Neural and fuzzy dynamic programming for under-actuated systems

This paper aims to integrate the fuzzy control with adaptive dynamic programming (ADP) scheme, to provide an optimized fuzzy control performance, together with faster convergence of ADP for the help of the fuzzy prior knowledge. ADP usually consists of two neural networks, one is the Actor as the controller, the other is the Critic as the performance evaluator. A fuzzy controller applied in many fields can be used instead as the Actor to speed up the learning convergence, because of its simplicity and prior information on fuzzy membership and rules. The parameters of the fuzzy rules are learned by ADP scheme to approach optimal control performance. The feature of fuzzy controller makes the system steady and robust to system states and uncertainties. Simulations on under-actuated systems, a cart-pole plant and a pendubot plant, are implemented. It is verified that the proposed scheme is capable of balancing under-actuated systems and has a wider control zone.