Cooperative Distributed Model Predictive Control Research Articles

Cooperative distributed MPC via decentralized real-time optimization: Implementation results for robot formations

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion with nominal convergence guarantees. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

Cooperative distributed model predictive control for robot in-hand manipulation

PurposeThis study aims to process multi-agent system with kinds of limitations and constraints, and consider the robot in-hand manipulation as a problem of coordination and cooperation of multi-fingered hand.Design/methodology/approachA cooperative distributed model predictive control (MPC) algorithm is proposed to perform robot in-hand manipulation.FindingsA cooperative distributed MPC approach is formulated for robot in-hand manipulation problem, which enables address complex limitation and constraint conditions in object motion planning, and realizes tracking trajectory of the object more than tracking position of the object.Originality/valueThis method to implement the moving object task uses the kinematic parameters without the knowledge of dynamic properties of the object. The cooperative distributed MPC scheme is designed to guarantee the movement of the object to a desired position and trajectory at algorithmic level.

Synchronization tracking control of networked multi-axis motion systems: A cooperative distributed model predictive control approach

Synchronization tracking control is an essential technique in networked multi-axis motion systems (NMAMSs). However, the uncertainties induced by network, such as delay and packet disordering, have great influence on control performance of the motion systems. To improve the influence of the uncertainties induced by network on synchronization tracking control performance in NMAMSs, a cooperative distributed model predictive control (CDMPC) strategy for NMAMSs is proposed. Firstly, the synchronization tracking control of the NMAMS is designed in a networked control framework. By introducing the synchronization error into performance index as a coupling term, a local controller adopting a CDMPC strategy is designed for each subsystem. Then, a Nash optimization iteration strategy is presented to deal with the CDMPC optimization problem, and the convergence and stability of the system are also analyzed. Finally, experiments are carried out to demonstrate the practicability and effectiveness of the proposed control strategy.

Observer‐based distributed model predictive control of complex systems with state coupling constraints

In this paper, the cooperative distributed model predictive control (DMPC) problem of a class of complex systems consisting of several subsystems is studied. The states of these subsystems are coupled with each other, and thus bring challenges for the model predictive control algorithm. Moreover, though the subsystems can communicate with each other, they only can access to the output information of their neighboring subsystems. In this case, Luenberger observers are used to estimate the unknown states and a distributed prediction strategy is established for the studied system. Then, the optimal control of the closed-loop system is realized by designing distributed model predictive controller on the basis of the estimated states. The terminal constraints are introduced in the proposed DMPC algorithm to ensure the iterative feasibility and also the stability of the closed-loop. Finally, the effectiveness of the proposed method is verified by a numerical simulation.

An improved iterative solution for cooperative distributed MPC

This note proposes an improved iterative solution of the cooperative distributed model predictive control for large-scale linear systems with interconnected dynamics. In particular, for the purpose of improving the convergence rate, the iteration error is integrated into the iteration process, based on which an algorithm is proposed to optimize the gain matrix of the iteration error. The effectiveness of the proposed approach is verified through the numerical simulation.

Distributed Model Predictive Coordinated Control for Combined Heat and Power Load of an Integrated Energy System

Due to the strong coupling and multiple constraints of combined heat and power (CHP) generation in an integrated energy system (IES), the model predictive control (MPC) is widely adopted as the lower layer coordination controller. However, with the upgrade of capacity and the expansion of scale, centralized MPC (CMPC) is no longer capable of dealing with heavy-data, high dimensional IES optimization problem. To address this concern, distributed MPC (DMPC) is applied to coordinate the energy supply of CHP-IES. In view of the characteristics of CHP-IES, DMPC should be endowed with the capability of offset-free tracking and disturbance rejection. Hence, the disturbance augmentation method and the modification of objective function have been applied to facilitate each DMPC controller with the required abilities. Through simulation comparison with CMPC on the same theoretical model, the performance of modified cooperative DMPC (CDMPC) is on par with CMPC, while the computational burden is drastically relieved.

Stochastic Distributed Predictive Tracking Control Under Inexact Minimization

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.

Distributed model predictive control for nonlinear large-scale systems based on reduced-order cooperative optimisation

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.

Cooperative optimization-based distributed model predictive control for constrained nonlinear large-scale systems with stability and feasibility guarantees

This paper proposes a cooperative distributed model predictive control (DMPC) to control the constrained interconnected nonlinear large-scale systems. The main contribution of this approach is its proposed novel cooperative optimization that improves the global cost function of any subsystem. Each subsystem calculates its optimal control by solving the corresponding global cost function. For each subsystem, the global cost function is defined based on a combination of cost functions of all subsystems. If the sampling time is selected appropriately, then the feasibility of the proposed approach will be guaranteed. Furthermore, the sufficient conditions for stability and consequently, for the convergence of the whole system states towards the neighborhood of the origin’s positive region are provided. The effectiveness and performance of the proposed approach are demonstrated via applying it to a nonlinear quadruple-tank system for both minimum-phase and nonminimum-phase models.

