Decomposition principle in model predictive control for linear systems with bounded disturbances

Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based MPC approach with a decomposition principle. The idea of the paper is to extend the “pre-stabilizing” MPC, where the MPC control sequence is parameterized as perturbations to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard “pre-stabilizing” MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.     

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.     

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.     

Robust explicit model predictive control for linear systems via interpolation techniques

This paper presents a novel interpolation‐based model predictive control (IMPC) for constrained linear systems with bounded disturbances. The idea of so‐called ‘pre‐stabilizing’ MPC is extended by making interpolation among several ‘pre‐stabilizing’ MPC controllers, through which the domain of attraction can be magnificently enlarged. Compared with the standard ‘pre‐stabilizing’ MPC, the proposed approach has the advantage of combining the merits of having a large domain of attraction and a good behavior. Furthermore, such an IMPC problem can be solved off‐line by multi‐parametric programming. The optimal solution is given in an explicitly piecewise affine form. A simple algorithm for the implementation of the explicit MPC control laws is also proposed. Copyright © 2009 John Wiley & Sons, Ltd.     

切换非线性系统的分布式模型预测控制

针对一类具有预先指定切换序列的切换非线性系统,研究了具有通信信道干扰和时滞测量的分布式模型预测控制问题.在每个子系统都存在镇定控制器的假设下,利用基于Lyapunov函数的模型预测控制器设计了分布式模型预测控制器,并给出了闭环切换非线性系统最终有界的充分条件.最后,通过仿真结果表明了分布式模型预测控制策略的有效性.     

Stochastic model predictive control: Insights and performance comparisons for linear systems

In this paper, we define several instances of model predictive control (MPC) for linear systems, including both deterministic and stochastic formulations. We show by explicit computation of the associated control laws that, under certain conditions, different formulations lead to identical results. This paper provides insights into the performance of stochastic MPC. Amongst other things, it shows that stochastic MPC and traditional MPC can give identical results in special cases. In cases where the solutions are different, we show that the explicit formulation of the problem can give insight into the performance gap.     

Reduced order model predictive control for constrained discrete‐time linear systems

A reduced order model predictive control (MPC) is discussed for constrained discrete‐time linear systems. By employing a decomposition method for finite‐horizon linear systems, an MPC law is obtained from a reduced order optimization problem. The decomposition enables us to construct pairs of initial state and control sequence which have large influence on system responses, and it also characterizes the standard LQ control. The MPC law is obtained based on a combination of the LQ control and dominant input sequences over the prediction horizon. The proposed MPC method is illustrated with numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust model predictive control of constrained linear systems with bounded disturbances

This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances. The optimal control problem that is solved online includes, uniquely, the initial state of the model employed in the problem as a decision variable. The associated value function is zero in a disturbance invariant set that serves as the ‘origin’ when bounded disturbances are present, and permits a strong stability result, namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances, to be obtained. The resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control.     

Constrained control for uncertain discrete-time linear systems

In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm. © 1998 John Wiley & Sons, Ltd.     

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.     

Distributed iterative command governor schemes for interconnected linear systems

A novel distributed command governor (CG) supervision strategy relying on iterative optimization procedure is presented for multi‐agent interconnected linear systems subject to pointwise‐in‐time set‐membership coordination constraints. Unlike non‐iterative distributed CG schemes, here all agents undertake several optimization iterations and data exchange before arriving to the optimal solution. As a result, these methods are able to achieve Pareto‐optimal solutions not only in steady‐state conditions as the ones based on non‐iterative optimization procedures but also during transients and are not hampered by the presence of undesirable Nash‐equilibria or deadlock situations. The main properties of the method are fully investigated and in particular its optimality, stability, and feasibility properties rigorously proved. A final example is presented where the proposed distributed solution is contrasted with existing centralized and distributed non‐iterative CG solutions. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed optimal control of multiple systems

This article considers distributed optimal control of multiple linear systems. Distributed approximately optimal controllers are proposed for each system with the aid of communications between systems. The proposed controllers make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers if the communication digraph is strongly connected. If the communication digraph is switching and there are communication delays, the proposed controllers also make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers. Simulation results show effectiveness of the proposed controllers.     

