Steady-state target optimization designs for integrating real-time optimization and model predictive control

In industrial practice, the optimal steady-state operation of continuous-time processes is typically addressed by a control hierarchy involving various layers. Therein, the real-time optimization (RTO) layer computes the optimal operating point based on a nonlinear steady-state model of the plant. The optimal point is implemented by means of the model predictive control (MPC) layer, which typically uses a linear dynamical model of the plant. The MPC layer usually includes two stages: a steady-state target optimization (SSTO) followed by the MPC dynamic regulator. In this work, we consider the integration of RTO with MPC in the presence of plant-model mismatch and constraints, by focusing on the design of the SSTO problem. Three different quadratic program (QP) designs are considered: (i) the standard design that finds steady-state targets that are as close as possible to the RTO setpoints; (ii) a novel optimizing control design that tracks the active constraints and the optimal inputs for the remaining degrees of freedom; and (iii) an improved QP approximation design were the SSTO problem approximates the RTO problem. The main advantage of the strategies (ii) and (iii) is in the improved optimality of the stationary operating points reached by the SSTO-MPC control system. The performance of the different SSTO designs is illustrated in simulation for several case studies.     

On real-time robust model predictive control

High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem, which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade off computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the effectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.     

Nonlinear model predictive control of a magnetic levitation system

The paper presents a fast nonlinear model predictive control (MPC) scheme for a magnetic levitation system. A nonlinear dynamical model of the levitation system is derived that additionally captures the inductor current dynamics of the electromagnet in order to achieve a high MPC performance both for stabilization and fast setpoint changes of the levitating mass. The optimization algorithm underlying the MPC scheme accounts for control constraints and allows for a time and memory efficient computation of the single iteration. The overall control performance of the levitation system as well as the low computational costs of the MPC scheme is shown both in simulations and experiments with a sampling frequency of 700 Hz on a standard dSPACE hardware.     

预测控制优化变量的集结策略

为减少预测控制的在线计算量，提出了对优化变量进行集结的优化策略，通过一个集结矩阵将原优化变量与集结后的变量联系起来，从而为多种预测控制算法建立一个统一的框架，分析了现有的几种典型优化策略的集结表述，说明了所提出的集结优化框架具有一定的普适性，并在此框架下提出一种新的具有输出衰减形式的集结优化算法。     

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.     

基于粒子群优化的有约束模型预测控制器

研究了模型预测控制(MPC)中解决带约束的优化问题时所用到的优化算法,针对传统的二次规划(QP)方法的不足,引入了一种带有混沌初始化的粒子群优化算法(CPSO),将其应用到模型预测控制中,用十解决同时带有输入约束和状态约束的控制问题.最后,引入了一个实际的带有约束的线性离散系统的优化控制问题,分别用二次规划和粒子群优化两种算法去解决,通过仿真结果的比较,说明了基于粒子群优化(PSO)的模型预测控制算法的优越性.     

Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

Evolutionary algorithm enhancement for model predictive control and real-time decision support

Effective decision support and model predictive control of real-time environmental systems require that evolutionary algorithms operate more efficiently. A suite of model predictive control (MPC) genetic algorithms are developed and tested offline to explore their value for reducing combined sewer overflow (CSO) volumes during real-time use in a deep-tunnel sewer system. MPC approaches include the micro-GA, the probability-based compact GA, and domain-specific GA methods that reduce the number of decision variable values analyzed within the sewer hydraulic model, thus reducing algorithm search space. Minimum fitness and constraint values achieved by all GA approaches, as well as computational times required to reach the minimum values, are compared to large population sizes with long convergence times. Optimization results for a subset of the Chicago combined sewer system indicate that genetic algorithm variations with a coarse decision variable representation, eventually transitioning to the entire range of decision variable values, are best suited to address the CSO control problem. Although diversity-enhancing micro-GAs evaluate a larger search space and exhibit shorter convergence times, these representations do not reach minimum fitness and constraint values. The domain-specific GAs prove to be the most efficient for this case study. Further MPC algorithm developments are suggested to continue advancing computational performance of this important class of problems with dynamic strategies that evolve as the external constraint conditions change.     

采用预测控制的地铁节能优化控制算法

本文针对地铁列车自动运行系统(automatic train operation,ATO)一般运行情况以及晚点延迟发车情况下的节能问题,基于预测控制算法设计了地铁节能优化控制算法.利用预测控制算法的在线滚动优化特性,通过设计含有能量消耗趋势优化项的控制目标函数,控制算法能够针对节能目标实现快速动态调整.通过调节目标函数中各优化项权重的相对大小,节能算法可以在满足列车时间与路程运行指标的同时,达到降低能耗的目的.在MATLAB平台上利用真实车辆模型对提出的节能优化控制算法进行了仿真,在列车不延迟与延迟的情况下,算法都很好地平衡了跟踪目标与节能目标,为地铁能耗动态优化控制提供了可行方案.     

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.     

Periodic optimal control of nonlinear constrained systems using economic model predictive control

In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index. We demonstrate that the direct extension of existing methods to periodic orbits does not necessarily yield the desirable closed-loop economic performance. Instead, we carefully revise the constraints on the artificial trajectory, which ensures that the closed-loop average performance is no worse than a locally optimal periodic orbit. In the special case that the prediction horizon is set to zero, the proposed scheme is a modified version of recent publications using periodicity constraints, with the important difference that the resulting closed loop has more degrees of freedom which are vital to ensure convergence to an optimal periodic orbit. In addition, we detail a tailored offline computation of suitable terminal ingredients, which are both theoretically and practically beneficial for closed-loop performance improvement. Finally, we demonstrate the practicality and performance improvements of the proposed approach on benchmark examples.     

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.     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

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.     

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.     

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.     

Optimizing model predictive control of an industrial distillation column

The main scope of this work is the implementation of an MPC that integrates the control and the economic optimization of the system. The two problems are solved simultaneously through the modification of the control cost function that includes an additional term related to the economic objective. The optimizing MPC is based on a quadratic program (QP) as the conventional MPC and can be solved with the available QP solvers. The method was implemented in an industrial distillation system, and the results show that the approach is efficient and can be used, in several practical cases.     

基于混沌粒子群优化的约束状态反馈预测控制算法

提出一种基于混沌粒子群优化的约束状态反馈预测控制算法,用于解决带有输入约束和状态约束的控制问题.将混沌粒子群优化引入到约束状态反馈预测控制的滚动优化过程中,增强了算法在约束范围内的局部搜索和全局搜索能力.通过对一个实际的带有约束的线性离散系统控制优化问题的解决,验证了基于混沌粒子群优化的状态反馈预测控制算法的可行性和有效性,与传统的二次规划算法的比较结果说明了此算法的优越性,证明了状态反馈预测控制系统良好的鲁棒性.     

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed-loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling-hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed-loop system. The effectiveness of the proposed method is illustrated through a chemical process example.