jan 12 (17-18, Paris-Madrid-Berlin Time)
|| Guilherme Mazanti (Inria & L2S-CentraleSupelec)
|| Asymptotic behavior of one-dimensional wave equations with set-valued boundary damping
|| Wave equations with nonlinear boundary damping have been the subject of several works in the past decades due to their importance from both theoretical and applied points of view. Nonlinear boundary conditions often arise from nonlinear phenomena in the practical implementation of boundary control laws for linear wave equations, such as nonlinearities in the components used for the implementation or saturation phenomena, and they may have an important impact in the stability properties and the asymptotic behavior of the system.
In this talk, after providing a brief summary of some important previous works on wave equations with nonlinear boundary damping, we will present a new framework for addressing this problem. We shall consider wave equations in Lp functional spaces and with set-valued boundary dampings, which are a natural generalization of nonlinear dampings allowing to fully exploit some symmetry properties previously observed and for which we can provide some very general well-posedness results.
We will show how our techniques allow us to retrieve some known results on the asymptotic behavior of wave equations with nonlinear boundary damping and provide answers to previously open questions. In particular, we provide a complete characterization of the asymptotic behavior of systems in which the boundary condition is described by the sign function and we also address input-to-state stability with respect to boundary perturbations.
This talk is based on joint works with Yacine Chitour and Swann Marx.
| Tuesday, Jan 26 (17-18, Paris-Madrid-Berlin Time)
|| Thibault Liard (LS2N, Ecole Centrale de Nantes & CNRS UMR)
|| Boundary sliding mode control of hyperbolic systems
We study the asymptotic behavior of linear hyperbolic systems subject to unknown boundary disturbances. Our aim is to construct a boundary feedback law, based on a sliding mode procedure, which rejects the disturbance in finite time and which globally stabilizes the equilibrium point zero. The main novelty of our approach consists in defining a sliding variable and a corresponding sliding surface on which the global exponential stability is ensured. More precisely, the sliding surface is derived from the gradient of a Lyapunov function. We will extend this approach to an equation of conservation laws with simulations.
| Tuesday, Feb 9 (17-18, Paris-Madrid-Berlin Time)
|| Hoai-Minh Nguyen (Ecole polytechnique federale de Lausanne)
|| Stabilization and controllability related to the optimal time for hyperbolic systems in one dimensional space
|| In this talk, I discuss recent results on the stabilization and the controllability related to the optimal time for hyperbolic systems in one dimensional space with controls on one side. The time-varying coefficients are also considered and appealing phenomena are mentioned. The starting point for the analysis of many results is the backstepping technique. This was first proposed for hyperbolic systems by J. M. Coron, R. Vazquez, M. Krstic, and G. Bastin. The talk is based on joint work with Jean-Michel Coron.
| Tuesday, Feb 23 (17-18, Paris-Madrid-Berlin Time)
|| Weiwei Hu (University of Georgia)
|| Optimal Control Design for Fluid Mixing: Analysis and Computation
|| The question of what velocity fields effectively enhance or prevent transport and mixing, or steer a scalar field to a desired distribution, is of great interest and fundamental importance to the fluid mechanics community. In this talk, we mainly discuss the problem of optimal mixing of an inhomogeneous distribution of a scalar field via active control of the flow velocity, governed by the Stokes or the Navier-Stokes equations.
Specifically, we consider that the velocity field is steered by a control input which acts tangentially on the boundary of the domain through the Navier slip boundary
conditions. This is motivated by mixing within a cavity or vessel by rotating or moving walls. Our main objective is to design a Navier slip boundary control that optimizes mixing at a given final time. Non-dissipative scalars governed by the transport equation will be of our main focus in this talk. In the absence of molecular diffusion, mixing is purely determined by the flow advection. This essentially leads to a nonlinear control and optimization problem. A rigorous proof of the existence of an optimal controller and the first-order necessary conditions for optimality will be derived. Numerical experiments will be presented to demonstrate our ideas and control designs.
| Tuesday, Mar 23 (17-18, Paris-Madrid-Berlin Time)
|| Bassam Bamieh (University of California Santa Barbara)
|| Fragility in Distributed Systems
|| Certain networked control systems exhibit scaling fragilities in the limit of large system sizes. These fragilities are exhibited as loss of robustness or increased sensitivities to disturbances. These fragilities can be fundamental to the structure of the control problem, and are hard limits on performance once a control architecture is chosen. Some continuum models also exhibit similar fragilities in PDE systems. I will discuss these interrelated issues and show examples from vehicular formations and condensed matter physics. I will close by illustrating yet another fragility in a spatially distributed, active sensor network, namely the mammalian cochlea, where an instability mechanism appears to be related to certain clinical conditions.
