An optimal control regulator for nonlinear discrete-time systems with input delays

An optimal regulator is presented for a nonlinear discrete-time system with input delay and a quadratic criterion. First, the original problem is reduced to the nonlinear-quadratic regulator design for a system without delays by an extended Artstein model reduction approach. Then, An iterative process is proposed to find a solution sequence of the nonlinear two-point boundary value (TPBV) problem of the new transformed system, which is obtained from the necessary optimality conditions. Finally, by introducing an adjoint vector to compensate the separated nonlinearities in the system and using a successive approximation approach, we obtain an suboptimal solution. Simulation are conducted to demonstrate the performance of the regulator obtained.