Distributed nonlinear model predictive control based on contraction theory

A novel distributed model predictive control algorithm for continuous‐time nonlinear systems is proposed in this paper. Contraction theory is used to estimate the prediction error in the algorithm, leading to new feasibility and stability conditions. Compared to existing analysis based on Lipschitz continuity, the proposed approach gives a distributed model predictive control algorithm under less conservative conditions, allowing stronger couplings between subsystems and a larger sampling interval when the subsystems satisfy the specified contraction conditions. A numerical example is given to illustrate the effectiveness and advantage of the proposed approach.     

带有网络拓扑优化的分布式预测控制方法

通常在大系统中, 全局信息优化的系统, 其性能要高于局部信息优化系统. 全局信息优化的算法由于大系统的复杂程度往往不可行. 所以通常会用分布式算法来解决此类问题. 在分布式算法中, 为了获得更好的系统性能, 要尽可能多的采用更多的信息信息交换, 然而这样会带来信息网络的负担增大. 本文在预测控制性能指标中引入通信代价, 并提出了一种随着系统状态变化的通信网络拓扑切换方法. 文中给出了该算法在供水管网动态模型中的仿真结果, 表明本方法的可行性.     

Distributed adaptive control for time-varying formation of general linear multi-agent systems

An adaptive gain scheduling technique is investigated to discuss distributed time-varying formation (TVF) control problems for general linear time-invariant multi-agent systems (LTI-MASs), where two types of topologies are considered: (1) the interaction topology is undirected and connected, and (2) the interaction topology is directed. Two fully distributed adaptive TVF control protocols are, respectively proposed, which both assign a time-varying coupling weight to each node in the interaction topology. Two algorithms to design the constructed protocols are presented under the undirected and directed interaction topologies, respectively. A feasible TVF set is provided. The stabilities of two algorithms are, respectively proved based on the Lyapunov functional theory. For both undirected and directed interaction topologies, general LTI-MASs can achieve the given TVF using the designed fully distributed adaptive formation protocol without any global information about the interaction topology when the TVF satisfies the feasible set. Finally, theoretical results are illustrated with numerical simulation examples.     

Distributed predictive control of continuous-time systems

In the last years focus has been put in the development of distributed Model Predictive Control (MPC) algorithms. With a few exceptions, they have been mostly developed in the discrete-time framework. However, discretization of large-scale systems may destroy the sparsity of the original continuous-time models, making distributed control design and implementation more difficult. Also, more in general, discrete-time control of continuous-time systems does not allow to consider the process inter-sampling behavior. In this paper we present a novel non-cooperative distributed predictive control algorithm for continuous-time systems based on robust MPC concepts. The convergence properties of the proposed control scheme are stated, and its realizability is tested through a simulation case study.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

受扰线性离散系统的前馈2反馈最优控制

研究具有已知动态特性但未知初始条件的持续外界扰动的线性离散系统最优控制问题。给出了前馈一反馈最优控制律的存在唯一性条件，并提出了最优控制律的设计算法．通过降维扰动观测器解决了前馈一反馈最优控制律的物理不可实现问题．对近海结构物振动控制的实例仿真表明，该设计算法易于实现，在抑制外部持续扰动和鲁棒性方面优于经典的状态反馈最优控制。     

Distributed model predictive control for multiagent systems with improved consistency

This paper addresses an improved distributed model predictive control (DMPC) scheme for multiagent systems with an attempt to improving its consistency. The deviation between what an agent is actually doing and what its neighbors believe that agent is doing is penalized in the cost function of each agent. At each sampling instant the compatibility constraint of each agent is set tighter than the previous sampling instant. Like the traditional approach, the performance cost is utilized as the Lyapunov function to prove closed-looped stability. The closed-loop stability is guaranteed if the weight matrix for deviation in the cost function are sufficiently large. The proposed distributed control scheme is formulated as quadratic programming with quadratic constraints. A numerical example is given to illustrate the effectiveness of the proposed scheme.