Multi-agent model predictive control for transport phenomena processes

Throughout the last decades, control systems theory has thrived, promoting new areas of development, especially for chemical and biological process engineering. Production processes are becoming more and more complex and researchers, academics and industry professionals dedicate more time in order to keep up-to-date with the increasing complexity and nonlinearity. Developing control architectures and incorporating novel control techniques as a way to overcome optimization problems is the main focus for all people involved. Nonlinear Model Predictive Control (NMPC) has been one of the main responses from academia for the exponential growth of process complexity and fast growing scale. Prediction algorithms are the response to manage closed-loop stability and optimize results. Adaptation mechanisms are nowadays seen as a natural extension of prediction methodologies in order to tackle uncertainty in distributed parameter systems (DPS), governed by partial differential equations (PDE). Parameters observers and Lyapunov adaptation laws are also tools for the systems in study. Stability and stabilization conditions, being implicitly or explicitly incorporated in the NMPC formulation, by means of pointwise min-norm techniques, are also being used and combined as a way to improve control performance, robustness and reduce computational effort or maintain it low, without degrading control action. With the above assumptions, centralized (or single agent) or decentralized and distributed Model Predictive Control (MPC) architectures (also called multi-agent) have been applied to a series of nonlinear distributed parameters systems with transport phenomena, such as bioreactors, water delivery canals and heat exchangers to show the importance and success of these control techniques

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Multivariable boundary PI control and regulation of a fluid flow system

International audienceThe paper is concerned with the control of a fluid flow system gov-erned by nonlinear hyperbolic partial differential equations. The control and the output observation are located on the boundary. We study local stability of spatially heterogeneous equilibrium states by using Lyapunov approach. We prove that the linearized system is exponentially stable around each subcritical equilibrium state. A systematic design of proportional and integral controllers is proposed for the system based on the linearized model. Robust stabilization of the closed-loop system is proved by using a spectrum method

Commande des Systèmes Hyperboliques décrits par des Equations aux Dérivées Partielles

This work is part, from a theoretical point of view, of the control of systems describedby partial differential equations (PDE). The other aspect is the application of those resultsto real process’s applications.Great developments have been done on modelization technics, identification and thecontrol for systems in finite dimension since a long time. Those technics have reached amaturity level, and are applied to numerous applications. Nevertheless, the developmentof advanced technologies have for consequence to increase the size of the controlledmodels, rising which is the symbol of the passage from finite dimension system to infinitedimension system.In recent decades, a real work on the development of infinite dimension tools hasemerged. This work originally dedicated to rather academic cases are being extendedtoday to practical cases.My work has found its place at this level : since 10 years I am interested in stabilityproblems and in the development of controls for systems described by hyperbolic PDE.For this I use mathematical structures such as semigroups, "natural" invariants like theRiemann invariants, energy structures like the Hamiltonian functional, or by the extensionof existing results in finite dimension to the infinite dimension such for the LMI (LinearMatrices Inequalities) to LOI (Linear Operator Inequalities).All these theoretical results have no interest if they are not applied, at least that’sthe goal I would like to maintain. To this end, all results have been developed on realprocesses : irrigation channels, navigable waterways, extrusion process, and more tocome. The issue of water described by the shallow water equations is a central examplein my work, but this is simply because I have access to benchmarks allowing me tovalidate the developed approaches.All of my works has been published internationally, but also broadcasted on lessonsfrom doctoral schools, in training of masters students and PhD students.Ce travail s’inscrit, d’un point de vue théorique, dans le domaine du contrôle dessystèmes décrits par des équations aux dérivées partielles (EDP). L’autre versant de cetravail est l’application concrète à des procédés.Un grand effort de développement des techniques de modélisation, d’identification etde commande a été réalisé pour les systèmes de dimension finie depuis des années.Ces techniques ont atteint un certain degré de maturité et sont utilisées dans de nombreusesapplications. Néanmoins, les développements des technologies de pointes ontentrainé une hausse considérable de la taille des modèles de commande, hausse quiest le reflet dans beaucoup de cas, du passage de la commande d’un vrai système dedimension finie vers un système de dimension infinie.Depuis quelques décennies, un réel travail de développement des outils en dimensioninfinie a donc vu le jour. Ces travaux initialement dédiés à des cas plutôt académiquesse voient aujourd’hui étendus à des cas pratiques.Mes travaux se posent à ce niveau : depuis 10 ans je m’intéresse aux problèmes destabilité et au développement de commandes de systèmes décrits par des EDP hyperboliques.Pour cela, j’utilise des structures mathématiques telles que les semigroupes,des invariants "naturels" comme ceux de Riemann, des structures énergétiques commeles Hamiltoniens, ou par l’extension de résultats existants en dimension finie à la dimensioninfinie comme pour les LMI (linear matrices inequalities) en LOI (linear operatorinequalities).Tous ces résultats théoriques n’ont d’interêt que s’ils sont appliqués, du moins c’estl’objectif que je souhaite maintenir. A cette fin, tous les résultats ont été développés surde réels process : les canaux d’irrigation, les voies naviguables, l’extrusion, et d’autres àvenir. La problématique de l’eau décrite par les équations de Saint-Venant est certe unexemple central dans mon travail, mais cela est dû simplement au fait que j’ai accès àdes bancs d’essais me permettant de valider les approches développées.L’ensemble de mes travaux a été publié au niveau international, mais aussi diffusé enlocal lors d’enseignements auprès d’écoles doctorales, lors d’encadrement de mastersrecherche et de thésards

