Finite-horizon optimal control for affine nonlinear systems with dead-zone control input

For affine nonlinear systems with dead-zone control input and discount factor in performance index function, a finite-horizon adaptive dynamic programming (ADP) algorithm is proposed in this paper. To deal with dead-zone nonlinearity, a new utility function is defined, and the corresponding discrete-time Hamilton-Jacobi-Bellman (DTHJB) equation is derived. Then, finite-horizon ADP algorithm is developed to obtain the optimal control with convergence analysis. A dead-zone network is introduced for implementing the algorithm, which is different from implementing the traditional ADP algorithm. A simulation example is given to demonstrate the effectiveness of the presented algorithm.