Cooperative Distributed Model Predictive Control Research Articles

Robust output feedback distributed model predictive control of networked systems with communication delays in the presence of disturbance

In this work, an output feedback cooperative distributed model predictive control is developed for a class of networked systems composed of interacting subsystems interconnected through their states, in which it handles bounded disturbances and time varying communication delays. A distributed buffer based prediction strategy is used to compensate bounded delays and predict those states, which are coupled between subsystems that their actual values may not available due to delays. In the design of robust distributed model predictive control, distributed moving horizon estimation is employed so that convergence and boundedness of the estimation error are ensured. Furthermore, robust exponential stability of the closed loop system is established. The effectiveness of the proposed method is illustrated using two interconnected continuous stirred tank reactors.

A Distributed Voltage Control Strategy for Multi-Microgrid Active Distribution Networks Considering Economy and Response Speed

This paper presents a novel distributed voltage control strategy to maintain the voltage of active distribution networks containing multiple microgrids. Local voltage regulation characteristics, such as power reserve, adjustment cost, and regulating speed, are identified first. According to a neighbors’ voltage regulation characteristics, the microgrid coordinates neighborhood resources and asks them for coordination as soon as voltage problems occur. Microgrids schedule local resources based on a cooperative distributed model predictive control algorithm scheme with neighbor-to-neighbor communication. Tests are performed in an active distribution network with three microgrids. The numerical studies have shown that the proposed strategy mitigates the voltage fluctuation rapidly and efficiently with minimum operating cost.

State estimation‐based distributed model predictive control of large‐scale networked systems with communication delays

In this paper, a cooperative distributed model predictive control is proposed for a class of large-scale systems composed of discrete-time linear subsystems which are coupled via states. The subsystems communicate with each other through a network with communication delays and they do not have direct access to their local states. In the proposed scheme, each subsystem is associated with a local MPC unit, a local predictor and a local observer. The local model predictive controllers exchange predicted input sequences via a delayed communication network. The local predictor uses the explicit model of the subsystems and predicts those states which are coupled between subsystems and their actual values are not available due to delays. The states of each subsystem are estimated from local measurements by designing a local observer. Convergence analysis of the proposed estimation methodology is performed and it is shown that the observer and predictor have exponential convergence. Furthermore, the exponential stability of the closed-loop system is existed. Finally, the theoretical results are verified by a simulation study.

A New Cooperative Distributed MPC Method Based on Reduction and Classification

To decrease the overlarge calculation induced by the centralized processing, a new cooperative distributed Model predictive control (MPC) method is proposed for large-scale systems with coupled dynamics. Reduction and classification are investigated by defining the influence degree to reduce the whole system and then to classify the reduced system into several subsystem groups. These groups are mutually decoupled, while there is relativity between these subsystems comprised in the same group. Centralized/cooperative and distributed MPC algorithms for each group are implemented to ensure the feasibility and the stability of the whole system. Meanwhile, for practical applications, the finite times interactive control strategy between different groups is adopted to compensate information loss brought by the reduced subsystem and realize the global cooperative distributed MPC. This algorithm significantly decreases the computational load, has better control performance. Simulations are given to illustrate the effectiveness of these developed algorithms.

Distributed synthesis and stability of cooperative distributed model predictive control for linear systems

This paper presents a new formulation and synthesis approach for stabilizing cooperative distributed model predictive control (MPC) for networks of linear systems, which are coupled in their dynamics. The controller is defined by a network-wide constrained optimal control problem, which is solved online by distributed optimization. The main challenge is the definition of a global MPC problem, which both defines a stabilizing control law and is amenable to distributed optimization, i.e., can be split into a number of appropriately coupled subproblems. For such a combination of stability and structure, we propose the use of a separable terminal cost function, combined with novel time-varying local terminal sets. For synthesis, we introduce a method that allows for constructing these components in a completely distributed way, without central coordination. The paper covers the nominal case in detail and discusses the extension of the methodology to reference tracking. Closed-loop functionality of the controller is illustrated by a numerical example, which highlights the effectiveness of the proposed controller and its time-varying local terminal sets.

Distributed Satisficing MPC With Guarantee of Stability

This technical note develops conditions for the closed-loop stability of a new class of cooperative distributed model predictive control, called satisficing, whereby the relative importance of each controller changes dynamically depending on the prevailing conditions instead of being adjusted a priori. In the satisficing approach, the less satisfied controller will gain more importance. The main properties of the proposed approach are illustrated with an unstable dynamic system composed of three subsystems.

