Approximate optimal solution of the DTHJB equation for a class of nonlinear affine systems with unknown dead-zone constraints

Abstract

In this paper, an optimal control scheme of a class of unknown discrete-time nonlinear systems with dead-zone control constraints is developed using adaptive dynamic programming (ADP). First, the discrete-time Hamilton---Jacobi---Bellman (DTHJB) equation is derived. Then, an improved iterative ADP algorithm is constructed which can solve the DTHJB equation approximately. Combining with Riemann integral, detailed proofs of existence and uniqueness of the solution are also presented. It is emphasized that this algorithm allows the implementation of optimal control without knowing internal system dynamics. Moreover, the approach removes the requirements of precise parameters of the dead-zone. Finally, simulation studies are given to demonstrate the performance of the present approach using neural networks.