Abstract
At present, nonlinear L_1or induced L_inf ）optimal control design problem have not been solved by the conventional control methods for nonlinear discrete-time systems with persistent bounded disturbance. This study introduces a fuzzy control design to treat the nonlinear L_1 optimal control problem from the suboptimal point of view. First, the Takagi and Sugeno fuzzy model is employed to approximate the nonlinear discrete-time system. Next, based on the fuzzy model, the upper bound of norm of the closed loop system can be obtained under some linear inequality constraints. Therefore, the nonlinear optimal control problem is transformed to a suboptimal control problem, i.e. how to minimize the upper bound of the optimum subject to LMI constraints. In this situation, the very different nonlinear L_1 optimal control problem can be easily solved by a LMI-based optimization method. In this work, the approximation errors have been considered to guarantee the robust stability of the closed-loop system. If the state variables are unavailable, a fuzzy observer-based control design is developed by the LMI method from the suboptimal perspective, too. The proposed method can easily extend the optimal control from linear discrete-time system to nonlinear discrete-time system. To efficiently attenuate the peak of output signal due to persistent bounded external disturbance.