Tube-based model predictive full containment control for stochastic multi-agent systems

Abstract

In this paper, we develop a tube-based distributed model predictive full containment control (MPFCC) algorithm for leader-following systems with bounded disturbance under dynamic leaders. The proposed algorithm employs knowledge regarding the constraints on states and control inputs to extrapolate their admissible values in the entire predictive horizon. The Kalman filter is utilized to estimate the system states, introducing estimated error. The error and disturbance are both involved in the time-varying tubes to construct the tightened constraints. For each follower, by penalizing the control input difference from its neighbors' control inputs and the deviation of the states from the convex hull produced by its neighbors' states, the containment problem is optimized only by utilizing the local nominal state and control sequences. To overcome the problem that followers may fall slightly out of the convex hull of the leaders caused by disturbance, a full containment control algorithm is introduced by designing a tightened convex hull. Then the recursive feasibility and robust stability are proved through the design of proper distributed terminal controllers and constraints. Finally, the effectiveness and robustness of the proposed method are illustrated for both linear and nonlinear multi-agent systems by simulation examples.