An adaptive tracking controller design for non-linear singularly perturbed systems using fuzzy singularly perturbed model
Luyu Li, Fuchun Sun · IMA Journal of Mathematical Control and Information · 2009
For a class of non-linear singularly perturbed systems with unknown dynamic and external disturbance, an adaptive tracking controller using fuzzy singularly perturbed model is developed. First, a series of dynamic Takagi-Sugeno fuzzy singularly perturbed subsystems are built to approximate a non-linear singularly perturbed system and a stable reference model with the same fuzzy premise is chosen to design both expected trajectory and dynamic performance. Then, a kind of controller including adaptive feedback term is developed to make the states of the closed-loop system follow those of the reference model. The linear feedback gain of the controller can be solved by the linear matrix inequality approach. The adaptive sliding term is used to compensate the uncertainty and alleviate the disturbance. Lyapunov constitute techniques can be used to prove the stability of the closed-loop systems. Finally, the simulations results illustrate the effectiveness of this approach.