Data-based stable value iteration optimal control for unknown discrete-time systems with time delays

Abstract

In this study, a novel data-based stable value iteration (SVI) optimal control scheme is presented in order to tackle with the linear discrete-time (DT) system with multiple time delays. Due to the difficulty in acquiring the knowledge of system dynamics, the optimal control strategies could be computed with only history input and output database by employing an estimator on the basis of adaptive dynamic programming (ADP) technology. By analyzing features of time delay systems, a homologous equivalent notion of delay-free systems is proposed so that the optimal control policy against systems with multiple time delays could be designed indirectly. Moreover, four equivalent conditions are deduced between the two related systems. The convergence of the rising SVI algorithm with discount factor is discussed according to optimal control principles. The proposed SVI algorithm is proved to converge to optimal values with proper discount factor. In the end, two numerical examples are given, and simulation results illustrate that the presented data-based SVI method is effective.