Robust controller design for fuzzy parametric uncertain systems: an optimal control approach

A new approach of designing a robust controller for fuzzy parametric uncertain systems is proposed. A linear time invariant (LTI) system with fuzzy coefficients is called as fuzzy parametric uncertain system (FPUS). The proposed method envisages conversion of the FPUS into an uncertain (interval) state space controllable canonical form system in terms of its alpha cut. Further, the problem of designing a robust controller is translated into an optimal control problem minimizing a cost function. For matched uncertainty, it is shown that the optimal control problem is a linear quadratic regulator (LQR) problem, which can be solved to obtain a robust controller for FPUS. The numerical examples and simulation results show the effectiveness of the proposed method in terms of robustness of the controller.