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

This article focuses on the
$\mathcal {L}_{2}-\mathcal {L} _{\infty}/ \mathcal {H}_{\infty}$
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 to acquire a better
$\mathcal {L}_{2}-\mathcal {L}_{\infty}/ \mathcal {H}_{\infty}$
control effect. Different from the traditional method using an 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 the cost function. Finally, the superiority of this online optimization learning policy is confirmed via simulations.