Passivity-Based Control

Abstract

This chapter is devoted to investigate how the dissipativity properties of the various systems examined in the foregoing chapter can be used to design stable and robust feedback controllers (in continuous and discrete time). We start with a classical result of mechanics, which actually is the basis of Lyapunov stability and Lyapunov functions theory. The interest of this result is that its proof hinges on important stability analysis tools, and allows one to make a clear connection between Lyapunov stability and dissipativity theory. The next section is a brief survey on passivity-based control methods, a topic that has been the object of numerous publications. Then, we go on with the Lagrange–Dirichlet Theorem, state-feedback and position-feedback control for rigid-joint–rigid-link systems, set-valued robust control for rigid-joint–rigid-link fully actuated Lagrangian systems, state and output feedback for flexible-joint–rigid-link manipulators, with and without actuators dynamics, and constrained Lagrangian systems. Regulation and trajectory tracking problems, smooth and nonsmooth dynamical systems, are treated. The chapter ends with a presentation of state observers design for a class of differential inclusions represented by set-valued Lur’e systems.