LQR performance for multi-agent systems: Benefits of introducing delayed inter-agent measurements

This paper deals with the design of an optimal controller for a set of identical multi-agent systems. The problem under consideration is to examine if there is any benefit to adding to the classical local optimal control law, obtained from solving a Riccati equation, a term which depends on delayed relative information with respect to neighbouring agents. The resulting control law has a local linear feedback term (from solving the Riccati equation) and a consensus-like term which depends on a delayed version of the relative states with respect to its neighbours. The resulting closed loop system at a network level is linear and involves delayed states. A Lyapunov-Krasovskii approach is used to synthesize the gain associated with the consensus term to provide sub-optimal LQR-like performance at a network level. Situations are demonstrated when this approach provides better performance (in terms of the LQR cost) than when a traditional decentralised approach is adopted.