Native Space Embedding Control Methods
摘要
Leveraging the material presented in the previous chapters, this chapter presents robust and adaptive control techniques for nonlinear plants affected by multiple forms of uncertainties. These results are obtained by extending classical and advanced nonlinear control techniques to account for uncertainties modeled as unknown elements of some operator-valued native space. We begin by designing robust control Lyapunov functions for nonlinear dynamical systems, and, successively, we design backstepping control systems under the assumption that functional uncertainties lie in some RKHS. A large portion of this chapter is dedicated to the design of model reference adaptive control systems (MRAC) that are robust to parametric, matched, unmatched, and functional uncertainties. To this goal, we generalize the dead-zone modification of MRAC, the \(\sigma \) -modification of MRAC, and the use of convex projection operators. Finally, we extend variable structure methods, such as the error bounding control architecture and the adaptive error bounding architecture, to the native embedding setting. The same numerical example is worked out multiple times and the underlying codes are presented in an Appendix to this book.