Data-Based Adaptive Dynamic Programming for a Class of Discrete-Time Systems With Multiple Delays

In this paper, a data-based control method based on adaptive dynamic programming (ADP) algorithm is proposed for a class of discrete-time (DT) systems in the case of multiple delays. Data-based ADP method is implemented by virtue of the measured input and output data. The condition of the existence of the corresponding equivalent multiple delays system is derived according to the characteristics of time-delay system. A novel data-based state equation is developed that only composed of input and output data, which is very meaningful in practical applications. By using the data-based ADP method, the output feedback control problem is solved only by measuring the input and output of the system with multiple delays. The convergence proofs of the designed policy iteration and value iteration algorithms are given, respectively. The simulation example is presented to demonstrate the validity of the proposed data-based ADP method.