Global optimal fuzzy tracker design based on local concept approach

Abstract

In this paper, we propose a global optimal fuzzy tracking controller, implemented by fuzzily blending the individual local fuzzy tracking laws, for continuous and discrete-time fuzzy systems with the aim of solving, respectively, the continuous and discrete-time quadratic tracking problems with moving or model-following targets under finite or infinite horizon (time). The differential or recursive Riccati equations, and more, the differential or difference equations in tracing the variation of the target are derived. Moreover, in the case of time-invariant fuzzy tracking systems, we show that the optimal tracking controller can be obtained by just solving algebraic Riccati equations and algebraic matrix equations. Grounding on this, several fascinating characteristics of the resultant closed-loop continuous or discrete time-invariant fuzzy tracking systems can be elicited easily. The stability of both closed-loop fuzzy tracking systems can be ensured by the designed optimal fuzzy tracking controllers. The optimal closed-loop fuzzy tracking systems cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Moreover, the resulting closed-loop fuzzy tracking systems possess infinite gain margin; that is, their stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the performance of the proposed optimal fuzzy tracker design schemes and to demonstrate the proved stability properties.