Partitioned Based Cooperative Distributed Model Predictive Control for Large-Scale Nonlinear Systems

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems’ cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system.

Due to cooperative distributed model predictive control scheme is widely applied in large scale networks of systems, so asymptotic stability is a very important index for measuring the performance of cooperative distributed model predictive control. Based on the obvious inequality from classical Lyapunov stability condition, we derive a set of linear matrix inequalities to replace the common inequalities by using Schur complement and S-procedure. Furthermore when combining local state and input constraint sets, a set of more complex linear matrix inequalities is used to guarantee the asymptotically stable for cooperative distributed model predictive control.

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. Note to Practitioners —The proposed method is designed for the systems, which are composed of both strong and weak coupling subsystems and are controlled in a distributed structure. The aim of this method is to design a distributed model predictive control (MPC) network for the operational optimization of entire system. The designed control structure and the distributed MPC algorithm with the proposed method could guarantee the recursive feasibility and asymptotic stability of the entire system. To apply this method, the first step is to obtain the models of each subsystem. Then, design the distributed MPC network structure according to the proposed cluster algorithm, which determines the set of subsystems that each virtue MPC controls. Next step is to configure the network information exchanging among these subsystems and construct the optimization problem of each subsystem. Finally, use the existing quadratically constrained quadratic program solvers to calculate the optimal control laws and apply these optimal control laws to the corresponding subsystems. This method can be used in large-scale chemical processes, air conditioner systems for multizone buildings, distributed energy generation systems, and so on.

Distributed Model Predictive Control with Asymmetric Adaptive Terminal Sets for the Regulation of Large-scale Systems

This paper concerns a distributed model predictive control (DMPC) strategy in which each controller views the signals from other subsystems as disturbance inputs in its local model. The DMPC controllers exchange predictions on the bounds of their state trajectories and incorporate this information into their local DMPC problems. They also impose their own predicted state bounds as constraints in subsequent DMPC iterations to guarantee their subsystem satisfies the bounds broadcast to the other controllers. Each controller solves a local min-max problem on each iteration to optimize performance with respect to worst-case disturbances. Parameterized state feedback is introduced into the DMPC formulation to obtain less conservative solutions and predictions. The paper presents sufficient conditions for feasibility and stability. The approach is illustrated with an example.

In order to reduce the heavy communication burden of cooperative distributed model predictive control (DMPC), A DMPC algorithm based on event-trigger is proposed to balancing the control performance and communication burden through optimizing the interconnection structure of subsystems. An event-trigger using the system Lyapunov function is constructed to avoid solving the introduced MINLP optimization directly, the optimal interconnection structure will be updated only when the event-trigger is triggered. The feasibility of the proposed algorithm in system performance and communication burden decrease is validated by the load frequency control (LFC) problem simulation of interconnected power system.

In this article, we propose a chance-constrained cooperative distributed model predictive control scheme for reference tracking. We consider dynamically coupled linear time-invariant systems that are subject to local and coupling chance constraints. The proposed controller is based on the distributed alternating direction method of multipliers and is able to steer the system to any admissible setpoint while ensuring recursive feasibility under inexact dual optimization and unbounded additive disturbances. Under a central convex unimodality assumption, the chance constraints are guaranteed to hold in closed loop. This article closes with two numerical examples. The first one is of an academic nature in order to highlight the chance constraint satisfaction, convergence, and numerical properties of the proposed algorithm. The second one is a practical scenario of a benchmark process.

A tube-based distributed model predictive control (DMPC) scheme is proposed for dynamically coupled linear systems. The control scheme is designed to guarantee local performance even when neighboring controllers are not complying with the requirements of the algorithm (e.g., they are malicious or faulty). The resulting conservativeness is minimized, for controllers aim to minimize their state and input constraint sets to reduce mutual disturbances. Also, sufficient conditions for feasibility and exponential stability are given. Finally, these ideas are illustrated and assessed with respect to other robust DMPC via a simulated example.

This paper presents a distributed model predictive control(DMPC) strategy to achieve cooperative tasks like consensus and synchronization of linear systems with coupled constraints. Based on the error of state between each subsystem and the center of its cooperative set, a novel DMPC algorithm is designed with its robust feasibility guaranteed by permitting only one subsystem to optimize at each time instant, while renew other subsystems' plans. Illustrative examples are finally conducted to verify the effectiveness of the DMPC strategy.

SummaryIn this paper, a distributed model predictive control is proposed to control Lipschitz nonlinear systems. The cooperative distributed scheme is considered where a global infinite horizon objective function is optimized for each subsystem, exploiting the state and input information of other subsystems. Thus, each control law is obtained separately as a state feedback of all system's states by solving a set of linear matrix inequalities. Due to convexity of the design, convergence properties at each iteration are established. Additionally, the proposed algorithm is modified to optimize only one control input at a time, which leads to a further reduction in the computation load. Finally, two application cases are studied to show the effectiveness of the proposed method.

Using aggregated heterogeneous thermostatically controlled loads (TCLs) to provide ancillary services in a smart grid is a promising technique. This paper proposes an improved population model with lockout time considered to describe the aggregate dynamics. Based on that, a distributed model predictive control (DMPC) scheme is investigated to control a population of TCLs for the regulation service. Full derivations of the system model and the DMPC scheme are provided. A flexibility penalty is developed and added to the objective function to preserve the regulation flexibility. Simulation results, tested by real data, reveal the feasibility and effectiveness of the proposed method.

In this paper, a novel distributed Kalman filter (KF) algorithm along with a distributed model predictive control (MPC) scheme for large-scale multi-rate systems is proposed. The decomposed multi-rate system consists of smaller subsystems with linear dynamics that are coupled via states. These subsystems are multi-rate systems in the sense that either output measurements or input updates are not available at certain sampling times. Such systems can arise, e.g., when the number of sensors is smaller than the number of variables to be controlled, or when measurements of outputs cannot be completed simultaneously because of practical limitations. The multi-rate nature gives rise to lack of information, which will cause uncertainty in the system's performance. To circumvent this problem, we propose a distributed KF-based MPC scheme, in which multiple control and estimation agents each determine actions for their own parts of the system. Via communication, the agents can in a cooperative way take one another's actions into account. The main task of the proposed distributed KF is to compensate for the information loss due to the multi-rate nature of the systems by providing optimal estimation of the missing information. A demanding two-area power network example is used to demonstrate the effectiveness of the proposed method.

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Review for "Hierarchical smart energy management strategy based on cooperative distributed economic model predictive control for <scp>multi‐microgrids</scp> systems"

Review for "Hierarchical smart energy management strategy based on cooperative distributed economic model predictive control for <scp>multi‐microgrids</scp> systems"