Design and analysis of optimal controller for fuzzy systems with input constraint

In this paper, we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous-time Takagi-Sugeno (TS) fuzzy systems. In order to establish this design method, we consider an optimal and robust control problem for nonlinear dynamic systems. For this problem, we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach. Moreover, we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach. Then, based on the theoretical results presented in this paper, we formulate the design problem of the optimal and robust controller with input constraint for continuous-time TS fuzzy systems as the semidefinite programming problem, and find the controller by solving it. The usefulness of the proposed approach is illustrated by considering the three-axis attitude stabilization problem of rigid spacecraft.