Bounded robust control design for uncertain nonlinear systems using single-network adaptive dynamic programming

This paper is an effort towards developing an optimal learning algorithm to design the bounded robust controller for uncertain nonlinear systems with control constraints using single-network adaptive dynamic programming (ADP). First, the bounded robust control problem is transformed into an optimal control problem of the nominal system by a modified cost function with nonquadratic utility, which is used not only to account for all possible uncertainties, but also to deal with the control constraints. Then based on single-network ADP, an optimal learning algorithm is proposed for the nominal system by a single critic network to approximate the solution of Hamilton-Jacobi-Bellman (HJB) equation. An additional adjusting term is employed to stabilize the system and relax the requirement for an initial stabilizing control. Besides, uniform ultimate boundedness of the closed-loop system is guaranteed by Lyapunov's direct method during the learning process. Moreover, the equivalence of the approximate optimal solution of optimal control problem and the solution of bounded robust control problem is also shown. Finally, four simulation examples are provided to demonstrate the effectiveness of the proposed approach.