Distributed model predictive control over network information exchange for large-scale systems

A class of large scale systems, which is naturally divided into many smaller interacting subsystems, are usually controlled by a distributed or decentralized control framework. In this paper, a novel distributed model predictive control (MPC) is proposed for improving the performance of entire system. In which each subsystem is controlled by a local MPC and these controllers exchange a reduced set of information with each other by network. The optimization index of each local MPC considers not only the performance of the corresponding subsystem but also that of its neighbours. The proposed architecture guarantees satisfactory performance under strong interactions among subsystems. A stability analysis is presented for the unconstrained distributed MPC and the provided stability results can be employed for tuning the controller. Experiment of the application to accelerated cooling process in a test rig is provided for validating the efficiency of the proposed method.     

通讯信息约束下具有全局稳定性的分布式系统预测控制

本文针对一类由状态相互耦合的子系统组成的分布式系统, 提出了一种可以处理输入约束的保证稳定性的非 迭代协调分布式预测控制方法(distributed model predictive control, DMPC). 该方法中, 每个控制器在求解控制率时只与 其它控制器通信一次来满足系统对通信负荷限制; 同时, 通过优化全局性能指标来提高优化性能. 另外, 该方法在优化 问题中加入了一致性约束来限制关联子系统的估计状态与当前时刻更新的状态之间的偏差, 进而保证各子系统优化问 题初始可行时, 后续时刻相继可行. 在此基础上, 通过加入终端约束来保证闭环系统渐进稳定. 该方法能够在使用较少 的通信和计算负荷情况下, 提高系统优化性能. 即使对于强耦合系统同样能够保证优化问题的递推可行性和闭环系统的 渐进稳定性. 仿真结果验证了本文所提出方法的有效性.     

提高分布式多预测控制器协调及稳定性的鲁棒区域控制

大型复杂化工程过程控制中,常规的集中式控制方式不利于实时性、灵活性和容错控制。而采用多预测控制器协调的分布式控制是解决这一问题的有效方法:。针对子系统间的动态耦合行为严重影响多预测控制器协调以及稳定性的问题,提出一种鲁棒区域控制策略。即在每个子系统的目标函数中加入松弛因子增加控制器间协调时的余量来达到分布式预测控制的稳定性。通过以反应器-存储器分馏器组成的过程为事例,仿真结果:表明该方法:的可行性和有效性。     

Distributed model predictive control for polytopic uncertain systems subject to actuator saturation

In this paper, we present a distributed model predictive control (MPC) algorithm for polytopic uncertain systems subject to actuator saturation. The global system is decomposed into several subsystems. A set invariance condition for polytopic uncertain system with input saturation is identified and a min–max distributed MPC strategy is proposed. The distributed MPC controller is designed by solving a linear matrix inequalities (LMIs) optimization problem. An iterative algorithm is developed for making coordination among subsystems. Case studies are carried out to illustrate the effectiveness of the proposed algorithm.     

Distributed model predictive control of constrained nonlinear systems with communication delays

Distributed model predictive control (MPC), having been proven to be efficient for large-scale control systems, is essentially enabled by communication network connections among involved subsystems (agents). This paper studies the distributed MPC problem for a class of continuous-time decoupled nonlinear systems subject to communication delays. By using a robustness constraint and designing a waiting mechanism, a delay-involved distributed MPC scheme is proposed. Furthermore, the iterative feasibility and stability properties are analyzed. It is shown that, if the communication delays are bounded by an upper bound, and the cooperation weights and the sampling period are designed appropriately, the overall system state converges to the equilibrium point. The theoretical results are verified by a simulation study.     

Feedback Linearization Based Distributed Model Predictive Control for Secondary Control of Islanded Microgrid

In this paper, a distributed Model Predictive Control (DMPC) is proposed for the secondary voltage and frequency control of islanded microgrid, where each distributed generator (DG) is controlled by a Model Predictive Control (MPC) in the secondary control layer, individually. With considering the nonlinear dynamics of DG with primary control, input‐output feedback schemes are developed for voltage and frequency control separately. Then, all MPCs use the local and neighboring nodes information to solve the optimization problem instead of communicating with a central controller. In this way, the control of the whole system is fully distributed, which allows for a plug‐and‐play. The convergence and stability analysis of the overall closed‐loop system are provided. The simulation result shows the effectiveness of the proposed method.     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.     

