Robust Predictive Bipartite Bumpless Control for Markov Jump MASs Under Switching Topology: Application to Rotary-Wing Air Vehicles

Abstract

This article addresses the issue of bipartite consensus for Markov jump multi-agent systems subjected to bounded disturbance and input constraints under mode-dependent switching topology. To surmount the challenge of handling disturbance, hard constraints and bump suppression, which are not considered and difficult to deal with in existing literature on solutions to algebraic Riccati equation, a novel bipartite robust predictive bumpless control algorithm is proposed with integrating $H_\infty$ performance. To be specific, the offline designing process of bipartite controller parameters is firstly performed by investigating terminal constraint set and robust invariant set. In this sense, $H_\infty$ type cost function and consensus error state bump cost are constructed for achieving disturbance attenuation and suppressing bump in error state, respectively. This further avoids possible counterproductive results caused by setting constraints on bump with a small gain. Next, based on the optimization prediction dynamics, perturbation state of controller is optimized online for each agent, which efficiently reduces the computational burden compared with conventional online and efficient model predictive control. Furthermore, the recursive feasibility of the proposed method and stochastic stability of error dynamics are theoretically guaranteed. Finally, an application to rotary-wing air vehicles is utilized to verify the potential of theoretic results.