Optimal control design of fuzzy systems

Abstract

This thesis presents a novel optimization-based design methodology of the optimal controller for continuous-time Takagi-Sugeno (T-S) fuzzy systems subject to a constraint on control inputs. In order to establish this design methodology, an optimal control problem for general nonlinear dynamic systems is considered. And, an analytic way which can provide the optimal controller for general nonlinear dynamic systems is presented by utilizing the dynamic programming approach and the inverse optimal approach. Specifically, the dynamic programming approach gives the Hamilton-Jacobi-Bellman (H-J-B) equation associated with the optimal control problem for general nonlinear dynamic systems, and the inverse optimal approach is utilized to solve the H-J-B equation analytically. Then, the robustness property of the proposed optimal controller for a class of input uncertainties is investigated by utilizing the passivity approach. Based on the theoretical results presented in this thesis, the design problem of the optimal controller for T-S fuzzy systems subject to a constraint on control inputs is formulated as the semidefinite programming problem (SDP), which comprises of a linear objective and linear matrix inequality constraints. In the optimal controller design problem for T-S fuzzy systems, the SDP is employed to optimize the magnitude of control inputs, by which an optimized-performance of the controller in terms of the control effort can be obtained. The usefulness of the proposed approach is illustrated by considering the three-axis attitude stabilization problem of rigid spacecraft which is described in terms of the quaternion.