| Tuesday, Apr 20 (17-18, Paris-Madrid-Berlin Time) - PhD Session
|| Nicolas Vanspranghe (Univ. Grenoble Alpes, CNRS, Gipsa-lab, France)
|| Saturated boundary stabilization of the wave equation in the Dirichlet boundary condition: asymptotic stability and non-uniform decay rates
|| In this talk, I will discuss some results on nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation in the Dirichlet boundary condition. Initial data is taken in the optimal energy space associated with Dirichlet boundary control, meaning that we deal with (very) weak solutions. The feedback action under consideration is that of the natural linear controller subject to some (monotone) pointwise nonlinearity. Using nonlinear semigroup techniques, we prove that the associated closed-loop system is asymptotically stable. Under additional assumptions on the nonlinearity and the geometry of the problem, we are able to derive polynomial decay rates for strong solutions. Some finite element simulations will illustrate the stability results.
| Rami Katz (Department of Electrical Engineering, Tel Aviv University`)
|| On finite-dimensional observer-based control of parabolic PDEs
|| Finite-dimensional observer-based controller design for PDEs is a challenging problem. In this talk, construction of such controllers via modal decomposition method for linear parabolic 1D PDEs will be presented. We will start with a linear heat equation, where at least one of the control or observation operators is bounded. We will proceed with the case of both operators unbounded, where dynamic extension is helpful. Here the results for the Kuramoto-Sivashinsky and heat equations will be discussed. For both equations we use eigenvalues and eigenfunctions of a Sturm-Liouville operator. The controller dimension is defined by the number of unstable modes N_0, whereas the observer dimension N may be larger than N_0. We suggest a direct Lyapunov approach to the closed-loop system, which results in LMIs whose elements and dimension depend on N. The value of N and the decay rate are obtained from the LMIs. We prove that the LMIs are always feasible for large enough N. Delayed and sampled-data implementations of the controllers will be discussed.
| Tuesday, May 18 (17-18, Paris-Madrid-Berlin Time) - PhD Session
|| Drew Steeves (University of California San Diego, USA)
|| Prescribed-Time Regulation and Estimation of Parabolic Systems
|| From its inception, Lyapunov's fundamental concept of stability does not characterize the convergence rate to an equilibrium; asymptotic stability only necessitates that the desired equilibrium be reached as time approaches infinity. Yet many applications call for regulation within a finite time horizon, where exponential stability may not suffice. In this talk, I will discuss some techniques developed for prescribed-time boundary regulation and estimation of systems containing parabolic PDEs. A key ingredient in the featured work is time-varying PDE backstepping. Some practical considerations will be featured in this talk.
| Ala' Alalabi (University of Waterloo, Canada)
|| Boundary Stabilization of the Modified Generalized Korteweg-de Vries-Burgers Equation
|| This main objective of this talk is two-fold. First, we discuss the linear boundary stabilization problem of the modified generalized Korteweg-de Vries-Burgers (MGKdVB) equation when the spatial variable lies in [0,1]. In this case, the existence and uniqueness of a global solution are proved, and the exponential stability of the MGKdVB equation in the L^2-sense is established. In addition, we propose a linear adaptive boundary control law for the MGKdVB equation. Secondly, we consider the nonlinear non-adaptive and adaptive boundary control problem of the MGKdVB equation. Two nonlinear non-adaptive controllers are given. Furthermore, four different nonlinear adaptive control laws are designed when there is uncertainty in one or all of the equation's parameters. Using Lyapunov theory, we investigate the global exponential stability of the solution in L^2(0,1) for each of the proposed controllers. Finally, numerical simulations for both non-adaptive and adaptive problems are provided to illustrate the theoretical findings. This talk is based on joint works with Nejib Smaoui and Boumediene Chentouf.
| Tuesday, June 8 (17-18, Paris-Madrid-Berlin Time) - Junior Session
|| Shumon Koga (University of California San Diego, USA)
|| Future Perspectives on Control of Parabolic PDEs with Moving Boundaries
|| In this talk, I will present some existing results and future perspectives on the control of parabolic PDEs with a moving boundary governed by an ODE. Such a class of PDE has been originally formulated for modeling a thermal phase change process such as melting and solidification, known as the Stefan problem, arising in numerous real-world phenomena, including polar ice melting and additive manufacturing. First, I will briefly introduce the Stefan problem of the thermal phase change and existing results on control problems. Next, non-thermal models in the class of Stefan systems will be addressed, including chemical reactions in lithium-ion batteries and the biological growth process in neurons. Finally, several open problems of PDEs with moving boundaries will be discussed, from both control-theoretic and application-driven perspectives.
| Hugo Parada (Universite Grenoble Alpes - CNRS, France)
|| Delayed stabilization of the Korteweg-de Vries equation on a Star-shaped network
|| In this work we deal with the exponential stability of the nonlinear Kortewegde Vries (KdV) equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then we state an exponential stabilization result using a Lyapunov function by imposing small initial data and a restriction over the lengths. In this part also, we are able to obtain an explicit expression for the rate of decay. Then we prove the exponential stability of the solutions without restriction on the lengths and for small initial data, this result is based on an observability inequality. After that, we obtain a semi-global stabilization result working directly with the nonlinear system. Next we study the case where it may happen that a control domain with delay is outside of the control domain without delay. In that case, we obtain also a local exponential stabilization result. Finally, we present some numerical simulations in order to illustrate the stabilization.