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Model-free optimal consensus control for multi-agent systems using kernel-based ADP method

Adaptive dynamic programming (ADP) is a prevalent way to solve the coupled Hamilton-Jacobi-Bellman (HJB) equations of the optimal consensus control for multi-agent systems (MAS). Neural networks (NNs) are normally used to approximate the value functions in ADP. However, NNs with manually designed features may influence the approximation ability. In this study, kernel-based methods which do not need to set the value function model structure in advance are adopted for value functions approximation. Moreover, to overcome the deficiency that most of the system dynamics are unknown, or the system is too complex to obtain the accurate dynamics. Local action value functions are defined, and kernel-based methods are used to approximate the local action value functions. Thus, an action dependent heuristic dynamic programming (ADHDP) approach using kernel-based local action value functions approximation is developed to achieve the optimal consensus control model-freely. The developed approach uses historical sample data to learn the system dynamics, and avoids the traditional system identification scheme. Simulation results are provided to demonstrate the effectiveness of the presented approach.