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.     

Distributed robust MPC for nonholonomic robots with obstacle and collision avoidance

Considering that the inevitable disturbances and coupled constraints pose an ongoing challenge to distributed control algorithms, this paper proposes a distributed robust model predictive control (MPC) algorithm for a multi-agent system with additive external disturbances and obstacle and collision avoidance constraints. In particular, all the agents are allowed to solve optimization problems simultaneously at each time step to obtain their control inputs, and the obstacle and collision avoidance are accomplished in the context of full-dimensional controlled objects and obstacles. To achieve the collision avoidance between agents in the distributed framework, an assumed state trajectory is introduced for each agent which is transmitted to its neighbors to construct the polyhedral over-approximations of it. Then the polyhedral over-approximations of the agent and the obstacles are used to smoothly reformulate the original nonconvex obstacle and collision avoidance constraints. And a compatibility constraint is designed to restrict the deviation between the predicted and assumed trajectories. Moreover, recursive feasibility of each local MPC optimization problem with all these constraints derived and input-to-state stability of the closed-loop system can be ensured through a sufficient condition on controller parameters. Finally, simulations with four agents and two obstacles demonstrate the efficiency of the proposed algorithm.     

Distributed model predictive control of linear systems with persistent disturbances

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication.     

Constrained nonlinear MPC for accelerated tracking piece-wise references and its applications to thermal systems

In this paper, we propose a model predictive control (MPC) strategy for accelerated offset-free tracking piece-wise constant reference signals of nonlinear systems subject to state and control constraints. Some special contractive constraints on tracking errors and terminal constraints are embedded into the tracking nonlinear MPC formulation. Then, recursive feasibility and closed-loop convergence of the tracking MPC are guaranteed in the presence of piece-wise references and constraints by deriving some sufficient conditions. Moreover, the local optimality of the tracking MPC is achieved for unreachable output reference signals. By comparing to traditional tracking MPC, the simulation experiment of a thermal system is used to demonstrate the acceleration ability and the effectiveness of the tracking MPC scheme proposed here.     

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 noncausal model predictive control of wave energy converters

In this paper, a novel feedback noncausal model predictive control (MPC) strategy for sea wave energy converters (WECs) is proposed, where the wave prediction information can be explicitly incorporated into the MPC strategy to improve the WEC control performance. The main novelties of the MPC strategy proposed in this paper include: (i) the recursive feasibility and robust constraints satisfaction are guaranteed without a significant increase in the computational burden; (ii) the information of short-term wave prediction is incorporated into the feedback noncausal MPC method to maximise the potential energy output; (iii) the sea condition for the WEC to safely operate in can be explicitly calculated. The proposed feedback noncausal MPC algorithm can also be extended to a wide class of control design problems, especially to the energy maximisation problems with constraints to be satisfied and subject to persistent but predictable disturbances. Numerical simulations are provided to show the efficacy of the proposed feedback noncausal MPC.     

Feasible parallel-update distributed MPC for uncertain linear systems sharing convex constraints

A distributed MPC approach for linear uncertain systems sharing convex constraints is presented. The systems, which are dynamically decoupled but share constraints on state and/or inputs, optimize once, in parallel, at each time step and exchange plans with neighbours thereafter. Coupled constraint satisfaction is guaranteed, despite the simultaneous decision making, by extra constraint tightening in each local problem. Necessary and sufficient conditions are given on the margins for coupled constraint satisfaction, and a simple on-line scheme for selecting margins is proposed that satisfies the conditions. Robust feasibility and stability of the overall system are guaranteed by use of the tube MPC concept in conjunction with the extra coupled constraint tightening.     

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.     

Distributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems

This paper considers the problem of distributed control of dynamically coupled nonlinear systems that are subject to decoupled constraints. Examples of such systems include certain large scale process control systems, chains of coupled oscillators and supply chain management systems. Receding horizon control (RHC) is a method of choice in these venues as constraints can be explicitly accommodated. In addition, a distributed control approach is sought to enable the autonomy of the individual subsystems and reduce the computational burden of centralized implementations. In this paper, a distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints. By this algorithm, each subsystem computes its own control locally. Provided an initially feasible solution can be found, subsequent feasibility of the algorithm is guaranteed at every update, and asymptotic stabilization is established. The theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment. In simulations, distributed and centralized receding horizon controllers are employed for stabilization of the oscillators. The numerical experiments show that the controllers perform comparably, while the computational savings of the distributed implementation over the centralized implementation is clearly demonstrated.     

