Networked model predictive control based on neighbourhood optimization for serially connected large-scale processes

In this paper, two novel networked model predictive control schemes based on neighbourhood optimization are presented for on-line optimization and control of a class of serially connected processes (known as the cascade processes in some references), in which the on-line optimization of the whole system is decomposed into that of several small-scale subsystems in distributed structures. Under network environment, the connectivity of the communication network is assumed to be sufficient for each subsystem to exchange information with its neighbour subsystems. An iterative algorithm for networked MPC and a networked MPC algorithm with one-step delay communication are developed according to different network capacities. The optimality of the iteration based networked MPC algorithm is analyzed and the nominal stability is derived for unconstrained distributed control systems. The nominal stability with one-step delay communication is employed for distributed control systems without the inequality constraints. Finally, an illustrative example and the simulation study of the fuel feed flow control for the walking beam reheating furnace are provided to test the effectiveness and practicality of the proposed networked MPC algorithms.     

Mixed H2/H∞ distributed robust model predictive control for polytopic uncertain systems subject to actuator saturation and missing measurements

In this paper, we discuss the mixed H₂/H_∞ distributed robust model predictive control problem for polytopic uncertain systems subject to randomly occurring actuator saturation and packet loss. The global system is decomposed into several subsystems, and all the subsystems are connected by a fixed topology network, which is the definition for the packet loss among the subsystems. To better use the successfully transmitted information via Internet, both the phenomena of actuator saturation and packet loss resulting from the limitation of the communication bandwidth are taken into consideration. A novel distributed controller model is established to account for the actuator saturation and packet loss in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. With the nonlinear feedback control law represented by the convex hull of a group of linear feedback laws, the distributed controllers for subsystems are obtained by solving an linear matrix inequality (LMI) optimisation problem. Finally, numerical studies demonstrate the effectiveness of the proposed techniques.     

事件触发双模分布式预测控制

本文针对有界扰动作用下的线性离散大系统,提出了事件触发双模分布式预测控制设计方法.利用输入状态稳定性(input-to-state stability,ISS)理论建立了仅与子系统自身信息相关的事件触发条件.只有子系统满足相应的事件触发条件,才进行状态信息的传输和分布式预测控制优化问题的求解,并与邻域子系统交互最优解作用下的关联信息.当子系统进入不变集时,采用状态反馈控制律进行镇定,并与进入不变集的邻域子系统不再交互信息.分析了算法的递推可行性和系统的闭环稳定性,给出了扰动的上界.最后,通过车辆控制系统对算法进行仿真验证,结果表明,本文提出的方法能够有效降低优化问题的求解次数和关联信息的交互次数,节约计算资源和通信资源.     

Simultaneous Stability of Large-scale Systems via Distributed Control Network with Partial Information Exchange

This paper is concerned with the simultaneous stability of the multi-mode large-scale systems composed of the interaction subsystems. A novel distributed control network consisting of multiple network-based controllers with the partial information exchange is adopted to simultaneously stabilize the large-scale systems in multiple operation modes. In the distributed control network (DCN), a partial state information exchange approach is developed to save the real-time communication and computation resources. To compensate for the effects of dynamic couplings between interaction subsystems, the designed controllers use both the local states and the neighbors’ partial information with packet dropouts for local feedback design. Then, a series of Lyapunov functions are constructed to derive a matrix-inequality-based sufficient condition for the existence of the desired controllers. Based on an orthogonal complement technique, the gains of the controllers in DCN are parameterized. The iterative algorithm for the solution of simultaneous stabilization problem is also developed. Finally, a numerical example is performed to show the relevant feature of the proposed method.     

Coordinating multiple optimization-based controllers: New opportunities and challenges

The status of using many, distributed optimization-based controllers for feedback control of large-scale, dynamic processes is presented and evaluated. We show that modeling the interactions between subsystems and exchanging trajectory information among subsystem model predictive controllers (MPCs) is insufficient to provide even closed-loop stability. The cause of this closed-loop instability is competition between the local agents. We next discuss the cooperative distributed MPC framework, in which the objective functions of the local MPCs are modified to achieve systemwide control objectives. This approach provides guaranteed nominal stability and performance properties, but at the cost of a high degree of communication between the local controllers. We next discuss the issue of taking advantage of the structure of the connections between the subsystems to reduce the required communication. The paper concludes by briefly presenting seven current and unsolved research challenges.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

Distributed output feedback MPC with randomly occurring actuator saturation and packet loss