Model predictive control of distributed networked control systems with quantization and switching topology

This work is concerned with the robust model predictive control (MPC) for a class of distributed networked control systems (NCSs), in which the input quantization and switching topology are both considered. By utilizing the sector bound approach, the NCSs with quantization are converted into the linear systems with sector bound uncertainties. The topology switching is governed by a switching signal and the dynamic behavior is modeled as a switched control system. A new robust MPC design technique is derived to minimize the upper bound of a weighted quadratic performance index. Moreover, the conditions of both the recursive feasibility of the MPC design and the stability of the resulting closed‐loop system are developed. Finally, simulation results are presented to verify the effectiveness of the proposed MPC design.     

网络信息模式下分布式系统协调预测控制

工业系统中广泛存在一类由多个相互关联的子系统组成的大系统. 尽管分布式控制结构的性能没有集中式控制好,但由于其具有较高的灵活性和容错性,相对于集中控制更加适合控制上述系统.在保持容错性的情况下如何提高系统的整体性能是分布式控制的一个难点问题.本文提出了一种分布式预测控制(Distributed model predictive control, DMPC)方法,该方法通过在各子系统预测控制器的性能指标中加入输入变量对其下游子系统的影响的二次函数,来扩大分布式预测控制的协调度,进而在不增加网络连通度,不改变系统容错性的前提下,提高系统的性能.另外,本文给出了基于该协调策略的带输入约束的分布式预测控制器的设计方法,在初始可行的前提下,该方法相继可行并可保证系统渐近稳定.     

Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

Distributed MPC of polytopic uncertain systems: handling quantised communication and packet dropouts

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.     

Distributed stochastic MPC for systems with parameter uncertainty and disturbances

A distributed stochastic model predictive control algorithm is proposed for multiple linear subsystems with both parameter uncertainty and stochastic disturbances, which are coupled via probabilistic constraints. To handle the probabilistic constraints, the system dynamics is first decomposed into a nominal part and an uncertain part. The uncertain part is further divided into 2 parts: the first one is constrained to lie in probabilistic tubes that are calculated offline through the use of the probabilistic information on disturbances, whereas the second one is constrained to lie in polytopic tubes whose volumes are optimized online and whose facets' orientations are determined offline. By permitting a single subsystem to optimize at each time step, the probabilistic constraints are then reduced into a set of linear deterministic constraints, and the online optimization problem is transformed into a convex optimization problem that can be performed efficiently. Furthermore, compared to a centralized control scheme, the distributed stochastic model predictive control algorithm only requires message transmissions when a subsystem is optimized, thereby offering greater flexibility in communication. By designing a tailored invariant terminal set for each subsystem, the proposed algorithm can achieve recursive feasibility, which, in turn, ensures closed‐loop stability of the entire system. A numerical example is given to illustrate the efficacy of the algorithm.     

Decentralized summation‐based triggering mechanism for Lipschitz nonlinear systems

In this paper, a decentralized event‐based triggering mechanism for a class of nonlinear control systems is studied. It is assumed that the measurement sensors are geographically distributed and so local event generator modules are employed. Then, a novel periodic triggering condition is proposed for each module, which can potentially reduce the information exchange between subsystems compared with traditional control approaches, while maintaining closed‐loop asymptotic stability. The triggering condition parameters are designed through a convex optimization problem with LMI constraints. Finally, simulations are carried out to illustrate the performance of the introduced scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Augmented Lagrangian Pattern Search Based Multi‐Agent Model Predictive Control of Rhine‐Meuse Delta

In Large Scale Systems the concept of centrality fails due to the lack of centralized computing capability. The control of such systems has to be performed using multiple control agents. In this case, the matter of interactions among neighboring subsystems needs to be considered. In this paper, a water control system in the Netherlands is studied as a real large scale system. A multi‐agent scheme is applied to control the flow through the system which is decomposed into two interconnected subsystems. Each agent employs a model‐based predictive control (MPC) technique. The model of this large scale system is nonlinear and nonconvex. Therefore, an augmented Lagrangian pattern search optimization algorithm is used to implement multi‐agent MPC for this system. This proposed algorithm is applied by each control agent to solve its own interconnected optimization problem, at each subsystem of whole the water system. Simulation results show the effectiveness of the proposed approach.     