Parsimonious Cooperative Distributed MPC for Tracking Piece-Wise Constant Setpoints

Distributed Model Predictive Control refers to a class of predictive control architectures in which a number of local controllers manipulate a subset of inputs to regulate a subset of outputs composing the overall system. These controllers may cooperate to find an optimal control sequence that minimizes a global cost function, as in the case of Cooperative Distributed Model Predictive Control (CD-MPC). In this paper two linear CD-MPC algorithms for tracking are proposed. The aim of these controllers is to drive the outputs of the overall system to any admissible piece-wise constant set-point, satisfying input and state constraints. However, in the available literature this result is achieved by using a set of centralized variables that keep track of the global state of the system. In contrast, we develop novel CD-MPC approaches for tracking that rely on “as local as possible” information instead of the plant-wide information flow. These new control strategies reduce the required communication overhead, local computational demands, and are more scalable than CD-MPC algorithms available in the literature. We illustrate the main characteristics and benefits of the proposed approaches by means of a multiple evaporator process example.

Networked Cooperative Distributed Model Predictive Control Based on State Observer

Although distributed model predictive control has caused significant attention and received many good results, the results are mostly under the assumption that the system states can be observed. However, the states are difficult to be observed in practice. In this paper, a novel distributed model predictive control is proposed based on state observer for a kind of linear discrete-time systems where states are not measured. Firstly, an output feedback control law is designed based on Lyapunov function and state observer. And the stability domain is described. Furthermore, the stability domain as a terminal constraint is added into the constraint conditions of the algorithm to make systems stable outside the stability domain. The simulation results show the effectiveness of the proposed method.

Cooperative distributed model predictive control of multiple coupled linear systems

This study presents a cooperative distributed model predictive control (CDMPC) algorithm for a team of linear subsystems with the coupled cost and coupled constraints. At each sampling time, all the subsystems are permitted to synchronously optimise. An improved compatibility constraint, which plays an important to ensure the stability, is constructed to ensure that the actual state trajectory of each subsystem does not deviate too much from its assumed one. Moreover, a positive invariant terminal set and an associated terminal cost (a local control-Lyapunov function) are designed in the distributed manner. By applying the proposed algorithm, the recursive feasibility with respect to both local and coupled constraints and the closed-loop stability of the whole system are ensured. In final, the numerical results of the comparisons between the CDMPC algorithm and the centralised model predictive control are given to show the effectiveness of the proposed algorithm.

Cooperative distributed stochastic MPC for systems with state estimation and coupled probabilistic constraints

A cooperative distributed stochastic model predictive control (CDSMPC) algorithm is given for multiple dynamically decoupled subsystems with additive stochastic disturbances and coupled probabilistic constraints, for which states are not measurable. Cooperation between subsystems is promoted by a scheme in which a local subsystem designs hypothetical plans for others in some cooperating set, and considers the weighted costs of these subsystems in its objective. To achieve satisfaction of coupled probabilistic constraints in a distributed way, only one subsystem is permitted to optimize at each time step. In addition, by using a lifting technique and the probabilistic information on additive disturbances, measurement noise and the state estimation error, a set of deterministic constraints is constructed for the predictions of nominal models. Recursive feasibility with respect to both local and coupled probabilistic constraints is guaranteed and stability for any choice of update sequence and any structure of cooperation is ensured. Numerical examples illustrate the efficacy of the proposed algorithm.

Distributed model predictive control

Distributed model predictive control

Cooperative Distributed Model Predictive Control via Linear Programming★A Divide and Conquer Approach

Motivated by the recent progress in centralized Model Predictive Control (MPC) design using a linear program (LP) and distributed MPC with quadratic program (QP) formulations, this paper discusses the design of LP-based cooperative distributed MPC for large scale linear systems with coupled dynamics and decoupled input constraints. As such, we examine the applicability of the Divide and Conquer approach to QP-based cooperative distributed MPC, recently proposed by the authors, to the LP-based case. It is shown that within the Divide and Conquer framework, an upbound of the original LP-based cooperative cost function (instead of itself), can be optimized for computing local inputs, resulting in suboptimal policies. However, advantages of doing so include the independency of the computation of local inputs and a large amount of communication burden reduction, as guaranteed by theoretical analysis and illustrated through numerical simulation. We also present closed-loop stability analysis and point out some questions worth further investigation.