Robust Data Predictive Control Framework for Smart Multi-Microgrid Energy Dispatch Considering Electricity Market Uncertainty

With the emerging technologies for Energy Intent (EI) and data-driven applications, the conventional power grid network is undergoing a radical modernization. An efficient energy management and electricity price forecasting remains a challenging task. In this paper, a new Robust Data Predictive Control framework for Energy Management System (RDPC-EMS) is developed to overcome the uncertainty of the electricity retail price market and minimize the total operating costs for the multi-microgrids (MMG) system. The proposed framework solves the economic energy dispatch based on an accurate Electricity Price Forecasting (EPF) by an Outlier-Robust Extreme Learning Machine (OR-ELM) algorithm and a two layers cooperative Distributed Model Predictive Control (DMPC). The First level provides an optimal energy scheduling between the Distribution System Operator (DSO) and cooperative microgrids systems to minimize the operating cost based on the forecasted electricity price. In contrast, second level maintains the supply-demand balance by applying the optimal energy scheduling from the first layer through an adjustment of the distributed energy resources (DER). The electricity retail price prediction is assessed using real dataset from the Iso New England electricity market. The OR-ELM regression method shows a significant forecasting performance in terms of error metrics. For instance, the mean absolute error in the training stage 2.05% for OR-ELM with a comparison of 4.17% and 6.29% for Support Vector Regression (SVR), and Artificial Neural Network (ANN) models respectively. Finally, simulation results demonstrate the efficiency RDPC-EMS for daily operating cost reduction, with decrease of 15% for MG 1 and 16% for MG 2.

Hierarchical smart energy management strategy based on cooperative distributed economic model predictive control for multi‐microgrids systems

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

Cooperative distributed model predictive control based on topological hierarchy decomposition

In this paper, a cooperative distributed model predictive control (DMPC) algorithm based on topological hierarchy decomposition is proposed. Utilizing the connection topology information of the distributed system, we decompose subsystems into a hierarchy structure model through interpretative structural modeling. Subsystems with strong coupling are grouped into the same layer, and weak coupling exists between subsystems in different layers. Then, we propose an improved cooperative DMPC algorithm, in which the optimal input trajectories of subsystems in each layer are evaluated and propagated in a hierarchical order. Instead of all-to-all communication, only intra-layer communication is required at each iteration of DMPC optimization, which can significantly lessen the communication burden without losing much performance. Furthermore, the feasibility and stability of the proposed algorithm are proven in detail. Finally, the effectiveness and merits of the proposed method are demonstrated by applying it to a reheating furnace system and a six-area power system.

Event‐triggered distributed model predictive control with optimal network topology

SummaryIn this paper, we consider a novel iterative DMPC (distributed model predictive control) scheme for linear discrete‐time systems which are connected by network. Every system is dynamically coupled to neighbors. The proposed method can reduce the communication load without degrading performance compared to cooperative DMPC by sensitivity and information topology analysis. The proposed algorithms are applied in a four‐water‐tanks numerical example, and the simulation results show the effectiveness of the proposed algorithms.

Fast cooperative distributed model predictive control based on parametric sensitivity

This paper deals with computational delay in distributed nonlinear model predictive control. A fast, cooperative distributed model predictive control algorithm is proposed based on parametric sensitivity. The implementation strategy is divided into two different stages. In the background stage, the future state is estimated one step forward with the current state and input. The local MPC controllers perform distributed optimization based on the predicted state and iterate to obtain the nominal optimal solutions. In the online stage, all the controllers correct their nominal optimal inputs through parametric sensitivity. Specifically, each controller formulates its local sensitivity equation based on the state estimation error. In order to solve these linear equations in a distributed way, Jacobi iterative method is applied. The overall algorithm can provide fast control action. A case study is provided to show the promising performance of the proposed method.

LMI‐based cooperative distributed model predictive control for Lipschitz nonlinear systems

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.

Enhancing cooperative distributed model predictive control for the water distribution networks pressure optimization

In water distribution networks (WDNs), the supply pressure to users should be homogeneous and close to the lower bound so as to reduce leakages and energy consumption while meeting users’ water demand. The large-scale features and incomplete structure information of modern WDNs increase the difficulty in modeling and pressure optimization. In this paper, an enhancing cooperative distributed model predictive control (EC-DMPC) strategy is proposed to solve this problem with enhanced operating performance. Firstly, an efficient modeling method and a partitioning method based on operation data are proposed to decompose the WDNs and construct the subsystem models. These methods are based on k-Shape clustering and canonical correlation analysis with considering the mechanism of WDNs. In order to increase the flexibility of coordination while guaranteeing the global optimization performance, a neighbourhood optimization coordination strategy is adopted, where each subsystem considers the performance of itself and that of strongly affected subsystems. Moreover, a robust invariant set and a robust invariant set control law are utilized to handle the disturbance caused by the ignored weak couplings. Part of Shanghai’s WDNs is used as the study case to demonstrate the application of the proposed methods. A comparative experiment study is developed. Results have shown the efficiency of the proposed methods. By the coordination of the EC-DMPC strategy, when the water demand of users changes, the users’ pressure can be maintained homogeneous, and the average pressure decreases, which is beneficial in the reduction of leakages and energy consumption. The distributed strategy could also improve the flexibility and scalability for large-scale WDNs.

A Cooperative Distributed Model Predictive Control Approach to Supply Chain Management

Effective supply chain management is a crucial competency for modern enterprises, but the issue has not been systemically addressed. To this end, we develop a distributed model predictive control (DMPC) approach with minimal information exchange and communication to handle supply chain operations and management. Therein, each decision maker relies on an agent with local information and they are collaborating to minimize a global cost function that measures the control performance of the entire network. The information flow topology is utilized to sequentially solve the DMPC optimization problem. The control sequence of downstream nodes is predicted with information transmitted to the upstream nodes. The stability of the proposed DMPC scheme is provably guaranteed. Finally, a numerical example is presented to verify the effectiveness of the proposed scheme.

Stability analysis in cooperative distributed model predictive control

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.

Stability analysis in cooperative distributed model predictive control

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.

Coupling Degree Clustering-Based Distributed Model Predictive Control Network Design

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.