Optimal Consensus Control Design for Multiagent Systems With Multiple Time Delay Using Adaptive Dynamic Programming

In this article, a novel data-based adaptive dynamic programming (ADP) method is presented to solve the optimal consensus tracking control problem for discrete-time (DT) multiagent systems (MASs) with multiple time delays. Necessary and sufficient conditions of the corresponding equivalent time-delay system are provided on the basis of the causal transformations. Benefitting from the construction of tracking error dynamics, the optimal tracking problem can be transformed into settling the Nash-equilibrium in the graphical game, which can be completed by solving the coupled Hamilton-Jacobi (HJ) equations. An error estimator is introduced to construct the tracking error of the MASs only using the input and output (I/O) data. Therefore, the designed data-based ADP algorithm can minimize the cost functions and ensure the consensus of MASs without the knowledge of system dynamics. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Automated summary

This article presents a novel data-based adaptive dynamic programming (ADP) method for solving the optimal consensus tracking control problem for discrete-time multiagent systems (MASs) with multiple time delays. The method utilizes causal transformations to provide necessary and sufficient conditions of the equivalent time-delay system, and introduces an error estimator to construct the tracking error using only input and output data. By transforming the tracking error dynamics, the optimal tracking problem is solved by settling the Nash-equilibrium in a graphical game through solving coupled Hamilton-Jacobi equations. The designed data-based ADP algorithm minimizes cost functions and ensures the consensus of MASs without requiring knowledge of system dynamics.