13. ROBUSTNESS AGAINST UNMODELED EFFECTS AND SYSTEM STABILITY

Abstract

Various engineering systems are described by complex dynamic models that include nonlinearities, time-varying parameters and high-order terms. Because of the difficulties connected with the structural identification and parameter estimation of such complex models, simplified and linearized models are commonly used for the controller design. The theory of robust adaptive control considers the problems of system synthesis based on simplified models taking into account various unmodeled effects, such as nonlinearities, time-varying parameters and dynamics of high order (Ortega and Tang, 1989; Koust et al., 1992; Lozano-Leal, 1989; Praly, 1983). Ortega and Tang (1989) gave a survey of the design of various robust adaptive controllers. Robust adaptive control can be based on different theoretical concepts. In the paper of Koust et al. (1992), the system uncertainty is described and bounded by the H^∞-norm. Lozano-Leal (1989) proposed another approach, where the uncertainty is represented by bounds that depend on the system state. A similar approach was considered by Praly (1983), where the uncertainty bounds depend dynamically on the system state.