Iterative Nonconvex Distributed MPC With Flexible Termination Strategy

Abstract

This article proposes an iterative distributed model predictive control (DMPC) algorithm for multiple dynamically decoupling linear systems subject to both local state and input constraints, as well as coupling constraints that may be nonconvex (e.g., collision avoidance constraints). This issue has not been extensively explored, particularly in the context of allowing flexible termination of inner optimization problem calculations in accordance with the sample time. In this article, we present a framework based on the successive convex approximation for iteratively solving the MPC optimal control problem (OCP) at each time step. The framework has several attractive features. Specifically, 1) it transforms the MPC OCP into a series of strongly convex subproblems that can be effectively handled by distributed systems; 2) it allows termination at any time, with the potential for solutions to converge to a stationary point of the original nonconvex OCP if the sample time permits; and 3) the customized distributed version of the Newton method used in this framework notably accelerates the convergence rate for solving each subproblem, outperforming existing gradient-based methods. Under reasonable assumptions, recursive feasibility of the proposed DMPC algorithm and stability of the resulting closed-loop systems are ensured. The effectiveness of the DMPC algorithm is demonstrated through a multiagent formation control scenario, which includes collision avoidance among agents and obstacles.