Robust receding horizon control of uncertain fuzzy systems

The optimal control of uncertain fuzzy systems with constraints is still an open problem. One candidate to deal with this problem is robust receding horizon control (RRHC) schemes, which can be formulated as a differential game. Our focus concerns numerically solving Hamilton-Jacobi-Issac (HJI) equations derived from RRHC schemes for uncertain fuzzy systems. The developed finite difference approximation scheme with sigmoidal transformation is a stable and convergent algorithm for HJI equations. Accelerated procedures with boundary value iteration are developed to increase the calculation accuracy with less time consumption. Then, the state-feedback RRHC controller is designed for some class of uncertain fuzzy systems with constraints. The value function calculated by numerical methods acts as the design parameter. The closed-loop system is proven to be asymptotically stable. An engineering implementation of the controller is discussed.