In this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed Optimization for Model Predictive Control of Linear-Dynamic Networks

A linear-dynamic network consists of a directed graph in which the nodes represent subsystems and the arcs model dynamic couplings. The local state of each subsystem evolves according to discrete linear dynamics that depend on the local state, local control signals, and control signals of upstream subsystems. Such networks appear in the model predictive control (MPC) of geographically distributed systems such as urban traffic networks and electric power grids. In this correspondence, we propose a decomposition of the quadratic MPC problem into a set of local subproblems that are solved iteratively by a network of agents. A distributed algorithm based on the method of feasible directions is developed for the agents to iterate toward a solution of the subproblems. The local iterations require relatively low effort to arrive at a solution but at the expense of high communication among neighboring agents and with a slower convergence rate.     

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.     

Distributed adaptive high‐gain extended Kalman filtering for nonlinear systems

In this work, we propose a distributed adaptive high‐gain extended Kalman filtering approach for nonlinear systems. Specifically, we consider a class of nonlinear systems that are composed of several subsystems interacting with each other via their states. In the proposed approach, an adaptive high‐gain extended Kalman filter is designed for each subsystem. The distributed Kalman filters communicate with each other to exchange estimated subsystem state information. First, assuming continuous communication among the distributed filters within deterministic form of subsystems, an implementation strategy that specifies how the distributed filters should communicate is designed and the detailed design of the subsystem filter is described. Second, we consider the case of stochastic subsystems for which the designed subsystem filters communicate to exchange information at discrete‐time instants. A state predictor in each subsystem filter is used to provide predictions of states of other subsystems. The stability properties of the proposed distributed estimation schemes with both continuous and discrete communications are analyzed. Finally, the effectiveness and applicability of the proposed schemes are illustrated via the application to a chemical process example. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust decentralized model reference adaptive control of discrete-time interconnected systems

A robust decentralized model reference adaptive controller is proposed for a class of large-scale systems composed of several interconnected subsystems and described by state space equations. We have formulated a local adaptive controller for each subsystem using only local information such that the state of this subsystem tracks the corresponding state of a reference model. The content of the paper is limited to interconnected subsystems which are described by linear, deterministic, single-input single-output and discrete-time models with unknown and/or slowly time-varying parameters. Sufficient conditions, formulated by utilizing Lyapunov theory, are given for the overall system to be stabilizable by decentralized state feedback adaptive control laws. The results are illustrated by a numerical example.     

Distributed adaptive consensus for linear multi-agent systems with quantised information

This paper considers the distributed adaptive consensus problem for linear multi-agent systems with quantised relative information. By using a lemma in algebraic graph theory and introducing a projection operator in adaptive law, a novel distributed adaptive state feedback controller is designed with quantised relative state information. It is shown that the practical consensus for multi-agent systems with a uniform quantiser is achieved via the Lyapunov theory and the non-smooth analysis. In contrast with the existing quantised controllers, which rely on the minimum nonzero eigenvalue of the Laplacian matrix, the developed controller is only dependent on the number of nodes. Furthermore, a dynamic output feedback controller based on quantised relative output information is proposed. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

Enhanced information reconfiguration for distributed model predictive control for cyber‐physical networked systems

This paper considers a class of cyber‐physical networked systems, which are composed of many interacted subsystems, and are controlled in a distributed framework. The operating point of each subsystem changes with the varying of working conditions or productions, which may cause the change of the interactions among subsystems correspondingly. How to adapt to this change with good closed‐loop optimization performance and appropriate information connections is a problem. To solve this problem, the impaction of a subsystem's control action on the performance of related closed‐loop subsystems is first deduced for measuring the coupling among subsystems. Then, a distributed model predictive control (MPC) for tracking, whose subsystems online reconfigure their information structures, is proposed based on this impaction index. When the operating points changed, each local MPC calculates the impaction indices related to its structural downstream subsystems. If and only if the impaction index exceeds a defined bound, its behavior is considered by its downstream subsystem's MPC. The aim is to improve the optimization performance of entire closed‐loop systems and avoid the unnecessary information connections among local MPCs. Besides, contraction constraints are designed to guarantee that the overall system converges to the set points. The stability analysis is also provided. Simulation results show that the proposed impaction index is reasonable along with the efficiency of the proposed distributed MPC.     

