Adaptive Tracking Games for Coupled Stochastic Linear Multi-Agent Systems: Stability, Optimality and Robustness
Adaptive control for a multi-agent uncertain dynamical system is studied in this paper. The system studied has the following characteristics: (i) there are many agents in this system and the state of each agent dynamically evolves with time; (ii) for each agent, its state evolves like an ARMAX model with unknown coefficients; (iii) each agent is locally intervened by neighborhood agents with unknown linear reactions; (iv) each agent can only use its history information and local information on its neighborhood agents to design its control law aimed at achieving its own local goal, i.e. tracking a local signal sequence. In this paper, the Astrom-Wittenmark self-tuning regulator, which is a special ease (with known high-frequency gain) of extended least squares (ELS) algorithm, is adopted by each agent to estimate the local unknown parameters (including internal parameters and coupling coefficients) and control the local states based on the "certainty equivalence" principle. For the decentralized Astrom-Wittenmark self-tuning regulator discussed here, its stability and optimality are established rigorously in this paper. Simulation studies demonstrate the effectiveness of the local ELS learning and control algorithm.