A Novel Mixed Control Approach for Fuzzy Systems via Membership Functions Online Learning Policy

This article focuses on the L2-L/H optimization control issue for a family of nonlinear plants by Takagi-Sugeno (T-S) fuzzy approach with actuator failure. First, considering unmeasurable system states, sufficient criteria for devising fuzzy imperfect premise matching dynamic output feedback controller to maintain asymptotic stability while guaranteeing a mixed performance for T-S fuzzy systems are provided. Therewith, in the light of feasible areas of dynamic output feedback controller membership functions (MFs), a new MFs online learning policy using gradient descent algorithm is proposed to learn the real-time values of MFs so as to acquire a better L2-L/H control effect. Different from the traditional method using imperfect premise matching scheme, under the proposed optimization algorithm, the trajectory of mixed performance index is lowered effectively. Afterward, a sufficient criterion is presented for assuring the convergence of the error of cost function. Lastly, the superiority of this online optimization learning policy is confirmed via simulations.