Robust economic model predictive control based on a periodicity constraint

This paper proposes robust economic model predictive control based on a periodicity constraint for linear systems subject to unknown‐but‐bounded additive disturbances. In this economic MPC design, a periodic steady‐state trajectory is not required and thus assumed unknown, which precludes the use of enforcing terminal state constraints as in other standard economic formulations. Instead, based on the desired periodicity of system operation, we optimize the economic performance over a set of periodic trajectories that include the current state. To achieve robust constraint satisfaction, we use a tube‐based technique in the economic MPC formulation. The mismatches between the nominal model and the closed‐loop system with perturbations are limited using a local control law. With the proposed robust tube‐based strategy, recursive feasibility is guaranteed. Moreover, under a convexity assumption, the closed‐loop convergence of the closed‐loop system is analyzed, and an optimality certificate is provided to check if the closed‐loop trajectory reaches a neighborhood of the optimal nominal periodic steady trajectory using Karush‐Kuhn‐Tucker optimality conditions. Finally, through numerical examples, we show the effectiveness of the proposed approach.     

一类干扰有界约束非线性系统的鲁棒模型预测控制

针对一类干扰有界约束非线性系统设计了基于控制不变集切换策略的鲁棒模型预测控制算法.针对非线性系统线性化之后的结果,给出了平衡点的非线性标称系统控制不变集的计算方法.然后在考虑线性化误差和加性有界干扰影响的基础上,构造了平衡点附近最小鲁棒正不变集.结合不变集切换策略和Tube不变集控制方法,提出了干扰有界约束非线性系统的不变集切换策略.最后将该算法应用到一类典型的非线性化工过程连续搅拌反应釜(CSTR)中,仿真结果验证了算法的有效性.     

Computation delay compensation for real time implementation of robust model predictive control

The implementation of model predictive control (MPC) requires to solve an optimization problem online. The computation time, often not negligible especially for nonlinear MPC (NMPC), introduces a delay in the feedback loop. Moreover, it impedes fast sampling rate setting for the controller to react to uncertainties quickly. In this paper, a dual time scale control scheme is proposed for linear/nonlinear systems with external disturbances. A pre-compensator works at fast sampling rate to suppress uncertainty, while the outer MPC controller updates the open loop input sequence at a slower rate. The computation delay is explicitly considered and compensated in the MPC design. Four robust MPC algorithms for linear/nonlinear systems in the literature are adopted and tailored for the proposed control scheme. The recursive feasibility and stability are rigorously analysed. Three simulation examples are provided to validate the proposed approaches.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Nash-based robust distributed model predictive control for large-scale systems

In this paper, a new robust distributed model predictive control (RDMPC) is proposed for large-scale systems with polytopic uncertainties. The time-varying system is first decomposed into several interconnected subsystems. Interactions between subsystems are obtained by a distributed Kalman filter, in which unknown parameters of the system are estimated using local measurements and measurements of neighboring subsystems that are available via a network. Quadratic boundedness is used to guarantee the stability of the closed-loop system. In the MPC algorithm, an output feedback-interaction feedforward control input is computed by an LMI-based optimization problem that minimizes an upper bound on the worst case value of an infinite-horizon objective function. Then, an iterative Nash-based algorithm is presented to achieve the overall optimal solution of the whole system in partially distributed fashion. Finally, the proposed distributed MPC approach is applied to a load frequency control (LFC) problem of a multi-area power network to study the efficiency and applicability of the algorithm in comparison with the centralized, distributed and decentralized MPC schemes.     

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.     

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。     

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.     

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.     

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.     

Conditions under which suboptimal nonlinear MPC is inherently robust

We address the inherent robustness properties of nonlinear systems controlled by suboptimal model predictive control (MPC), i.e., when a suboptimal solution of the (generally nonconvex) optimization problem, rather than an element of the optimal solution set, is used for the control. The suboptimal control law is then a set-valued map, and consequently, the closed-loop system is described by a difference inclusion. Under mild assumptions on the system and cost functions, we establish nominal exponential stability of the equilibrium, and with a continuity assumption on the feasible input set, we prove robust exponential stability with respect to small, but otherwise arbitrary, additive process disturbances and state measurement/estimation errors. These results are obtained by showing that the suboptimal cost is a continuous exponential Lyapunov function for an appropriately augmented closed-loop system, written as a difference inclusion, and that recursive feasibility is implied by such (nominal) exponential cost decay. These novel robustness properties for suboptimal MPC are inherited also by optimal nonlinear MPC. We conclude the paper by showing that, in the absence of state constraints, we can replace the terminal constraint with an appropriate terminal cost, and the robustness properties are established on a set that approaches the nominal feasibility set for small disturbances. The somewhat surprising and satisfying conclusion of this study is that suboptimal MPC has the same inherent robustness properties as optimal MPC.