Showing papers by "Bernard Brogliato published in 2000"

Dissipative Systems Analysis and Control: Theory and Applications

Abstract: Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and passivity-based and adaptive controllers are covered thoroughly). The second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. Some of the changes introduced are: * Complete proofs of the main theorems and lemmas. * The Kalman-Yakubovich-Popov Lemma for non-minimal realizations, singular systems, and discrete-time systems (linear and nonlinear). * Passivity of nonsmooth systems (differential inclusions, variational inequalities, Lagrangian systems with complementarity conditions). * Sections on optimal control and H-infinity theory. * An enlarged bibliography with more than 550 references, and an augmented index with more than 500 entries. * An improved appendix with introductions to viscosity solutions, Riccati equations and some useful matrix algebra.

On the control of complementary-slackness juggling mechanical systems

Abstract: Studies the feedback control of a class of complementary-slackness hybrid mechanical systems. Roughly, the systems we study are composed of an uncontrollable part (the "object") and a controlled one (the "robot"), linked by a unilateral constraint and an impact rule. A systematic and general control design method for this class of systems is proposed. The approach is a nontrivial extension of the one degree-of-freedom (DOF) juggler control design. In addition to the robot control, it is also useful to study some intermediate controllability properties of the object's impact Poincare mapping, which generally takes the form of a nonlinear discrete-time system. The force input mainly consists of a family of dead-beat feedback control laws, introduced via a recursive procedure, and exploiting the underlying discrete-time structure of the system. The main goal of the paper is to highlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases.

Impacts in Mechanical Systems: Analysis and Modelling

Abstract: An Introduction to Moreau's Sweeping Process.- Dynamic Simulation of Rigid Bodies: Modelling of Frictional Contact.- Stability of Periodic Motions with Impacts.- Contact Problems for Elasto-Plastic Impact in Multi-Body Systems.- Impulse Correlation Ratio in Solving Multiple Impact Problems.

Positive Real Systems

Abstract: In the study and control of general dynamical systems the energy stored in the system is an important information. Some autonomous dynamical systems (i.e. with input equal to zero) have the important property that the amount of energy stored in the system remains unchanged or even decreases. This gives rise to the definition of Dissipative systems which is very useful in the synthesis of control systems. Different definitions are introduced to distinguish different classes of systems. Linear systems and nonlinear systems are two important classes of dynamical systems which for simplicity reasons have been usually studied separately in what concerns their dissipative properties. Linear systems whose stored energy remains constant or decreases are called Positive Real (PR) systems or Strictly Positive Real (SPR) respectively while we usually reserve the term dissipative for nonlinear systems in general. We can certainly use the term dissipative for a linear system however the term positive real is only reserved for transfer functions. Furthermore, there exists several important subclasses of linear and nonlinear systems with slightly different properties which are important in the analysis. This will lead us to introduce a series of different definitions of PR and dissipative systems. This chapter deals with Positive Real systems. The next chapter will be devoted to dissipative nonlinear systems.

Dissipative Physical Systems

Abstract: In this chapter we shall present a class of dissipative systems which correspond to models of physical systems and hence embed in their structure the conservation of energy (first principle of thermodynamics) and the interaction with their environment through pairs of conjugated variables with respect to the power. Firstly, we shall recall three different definitions of systems obtained by an energy based modeling: controlled Lagrangian, input-output Hamiltonian systems and port controlled Hamiltonian systems. We shall illustrate and compare these definitions on some very simple examples. Secondly we shall treat a class of systems which gave rise to numerous stabilizing control using passivity theory and corresponds to models of robotic manipulators. In each worked case we show how the main functions associated to a dissipative system (the available storage, the required supply, storage functions) can be computed analytically and related to the energy of the physical system.