Cooperative distributed model predictive control for wind farms

SUMMARYThis paper focuses on cooperative distributed model predictive control (MPC) of wind farms, where the farms respond to active power control commands issued by the transmission system operator. A distributed MPC scheme is proposed, which aims at satisfying the requirements imposed by the grid code while minimizing the farm‐wide mechanical structure fatigue. The distributed MPC control law is defined by a global finite‐horizon optimal control problem, which is solved at every time step by distributed optimization. The computational approach is completely distributed, that is, every turbine evaluates its own globally optimal input by considering local measurements and communicating to neighboring turbines only. Two MPC versions are compared, in the first of which the farm‐wide power output constraint is implemented as a hard constraint, whereas in the second, it is implemented as a soft constraint. As for distributed optimization methods, the alternating direction method of multipliers as well as a dual decomposition scheme based on fast gradient updates are compared. The performance of the proposed distributed MPC controller, as well as the performance of the distributed optimization methods used for its operation, are compared in the simulation on four exemplary scenarios. The results of the simulations imply that the use of cooperative distributed MPC in wind farms is viable both from a performance and from a computational viewpoint. Copyright © 2014 John Wiley & Sons, Ltd.

Set-point tracking using distributed MPC

We consider the output tracking of a set-point using cooperative distributed model predictive control. We propose a framework to avoid the loss of feasibility, guarantee stability, constraint satisfaction as well as convergence to admissible set-points. To enable a distributed implementation of the model predictive control law we utilize a cyclic varying horizon length. A simulation example illustrates the approach and its applicability for interconnected systems.

Distributed model predictive control with asynchronous controller evaluations

AbstractIn this work, we focus on the reduction of network communication burden of cooperative distributed model predictive control (DMPC) of a class of nonlinear processes. Specifically, we propose a cooperative DMPC design in which the evaluations of the distributed controllers are triggered by the difference between the subsystem state measurements and the estimates of them. The individual model predictive controllers in this DMPC are designed via Lyapunov techniques. Under the assumption that state measurements of the subsystems are available, sufficient conditions for the closed‐loop stability are derived. The proposed DMPC is applied to a reactor–separator chemical process example and is compared with a cooperative DMPC in which distributed controllers are evaluated every sampling time extensively. The results demonstrate the applicability and effectiveness of the proposed approach.

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013

Networked Cooperative Distributed Model Predictive Control for Dynamic Coupling Systems

For the control of a class of large-scale systems, which consists of many individual subsystems, the distributed contort framework is more suitable because of its good flexibility and error tolerant, despite the fact that its performance is not as good as that of centralized control. How to improve the performance of the entire system and, at the same time,maintain the flexibility and error tolerance characterises under the distributed framework is an important problem. In this paper, a novel distributed model predictive control(DMPC) is proposed, which enlarges the coordinate degree of DMPC through adding a quasi-function of the impact of control input to its downstream subsystems to the performance index of each subsystem-based model predictive control(MPC). Then, the performance of the entire system is improved with unchanged network connectivity. In addition, a design method with this coordination strategy and inputs constraints is provided, which guarantees the recursive feasiblity of the designed DMPC and asymptotic stablility of the closed-loop system.

Cooperative Distributed MPC using the Alternating Direction Multiplier Method

We consider cooperative distributed model predictive control of a linear, time-invariant, discrete-time plant, which consists of coupled subsystems. The cooperating controllers minimize a quadratic cost criterion subject to input and state constraints. We outline two approaches for such distributed controllers using the alternating direction multiplier method, which allows to obtain convergence guarantees. We outline suitable stability criterions and illustrate the applicability and performance of the proposed methods by a simple example.

Cooperative distributed model predictive control for nonlinear systems

Abstract In this paper, a distributed controller is presented that can stabilize nonlinear systems. A novel nonlinear nonconvex optimizer is proposed that improves the objective function and is feasible at every iterate. The optimization uses gradient projection and converges to stationary points. The proposed optimization does not require a coordination layer, and hence the controller is truly distributed. Asymptotic stability is established for the controlled system, and an illustrative example is presented.

Cooperative distributed model predictive control

In this paper we propose a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems satisfying a stabilizability condition. The control strategy has the following features: hard input constraints are satisfied; terminating the iteration of the distributed controllers prior to convergence retains closed-loop stability; in the limit of iterating to convergence, the control feedback is plantwide Pareto optimal and equivalent to the centralized control solution; no coordination layer is employed. We provide guidance in how to partition the subsystems within the plant. We first establish exponential stability of suboptimal model predictive control and show that the proposed cooperative control strategy is in this class. We also establish that under perturbation from a stable state estimator, the origin remains exponentially stable. For plants with sparsely coupled input constraints, we provide an extension in which the decision variable space of each suboptimization is augmented to achieve Pareto optimality. We conclude with a simple example showing the performance advantage of cooperative control compared to noncooperative and decentralized control strategies.