Distributed Model Predictive Control: An overview of features and research opportunities

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.

The complicated formation flight for multi-unmanned aerial vehicles is a challenge, especially when multi-mission requirements are taken into account. This paper studies the adaptive differential evolution-based distributed model predictive control approach to deal with the multi-unmanned aerial vehicle flight achieving obstacle/collision avoidance and formation keeping simultaneously in the complex environment. Specifically, the distributed model predictive controller is designed to achieve stable flight for each unmanned aerial vehicle as well as taking the state and input saturation into account, where the local optimization problem is solved by the adaptive differential evolution algorithm. Besides, the adaptive adjustment to the prediction horizon for the model predictive controller is introduced, while the asymptotic convergence of the rolling optimization is analyzed as well. Finally, simulation examples are provided to illustrate the validity of the proposed control structure.

This paper utilizes the distributed model predictive control (DMPC) method to investigate the formation control problem of unmanned aerial vehicles (UAVs) in the obstacle environment and establishes cooperative capability evaluation metrics of the swarm. Based on the DMPC approach, the formation cost function is constructed to adjust the relative positions and velocities of UAVs, ensuring the desired formation. Additionally, to address the obstacle avoidance problem in the formation, the obstacle avoidance function is designed to provide safe formation control in the obstacle environment. To evaluate the cooperative capability of UAVs, we design evaluation metrics from multiple dimensions to reflect the swarm’s cooperative capability. Finally, the simulation results show the effectiveness of the formation control method with obstacle avoidance and the applicability of the swarm’s cooperative capability evaluation metrics.

This article investigates the formation composition and keeping problem for multi‐quadrotor systems under time‐varying communication delays. First, a distributed model predictive control (MPC) approach is employed to transform the formation composition and keeping of multi‐quadrotor systems into an online rolling optimization issue, accompanied by the event‐triggered mechanism to reduce solution frequency and communication load. Second, to address the asynchrony and time‐varying communication delays introduced by event‐triggered distributed MPC, a set of constraints is designed to restrict deviations between the current predictive state and previously broadcasted states. Consequently, based on the previously predicted states of neighbors, the cooperation of the multi‐quadrotor systems is achieved under asynchronous communication and time‐varying delays. This approach guarantees robust asymptotic stability and satisfactory formation performance for multi‐quadrotor systems under various delay scenarios. Finally, the numerical and software‐in‐the‐loop simulations validate the effectiveness of the proposed algorithm of multi‐quadrotors under communication delays.

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

Fil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional; Argentina

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 this paper, we study the distributed model predictive control (MPC) of polytopic uncertain systems with quantised communication and packet dropouts. The model of the whole plant is divided into a certain number of incomplete subsystems. Due to the nature of the distributed control structure, there is generally a lack of information about the state of the overall system. Each subsystem shares its information with neighbour subsystems via reliable connection. Distributed MPC controllers are designed for each subsystem by solving the linear matrix inequalities optimisation problem. The distributed state feedback laws are quantised and transmitted via communication network. An iterative algorithm is presented to make coordination among distributed state feedback laws. The communication is assumed to be affected by random packet dropouts in a representation of Bernoulli distributed white sequences with known conditional probabilities. A case study is carried out to demonstrate the effectiveness of the proposed distributed MPC technique.

Combined environmental and economic dispatch of smart grids using distributed model predictive control

This paper investigates intersection control of multiple vehicles using a Model Predictive Control (MPC) framework. Vehicles follow pre-defined paths across the intersection and adjust their velocities to ensure collision-free passage while maximizing an objective. We choose a non-cooperative Distributed Model Predictive Control (DMPC) approach, where priorities need to be assigned to vehicles. The algorithm we present sets these priorities automatically by evaluating the vehicles’ time to react to stop before entering the intersection. We demonstrate our method in simulations of multiple vehicles and continuous traffic. It produces near-optimal velocity profiles and reduces the computation time in comparison to centralized MPC while avoiding vehicle collisions and deadlocks.

This work focuses on a class of nonlinear control problems that arise when new control systems which may use networked sensors and/or actuators are added to already operating control loops to improve closed‐loop performance. In this case, it is desirable to design the pre‐existing control system and the new control system in a way such that they coordinate their actions. To address this control problem, a distributed model predictive control method is introduced where both the pre‐existing control system and the new control system are designed via Lyapunov‐based model predictive control. Working with general nonlinear models of chemical processes and assuming that there exists a Lyapunov‐based controller that stabilizes the nominal closed‐loop system using only the pre‐existing control loops, two separate Lyapunov‐based model predictive controllers are designed that coordinate their actions in an efficient fashion. Specifically, the proposed distributed model predictive control design preserves the stability properties of the Lyapunov‐based controller, improves the closed‐loop performance, and allows handling input constraints. In addition, the proposed distributed control design requires reduced communication between the two distributed controllers since it requires that these controllers communicate only once at each sampling time and is computationally more efficient compared to the corresponding centralized model predictive control design. The theoretical results are illustrated using a chemical process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Water networks are large-scale systems, consisting of many interacting components. They are currently typically operated by local decentralized controllers which receive setpoints from human operators. We discuss how communication among the local controllers can be included and in particular propose the use of distributed model predictive control for enabling the local controllers to determine setpoints autonomously using communication and coordination. We consider the control of a particular class of water networks, viz. irrigation canals. A simulation study on a 7-reach irrigation canal illustrates the potential of the proposed approach.

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on‐line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

An event-triggered distributed model predictive control (DMPC) approach for a type of dynamically decoupled, independently constrained systems with a coupled performance objective, is presented. The approach employs, for each agent, a compatibility constraint (in the spirit of Dunbar and Murray) in the optimization problem. An event-triggering condition, based-on the overall stability condition of the system, is developed. If the triggering condition for an agent is satisfied, then the agent solves its optimization problem; otherwise, then the agent retain feasibility and stability by simply adopting the tail of its previous solutions. A simulation example is provided to illustrate the effectiveness of the provided approach.

A distributed model predictive controller (MPC) shows its higher efficacy than a centralized MPC scheme, especially when the number of controlled agents increases. In the smart grid, to realize load regulation using the demand side management idea, we present a distributed MPC scheme for controlling the aggregated power output of thermostatically controller appliances (TCAs) to provide this service. Minimum ON/OFF time constraints, which are converted from logic conditions into inequalities, are modelled inherently in the optimization problem. A simulation using realistic data reveals the feasibility and efficacy of the proposed distributed MPC scheme.