Pinning consensus control for switched multi-agent systems: A switched adaptive dynamic programming method

Abstract

Stability is fundamental to ensure the operation of control system, but optimality is the ultimate goal to achieve the maximum performance. This paper investigates an event-triggered pinning optimal consensus control for switched multi-agent system (SMAS) via a switched adaptive dynamic programming (ADP) method. The technical contribution mainly lies in two aspects. On the one hand, in order to optimize the control performance and ensure the consensus, the switched local value function (SLVF) and the minimum-error switching law are constructed. Based on SLVF, an algorithm of switched ADP policy iteration is proposed, and its convergence and optimality are proved. On the other hand, considering that it is impractical to install a controller for each agent in reality, a pinning strategy is developed to guide the setting of the ADP controller, which can reduce the waste of control resources. A new condition is constructed to determine the minimum number of controlled vertices of the SMAS. Lastly, a numerical example is given to verify the effectiveness of the proposed method.