Improving the Global Performance of a Fuzzy Gain Scheduler by Supervision

Abstract

The fundamental issue in gain scheduling on a desired reference trajectory is the question of guaranteed stability of the overall gain scheduled closed loop system. Since the gain scheduled design is based on linear time invariant approximation of the open loop system and since this system is actually 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 space into a finite number of fuzzy regions. The nonlinear system is Lyapunov-linearized at the center of each fuzzy region. Then linear controllers intended to locally stabilize the linearized system, and consequently the original nonlinear system, at the center of a fuzzy region are designed. With that, gain scheduling control of the original nonlinear system can be designed to cope with any (unknown in advance) slowly time varying desired trajectory. In this paper we show how the stability and robustness analysis of the gain scheduled closed loop sysem in terms of sliding mode control techniques can be used for the design of a supervisory system which avoids unstable behavior outside the region in which local stability is guaranteed.