6 - Adaptive nonlinear control: Passivation and small gain techniques

Abstract

The area of adaptive nonlinear control has moved on quickly since the early 1990s. The development of most adaptive nonlinear controller designs was based on Lyapunov methods. This chapter proposes methods to systematically design stabilizing adaptive controllers for new classes of nonlinear systems using passivation and small gain techniques. It is shown that for a class of linearly parameterized nonlinear systems with only unknown parameters, the concept of adaptive passivation can be used to unify and extend most of the known adaptive nonlinear control algorithms based on Lyapunov methods. A novel recursive robust adaptive control method by means of backstepping and small gain techniques is also developed to generate a new class of adaptive nonlinear controllers with robustness to nonlinear unmodeled dynamics.