Generalized Receding Horizon Control of Fuzzy Systems Based on Numerical Optimization Algorithm

Abstract

The optimal control of fuzzy systems with constraints is still an open problem. Our focus concerns the optimal control problem of fuzzy systems derived from receding horizon control (RHC) schemes. We consider methods to numerically compute the value function for general fuzzy systems. The numerical method that is developed using the finite difference with sigmoidal transformation is a stable and convergent algorithm for the Hamilton-Jacobi-Bellman (HJB) equation. An optimization procedure is developed to increase the calculation accuracy with less computation time. A parallel-processing method is employed in the optimization procedure. The optimization results are applied to the controller design of general fuzzy dynamic systems. Employing the principle of conventional RHC schemes, RHC-form controllers are designed for some classes of fuzzy dynamic systems. The basic ideas are as follows. First, the value function is calculated by numerical methods. Then, the value function is used as controller-design parameters to redesign RHC controllers for fuzzy systems, which is motivated by the inverse Lyapunov function design method. It is proven that the closed-loop system is asymptotically stable. An engineering implementation of the controller redesign scheme is discussed. Meanwhile, the parallel-processing framework that can improve the closed-loop performance is also introduced.