Mismatch-Index-Driven Coordinated Flexible-Step Terminal-Free DMPC with Adaptive Prediction Horizon for Asynchronous Perturbed Multiagent Systems Under Symmetric Communication Topology

Abstract

This paper proposes a mismatch-index-driven coordinated flexible-step terminal-free distributed model predictive control (DMPC) scheme with an adaptive prediction horizon for asynchronous multi-agent systems (MASs) subject to bounded disturbances. The proposed approach explicitly exploits the inherent symmetry of the undirected communication topology among the agents, which ensures reciprocal information exchange, balanced cooperative interactions, and facilitates the rigorous analysis of consensus under asynchrony. By extending the generalized discrete-time control Lyapunov function (g-dclf) framework to the perturbed setting, we introduce a robust g-dclf together with a robust average decrease constraint that explicitly accounts for the worst-case effect of disturbances. A coordinated self-triggering mechanism, built upon the cost prediction mismatch index and the flexible-step execution strategy, is developed to simultaneously determine the inter-execution times and the number of control steps to be applied in each iteration. In addition, an adaptive shrinking prediction horizon strategy is incorporated to further reduce the computational complexity of the local optimization control problems (OCPs) as the agents approach consensus. The resulting robust flexible-step terminal-free DMPC (RFSTDMPC) algorithm is fully distributed, handles asynchronous communication, and operates without any stability-related terminal constraint. Recursive feasibility of each local OCP and input-to-state stability (ISS) of the overall closed-loop MAS are rigorously established under the symmetric network structure. Simulation results on the consensus problem of three perturbed nonholonomic vehicles demonstrate the effectiveness of the proposed scheme in achieving practical full-state stabilization while significantly alleviating the online computational burden.