This paper considers the energy dispatching optimization of a grid-connected microgrid in a park in the city of Shanghai in a distributed framework, in order to improve its economic and environment-friendly performance. The microgrid is composed of distributed generations (DGs), energy storage systems, and shiftable loads. Some properties of the microgrid make the dispatching problem difficult. For example, the disturbance in renewable energy is unpredictable; the operation of shiftable loads is discrete and the relationship between the generated power and the total operation cost is nonlinear. A novel distributed model predictive control (MPC) is proposed for the power dispatching optimization of the microgrid in this paper, where there is a local MPC for each of the following entities: DGs, storage batteries, and shiftable loads. In this method, the centralized mix-integer programming problem of microgrid energy dispatching is converted into several interacted nonlinear programming problems and integer programming problems, and subsystem-based MPCs coordinate with each other via iteratively minimizing the cost over the entire system. In this way, the realization of plug-and-play property becomes easier and the computational load is reduced. The numerical results show the effectiveness of the proposed method.

Designing a stabilized distributed model predictive control (DMPC) with constraints is an open and important problem for a class of large-scale distributed systems, which are composed by both weakly and strongly coupled subsystems. This paper proposes a design of DMPC network to stabilize this class of large-scale systems. A coupling degree-based clustering method is first designed to classify subsystems into some middle-scale subsystems (M-subsystem) off-line according to the adjacent matrix, so that these M-subsystems are weakly coupled with each other. Then, each M-subsystem is controlled by a virtual model predictive control (MPC), which is realized by several individual controllers with running iterative cooperative DMPC algorithm, since the solution of cooperative DMPC is able to converge to a fixed point without coupling constraints. Each MPC communicates with the corresponding interacted M-subsystems' MPCs once in a control period for exchanging future state evolution estimation. All the subsystem-based MPCs are composed of the proposed peer-to-peer DMPC network. In addition, an additional consistency and stabilization constraints are added to guarantee the recursive feasibility and stability of the overall system. The convergence of the iterative DMPC algorithm for each M-subsystem and the stabilization analysis of the overall system are provided. The simulation results show the efficiency of the proposed method.

This article proposes a distributed model predictive control (DMPC) strategy for a class of large-scale systems composed of several interacting subsystems. When a certain subsystem is required to be removed or inserted, the topology change of the system network can lead to the infeasibility of interacting local controllers due to the existence of the interactions among subsystems. In this article, the interactions among subsystems are presented as state trajectory estimations of interacting subsystems, and the estimations are involved in each local MPC. To deal with the influence resulted from the change of system topology, optimization schemes for removal and plugging-in are designed and employed in the proposed strategy. They optimize related subsystems’ reference trajectories, which are used to approximate the interacting state trajectories here, to reduce the time it takes to drive the system states and reference trajectories to a region. This region ensures that the system topology change can be conducted with all controllers having feasible solutions. The proposed DMPC algorithm has the following characteristics: 1) all the optimization problems in each MPC are solved in a noniterative manner and each controller only communicates with its neighbors and 2) it guarantees the feasibility of all controllers throughout the topology change process and the convergence of the system after the topology change. Simulation results show the effectiveness of the proposed DMPC algorithm. Note to Practitioners —The DMPC algorithm proposed in this article is designed for networked systems where certain subsystems may be removed or inserted. The purpose is to obtain a fast response to this topology change of system. An integrated algorithm is provided for the application of the strategy. First, the parameters of the MPCs are initialized. Then, before the command of a switch in topology is given, local controllers for normal situations provide the real-time inputs. Once the switch of topology is commanded, additional optimization problems are solved in the related subsystems’ controllers to guarantee the feasibility of removal or plugging-in operation. The optimization problems involved in each MPCs can be solved by adopting efficiently quadratic programming solvers supported by MATLAB. Note that although the topology change is commanded, all the subsystems are still operated normally until the topology change is conducted. In general, the strategy introduced in this article can be applied to control a class of large-scale networked systems, where each subsystem-based controller can exchange information with its neighbors.

This paper aims to design a stabilized Adaptive Model Predictive Control (MPC) for nonlinear continuous systems with unknown dynamics at the start time. The proposed method is based on the Lyapunov MPC (LMPC) where the derivative of the Lyapunov function of the closed-loop system is limited to be less than that under an auxiliary Lyapunov controller. Different from the existing LMPC methods, this paper provides an online constraint updating strategy, which gradually reduces the conservation of the constraint. Specifically, the piece-wise linear (PWL) model updated by the Set-Membership (SM) identification method is adopted in the constraint and the auxiliary controller design, which can result in a non-increasing boundary of the model error. Then, a sufficient condition that guarantees the stabilization of the closed-loop system is deduced, which takes the effect of sample-and-hold implementation and the error boundary of the PWL model into account. By this condition, an optimization problem to update the Lyapunov controller for relaxing the constraints of MPC is proposed. We prove that, by the proposed method, the states will eventually converge to a small region around the equilibrium, both this small region and the conservatism of MPC decrease with the increasing of the accuracy of the PWL model. The application of the proposed method to a chemical process demonstrates the effectiveness of the proposed method. Note to Practitioners —The control problem of nonlinear continuous systems with unknown dynamics has attracted the attention of researchers. This article develops an Adaptive MPC for this kind of system, which updates the boundary of uncertainties according to the measurement, and updates the constraints of MPC according to the updated uncertainty boundary. It provides a guaranteed stabilization and continuously relaxed constraint design for MPC where machine learning-based models are employed to predict the future trajectory. In the process of implementation, the method solves two optimization problems: one is to get the parameters of constraints which is based on the PWL model, and the other is used to optimize the future trajectory with the updated constraints. To proceed, the initial boundary of the uncertainty should be given at the initial instant, the initialization of PWL models and constraints can be configured based on it. The proposed method can be used for tracking control of chemical processes, power systems, robots, etc., where the accurate dynamics are not provided in advance and an improved performance is required.