Ensembles of Hyperbolic PDEs: Stabilization by Backstepping

For the quite extensively developed PDE backstepping methodology for coupled linear hyperbolic PDEs, we provide a generalization from finite collections of such PDEs, whose states at each location in space are vector-valued, to previously unstudied infinite (continuum) ensembles of such hyperbolic PDEs, whose states are function-valued. The motivation for studying such systems comes from traffic applications (where driver and vehicle characteristics are continuously parametrized), fluid and structural applications, and future applications in population dynamics, including epidemiology. Our design is of an exponentially stabilizing scalar-valued control law for a PDE system in two independent dimensions, one spatial dimension and one ensemble dimension. In the process of generalizing PDE backstepping from finite to infinite collections of PDE systems, we generalize the results for PDE backstepping kernels to the continuously parametrized Goursat-form PDEs that govern such continuously parametrized kernels. The theory is illustrated with a simulation example, which is selected so that the kernels are explicitly solvable, to lend clarity and interpretability to the simulation results.Comment: 16 pages, 4 figures, to be publishe

Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks

Sliding Mode Observers for Distributed Parameter Systems: Theory and Applications

Many processes in nature and industry can be described by partial differential equations. PDEs employ quantities such as density, temperature, velocity, etc. and their partial derivatives to model these phenomena. However, in the case of distributed parameter systems, it is not always possible to have access to the states of the systems due to technical difficulties such as lack of sensors. Therefore, there is the need for state observers to estimate the states of the system only having the output of the system available. In this research, the theory of sliding mode and variable structure systems are employed in order to design observers for different classes of distributed parameter systems such as advection equation, Burgers’ equation, Euler equations, etc. Some contributions of this research are: suggesting the state transformation which allows the arbitrary design of sliding manifold in sliding mode observer, developing some formulae for observer gain, discussing the shock wave situation and its properties and solutions, designing sliding mode observer and anomaly detection system for a system of advection equations

Flat systems, equivalence and trajectory generation

3rd cycleIntroduction : Control systems are ubiquitous in modern technology. The use of feedback control can be found in systems ranging from simple thermostats that regulate the temperature of a room, to digital engine controllers that govern the operation of engines in cars, ships, and planes, to flight control systems for high performance aircraft. The rapid advances in sensing, computation, and actuation technologies is continuing to drive this trend and the role of control theory in advanced (and even not so advanced) systems is increasing..

Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks