Control of interval systems using 2DOF configuration

This contribution is focused on continuous-time control of interval systems by means of two-degree-of-freedom (2DOF) configuration. The controller design utilizes algebraic techniques in the ring of proper and (Hurwitz-)stable rational functions (RPS). Robust stability of resulting 2DOF loops is analyzed graphically, namely with the assistance of the value set concept and the zero exclusion condition. In the presented illustrative example, a third order interval plant is robustly stabilized. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

Implementation of Control Design Methods into Matlab Environment

The main aim of this chapter is to present two simple and freely downloadable Matlab programs which allow user-friendly work for two selected specific control design issues by means of Graphical User Interface (GUI).P(ED2.1.00/03.0089

Contributions à l’estimation robuste et à la commande prédictive robuste par méthodes ensemblistes

Dans le contexte de la commande prédictive robuste, ces travaux s’articulent autour de l’élaboration d’approches ensemblistes pour la prise en compte des incertitudes. Trois axes principaux sont proposés.Un premier axe s’intéresse à l’élaboration de lois de commande prédictives robustifiées vis-à-vis de plusieurs types d’incertitudes (par exemple des incertitudes structurées formulées à l’aide d’ensembles polytopiques), plus spécifiquement via la paramétrisation de Youla-Kučera. Un logiciel a été à cette occasion développé afin de simplifier l’implantation de ces structures de commande. Plusieurs applications dans des domaines très variés (robot médical, hélicoptère, système de gestion de la production, centrale électrique au charbon) illustrent les résultats obtenus.Une deuxième direction est liée aux méthodes ensemblistes pour l’estimation d’état des systèmes soumis à des incertitudes par intervalles et à des perturbations bornées. Une technique d’estimation ensembliste zonotopique fondée sur la minimisation du P-rayon d’un zonotope est tout d’abord proposée. Une deuxième étape vise ensuite à l’élaboration d’une loi de commande prédictive robuste reprenant explicitement l’estimation ensembliste.Une troisième partie est dédiée à la commande prédictive des systèmes multi-agents sous contraintes dynamiques. Plusieurs aspects sont examinés, faisant appel également aux techniques ensemblistes : la génération de trajectoire, l’allocation des tâches, le suivi de trajectoire par la formation, en respectant des contraintes d’évitement de collision entre les agents et avec présence éventuelle d’obstacles. Dans ce contexte, plusieurs approches de commande prédictive centralisée, distribuée et décentralisée ont été développées. Une application à des drones est présentée afin de valider certains de ces concepts

Control Engineering

Control means a speci?c action to reach the desired behavior of a system. In the control of industrial processes generally technological processes, are considered, but control is highly required to keep any physical, chemical, biological, communication, economic, or social process functioning in a desired manner

Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

L'abstract è presente nell'allegato / the abstract is in the attachmen

Model Order Reduction Based on Semidefinite Programming

The main topic of this PhD thesis is complexity reduction of linear time-invariant models. The complexity in such systems is measured by the number of differential equations forming the dynamical system. This number is called the order of the system. Order reduction is typically used as a tool to model complex systems, the simulation of which takes considerable time and/or has overwhelming memory requirements. Any model reflects an approximation of a real world system. Therefore, it is reasonable to sacrifice some model accuracy in order to obtain a simpler representation. Once a low-order model is obtained, the simulation becomes computationally cheaper, which saves time and resources. A low-order model still has to be "similar" to the full order one in some sense. There are many ways of measuring "similarity" and, typically, such a measure is chosen depending on the application. Three different settings of model order reduction were investigated in the thesis. The first one is H infinity model order reduction, i.e., the distance between two models is measured by the H infinity norm. Although, the problem has been tackled by many researchers, all the optimal solutions are yet to be found. However, there are a large number of methods, which solve suboptimal problems and deliver accurate approximations. Recently, research community has devoted more attention to large-scale systems and computationally scalable extensions of existing model reduction techniques. The algorithm developed in the thesis is based on the frequency response samples matching. For a large class of systems the computation of the frequency response samples can be done very efficiently. Therefore, the developed algorithm is relatively computationally cheap. The proposed algorithm can be seen as a computationally scalable extension to the well-known Hankel model reduction, which is known to deliver very accurate solutions. One of the reasons for such an assessment is that the relaxation employed in the proposed algorithm is tightly related to the one used in Hankel model reduction. Numerical simulations also show that the accuracy of the method is comparable to the Hankel model reduction one. The second part of the thesis is devoted to parameterized model order reduction. A parameterized model is essentially a family of models which depend on certain design parameters. The model reduction goal in this setting is to approximate the whole family of models for all values of parameters. The main motivation for such a model reduction setting is design of a model with an appropriate set of parameters. In order to make a good choice of parameters, the models need to be simulated for a large set of parameters. After inspecting the simulation results a model can be picked with suitable frequency or step responses. Parameterized model reduction significantly simplifies this procedure. The proposed algorithm for parameterized model reduction is a straightforward extension of the one described above. The proposed algorithm is applicable to linear parameter-varying systems modeling as well. Finally, the third topic is modeling interconnections of systems. In this thesis an interconnection is a collection of systems (or subsystems) connected in a typical block-diagram. In order to avoid confusion, throughout the thesis the entire model is called a supersystem, as opposed to subsystems, which a supersystem consists of. One of the specific cases of structured model reduction is controller reduction. In this problem there are two subsystems: the plant and the controller. Two directions of model reduction of interconnected systems are considered: model reduction in the nu-gap metric and structured model reduction. To some extent, using the nu-gap metric makes it possible to model subsystems without considering the supersystem at all. This property can be exploited for extremely large supersystems for which some forms of analysis (evaluating stability, computing step response, etc.) are intractable. However, a more systematic way of modeling is structured model reduction. There, the objective is to approximate certain subsystems in such a way that crucial characteristics of the given supersystem, such as stability, structure of interconnections, frequency response, are preserved. In structured model reduction all subsystems are taken into account, not only the approximated ones. In order to address structured model reduction, the supersystem is represented in a coprime factor form, where its structure also appears in coprime factors. Using this representation the problem is reduced to H infinity model reduction, which is addressed by the presented framework. All the presented methods are validated on academic or known benchmark problems. Since all the methods are based on semidefinite programming, adding new constraints is a matter of formulating a constraint as a semidefinite one. A number of extensions are presented, which illustrate the power of the approach. Properties of the methods are discussed throughout the thesis while some remaining problems conclude the manuscript

Co-Design of Time-Invariant Dynamical Systems

Design of a physical system and its controller has significant ramifications on the overall system performance. The traditional approach of first optimizing the physical design and then the controller may lead to sub-optimal solutions. This is due to the interdependence between the physical design and control parameters through the dynamic equations. Recognition of this fact paved the way for investigation into the ``Co-Design" research theme wherein the overall system's physical design and control are simultaneously optimized. Co-design involves simultaneous optimization of the design and the control variables with respect to certain structural property as constraint. The structural property may be in the form of stability, observability or controllability leading to different types of co-design problems. Co-design optimization problems are non-convex optimization problems involving bilinear matrix inequality (BMI) constraints and are NP-hard in general. In this dissertation, four interrelated research tasks in the area of co-design are undertaken. In the first research task, a theoretical and computational framework is developed to co-design a class of linear time invariant (LTI) dynamical systems. A novel solution procedure based on an iterative combination of generalized Benders decomposition and gradient projection method is developed guaranteeing convergence to a solution in a finite number of iterations which is within a tolerance bound from the nearest local/global minimum. In the second research task, the sparse and structured static feedback design problem is modeled as a co-design problem. A formulation based on the alternating direction method of multipliers is used to solve the sparse feedback design problem which has given robustness as a constraint. In the third research task, the optimal actuator placement problem is formulated as a co-design problem. The actuator positions are modeled as $0/1-$binary design variables and result in a mixed integer nonlinear programming (MINLP) problem. In the fourth research task, a heuristic procedure to place sensors and design observer is developed for a class of Lipschitz nonlinear systems. The procedure is based on the relation between Lipschitz constant, sensor locations and observer gain. The vast and diverse application potential of co-design across all engineering branches is the primary motivation and relevance of the research work carried out in this dissertation