Tube-Based Distributed Model Predictive Control of Nonlinear Multi-Agent Systems Based on Additive State Decomposition

For nonlinear leader-following stochastic multi-agent system, a tube-based distributed model predictive control (MPC) algorithm of followers is proposed in this paper to achieve containment control. Considering that nonlinear may greatly increase the complexity of the optimization problems, some scholars pay attention to linearization method, in which the model error may lead bad system performance. In order to compensate the model error between nonlinear system and linear system, additive state decomposition is utilized to separate the original nonlinear system into two parts: primary linear system and secondary nonlinear system. Based on pole assignment, the feedback control algorithm for the secondary nonlinear system is proposed, ensuring primary state convergence. To ensure the satisfaction of system constraints, the tightened constraints are constructed involving the disturbance and linearity error. Based on the constraints, the distributed tube-based MPC optimization problem is established for the primary system. Then in the combined action of the two controllers, all followers are steered to the convex hull of leaders under interference. Finally, the effectiveness of the proposed method is verified for the nonlinear system by numerical simulation.