Distributed MPC for Cooperative Tracking Periodic References of Heterogeneous Systems

This paper investigates a distributed model predictive control (DMPC) for linear heterogeneous systems tracking arbitrary periodic references. The control objective consists of two parts: (i) driving the output of each subsystem consensus; (ii) steering the outputs as close as possible to an exogenous periodic reference. The artificial state reference and control input are considered as decision variables to track unreachable references. The optimal control problem (OCP) is then solved in a distributed manner using Alternating Direction Multiplier Method (ADMM). The proposed method does not need ADMM convergence at each time step, which greatly reduces the computation time. Under several mild assumptions, the feasibility of the OCP and the closed-loop asymptotic stability with respect to an optimal reachable cooperative trajectory are presented. The performance of the approach is demonstrated with some simulation results. <italic>Note to Practitioners</italic>&#x2014;The paper is motivated by the problem of cooperative tracking unreachable references for heterogeneous systems. The generation of the reference signal often ignores the dynamics feature of systems, leading to such reference may not be fully tracked (unreachable reference). However, existing methods either lack optimality or cannot achieve cooperative tracking of unreachable references. Therefore, this study develops a novel DMPC approach to make up for the above lack. In addition, the proposed method greatly reduces the computation time while ensuring optimality, and has a wider initial feasibility. The proposed controller can be extended to cooperative track unreachable constant signal. The proposed method can be used for highly collaborative tasks, such as formation missions, collaborative transportation and spacecraft collaboration. In future research, we will address the problem of cooperative tracking unreachable references for nonlinear heterogeneous systems.