Real‐time model predictive control based on dual gradient projection: Theory and fixed‐point FPGA implementation

This paper proposes a method to design robust model predictive control (MPC) laws for discrete‐time linear systems with hard mixed constraints on states and inputs, in case of only an inexact solution of the associated quadratic program is available, because of real‐time requirements. By using a recently proposed dual gradient‐projection algorithm, it is proved that the discrepancy of the optimal control law as compared with the obtained one is bounded even if the solver is implemented in fixed‐point arithmetic. By defining an alternative MPC problem with tightened constraints, a feasible solution is obtained for the original MPC problem, which guarantees recursive feasibility and asymptotic stability of the closed‐loop system with respect to a set including the origin, also considering the presence of external disturbances. The proposed MPC law is implemented on a field‐programmable gate array in order to show the practical applicability of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed model predictive control for plant-wide hot-rolled strip laminar cooling process

Since hot-rolled strip laminar cooling (HSLC) process is a large-scale, nonlinear system, a distributed model predictive control (DMPC) framework is proposed for computational reason and enhancing the precision and flexibility of control system. The overall system is divided into several interconnected subsystems and each subsystem is controlled by local model predictive control (MPC). These local MPCs cooperate with its neighbours through the scheme of neighbourhood optimization for the improvement of global performance. The state space representation of each subsystem’s prediction model is designed by finite volume method firstly, and then is linearized around the current operating point at each step to overcome the computational obstacle of nonlinear model. Moreover, since the strip temperature is measurable only at a few positions in water cooling section due to the difficult ambient conditions, an Extended Kalman Filter (EKF) is used to estimate the transient temperature of strip. Both simulation and experiment results prove the efficiency of the proposed method.     

Dual closed‐loop tracking control for wheeled mobile robots via active disturbance rejection control and model predictive control

A dual closed‐loop tracking control is proposed for a wheeled mobile robot based on active disturbance rejection control (ADRC) and model predictive control (MPC). In the inner loop system, the ADRC scheme with an extended state observer (ESO) is proposed to estimate and compensate external disturbances. In the outer loop system, the MPC strategy is developed to generate a desired velocity for the inner loop dynamic system subject to a diamond‐shaped input constraint. Both effectiveness and stability analysis are given for the ESO and the dual closed‐loop system, respectively. Simulation results demonstrate the performances of the proposed control scheme.     

Distributed Model Predictive Control Method for Optimal Coordination of Signal Splits in Urban Traffic Networks

Coordination and control approaches based on model predictive control (MPC) have been widely investigated for traffic signal control in urban traffic networks. However, due to the complex non‐linear characters of traffic flows and the large scale of traffic networks, a basic challenge faced by these approaches is the high online computational complexity. In this paper, to reduce the computational complexity and improve the applicability of traffic signal control approaches based on MPC in practice, we propose a distributed MPC approach (DCA‐MPC) to coordinate and optimize the signal splits. Instead of describing the dynamics of traffic flow within each link of the traffic network with a simplified linear model, we present an improved nonlinear traffic model. Based on the nonlinear model, an MPC optimization framework for the signal splits control is developed, whereby the interactions between subsystems are accurately modeled by employing two interconnecting constraints. In addition, by designing a novel dual decomposition strategy, a distributed coordination algorithm is proposed. Finally, with a benchmark traffic network, experimental results are given to illustrate the effectiveness of the proposed method.     

Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

This paper studies the control of constrained systems whose dynamics and constraints switch between a finite set of modes over time according to an exogenous input signal. We define a new type of control invariant sets for switched constrained systems, called switch–robust control invariant (switch‐RCI) sets, that are robust to unknown mode switching and exploit available information on minimum dwell‐time and admissible mode transitions. These switch‐RCI sets are used to derive novel necessary and sufficient conditions for the existence of a control‐law that guarantees constraint satisfaction in the presence of unknown mode switching with known minimum dwell‐time. The switch‐RCI sets are also used to design a recursively feasible model predictive controller (MPC) that enforces closed‐loop constraint satisfaction for switched constrained systems. We show that our controller is nonconservative in the sense that it enforces constraints on the largest possible domain, ie, constraints can be recursively satisfied if and only if our controller is feasible. The MPC and switch‐RCI sets are demonstrated on a vehicle lane‐changing case study.     

Distributed model predictive control for constrained linear systems

We address the distributed model predictive control (MPC) for a set of linear local systems with decoupled dynamics and a coupled global cost function. By the decomposition of the global cost function, the distributed control problem is converted to the MPC for each local system associated with a cost involving neighboring system states and inputs. For each local controller, the infinite horizon control moves are parameterized as N free control moves followed by a single state feedback law. An interacting compatibility condition is derived, disassembled and incorporated into the design of each local control so as to achieve the stability of the global closed‐loop system. Each local system exchanges with its neighbors the current states and the previous optimal control strategies. The global closed‐loop system is shown to be exponentially stable provided that all the local optimizers are feasible at the initial time. Copyright © 2009 John Wiley & Sons, Ltd.