Optimal Containment Control for Stochastic Multiagent Systems via Simplified ADP Under Secure Communication

This article investigates the optimal containment control (OCC) problem of a class of nonlinear stochastic multiagent systems (MASs) under secure communication. A novel OCC strategy is designed, ensuring that all followers converge to the convex hull spanned by the leaders while maintaining secure information exchange and minimizing cost by the predefined performance function. To achieve this, an encryption and decryption mechanism is employed in the information exchange among agents, ensuring secure communication and preserving data integrity. Meanwhile, to solve the stochastic version of Hamilton-Jacobi-Bellman (HJB) equation arising in stochastic factor, a simplified adaptive dynamic programming (ADP) framework is introduced under the conditional expectation. Specifically, a single critic network weights tuning rule is developed based on the experience replay technique (ERT). The use of ERT relaxes the traditional persistence of excitation requirement. Theoretical analysis guarantees the uniform ultimate boundedness of the closed-loop system. The simulation results confirm the effectiveness of the designed OCC strategy.