Stability analysis of model-based networked distributed control systems

Networked distributed control systems (NDCSs) face serious challenges such as delays and packet dropouts induced by the communication network employed to connect local controllers of interacting subsystems. These two network-induced shortcomings may degrade the performance or even destabilize NDCSs. This paper is concerned with the problem of stability analysis and stabilization of the NDCSs, featuring both random delay and random packet loss in their communication networks. A model-based networked distributed control framework is proposed to stabilize the NDCS consisting of discrete-time subsystems interconnected through their states. In this control framework, to compensate for the adverse effects of these two network-induced shortcomings, an interaction estimator is provided in each local controller; in addition to a main control unit. This estimator uses the explicit model of the subsystems to estimate the evolution of the states of interacting subsystems, when information about their actual values is not available. A model for the NDCS subject to both random packet loss and random delay is developed. By providing a 3-step interaction estimating algorithm, the closed-loop model-based networked distributed control system (MB-NDCS) is formulated as a time-dependent impulsive system. Then, a quadratic Lyapunov function is constructed to derive a linear matrix inequality (LMI) based sufficient condition for stability analysis of the overall impulsive system. Finally, an illustrative example of a network of interconnected chemical reactors with recycle is presented to show the effectiveness of the proposed approach.     

Observer-enhanced distributed moving horizon state estimation subject to communication delays

In this work, we focus on distributed moving horizon estimation (DMHE) of nonlinear systems subject to time-varying communication delays. In particular, a class of nonlinear systems composed of subsystems interacting with each other via their states is considered. In the proposed design, an observer-enhanced moving horizon state estimator (MHE) is designed for each subsystem. The distributed MHEs exchange information via a shared communication network. To handle communication delays, an open-loop state predictor is designed for each subsystem to provide predictions of unavailable subsystem states (due to delays). Based on the predictions, an auxiliary nonlinear observer is used to generate a reference subsystem state estimate for each subsystem. The reference subsystem state estimate is used to formulate a confidence region for the actual subsystem state. The MHE of a subsystem is only allowed to optimize its subsystem state estimate within the corresponding confidence region. Under the assumption that there is an upper bound on the time-varying delays, the proposed DMHE is proved to give decreasing and ultimately bounded estimation error. The theoretical results are illustrated via the application to a reactor–separator chemical process.     

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.     

Pseudo-decentralized adaptive stabilization of large-scale feedforward nonlinear systems

In this paper, we propose a pseudo-decentralized adaptive control scheme for a class of large-scale feedforward nonlinear systems with unknown nonlinear effects within subsystems and unknown nonlinear interactions among subsystems. The local controller of each subsystem takes a nested saturation feedback, using the state of its own subsystem, and the saturation levels are tuned online in a switching manner via a set of switching logics, which requires some binary flag communication among subsystems. Global asymptotic regulation of the closed-loop states is achieved.     

基于协调的变风量空调系统分布式预测控制

在实验和系统动力学行为分析的基础上,建立了变风量空调实验系统的内部模型,并分解为7个子系统。各个子系统分别采用模型预测控制（MPC）进行局部优化控制。在保证各个子系统之间网络连通和信息共享的基础上,将各个MPC的局部目标组合成系统级目标,从而把大规模的变风量空调控制系统在线优化问题转化为各子系统小规模的分布式优化问题。通过仿真和实验研究,验证了系统控制的效果。     

带有随机丢包的空间关联系统的控制

研究当子系统之间信息传输存在随机丢包时空间关联系统的分析和设计问题. 通过引入空间移动算子和时间前向移动算子, 将关联系统建模为具有Markovian跳变参数的关于离散时间和空间变量的多维线性系统, 其中以Markovian跳变参数反映通信信道的状态, 得到整个关联系统在某一给定丢包率下适定且均方稳定的解析条件. 提出一种分布式动态输出反馈控制器的设计方法, 该控制器和被控对象具有相同的空间关联结构, 并基于线性矩阵不等式方法求解. 最后通过一个具有通信丢包影响的多机编队控制系统实例进一步阐明该模型及方法的正确性和有效性.     

Distributed non-cooperative robust MPC based on reduced-order models

In this paper, a non-cooperative distributed MPC algorithm based on reduced order model is proposed to stabilize large-scale systems. The large-scale system consists of a group of interconnected subsystems. Each subsystem can be partitioned into two parts: measurable part, whose states can be directly measured by sensors, and the unmeasurable part. In the online computation phase, only the measurable dynamics of the corresponding subsystem and neighbour-to-neighbour communication are necessary for the local controller design. Satisfaction of the state constraints and the practical stability are guaranteed while the complexity of the optimization problem is reduced. Numerical examples are given to show the effectiveness of this algorithm.