Improving the global performance of a fuzzy gain-scheduler by supervision

The fundamental issue in gain scheduling along a desired reference trajecto ry is the question of guaranteed stability of the overall gain-scheduled cl osed-loop system. Since the gain-scheduled design is based on linear-time-i nvariant approximation of the open-loop system, and since this system is ac tually nonlinear, the design guarantees only local stability. This requires a further restriction, namely that the desired reference trajectory should vary slowly. The design of a fuzzy gain scheduler requires a conventional model of the nonlinear system under control and a partition of the state sp ace into a finite number of fuzzy regions. The nonlinear system is Lyapunov -linearized at the center of each fuzzy region. Then linear controllers int ended to locally stabilize the linearized system, and consequently the orig inal nonlinear system, at the center of a fuzzy region are designed. In tha t way, gain-scheduling control of the original nonlinear system can be desi gned to cope with any (unknown in advance) slowly time-varying desired traj ectory. This paper shows how the stability and robustness analysis of the g ain-scheduled closed-loop system in terms of sliding-mode control technique s can be used for the design of a supervisory system which avoids unstable behavior outside the region in which local stability is guaranteed. (C) 199 9 Elsevier Science Ltd. All rights reserved.