Quadratic programming algorithms for large-scale model predictive control

Quadratic programming (QP) methods are an important element in the application of model predictive control (MPC). As larger and more challenging MPC applications are considered, more attention needs to be focused on the construction and tailoring of efficient QP algorithms. In this study, we tailor and apply a new QP method, called QPSchur, to large MPC applications, such as cross directional control problems in paper machines. Written in C++, QPSchur is an object oriented implementation of a novel dual space, Schur complement algorithm. We compare this approach to three widely applied QP algorithms and show that QPSchur is significantly more efficient (up to two orders of magnitude) than the other algorithms. In addition, detailed simulations are considered that demonstrate the importance of the flexible, object oriented construction of QPSchur, along with additional features for constraint handling, warm starts and partial solution.     

液位系统的多模型广义预测控制研究

用多模型的广义预测控制器对复杂的非线性液位系统进行仿真控制。通过在覆盖工况的若干个平衡点采用最小二乘法离线辨识建立多个线性模型,形成非线性系统的多模型表示,然后对各个子模型分别设计子控制器,采用基于相对残差的方法来实现控制增量的加权以获取控制增量。通过对单容液位系统的仿真,表明该方法的有效性。     

T-S模型的窑炉压力无超调快速广义预测控制设计

窑压是玻璃窑炉运行过程中重要的被控指标之一,直接影响窑炉能耗、寿命及产品成品率,优化窑炉压力控制具有重要的经济意义。由于受到众多因素的影响,窑压具有典型的非线性特性,现有方法的控制效果还有很大的提升空间。本文针对窑压设计了一套新型无超调快速模糊广义预测控制方法(NFGPC),先利用"离线+在线"组合辨识方法得到窑压对象的T-S模型;然后基于该模型对系统进行分片线性化得到时变CARIMA模型,以设计窑压广义预测控制律;结合柔化理论与新型滚动优化目标函数设计一种广义预测控制律,该方法无需求解逆矩阵即可得到控制输出,计算量更小;由于新目标函数的应用,该方法还能够克服传统GPC引起的超调效应。仿真结果表明该方法能够很好的处理窑压非线性系统建模问题,与PID控制、线性GPC(LGPC)以及模糊广义预测控制(FGPC)以及快速模糊广义预测控制(FFGPC)等方法控制效果的对比表明,NFFGPC在处理非线性系统控制问题上具有一定的优越性。     

稳定广义预测控制与性能分析

基于已有的一种稳定广义预测控制(SGPC)结构,以参考信号为优化变量对目标函数进行寻优,求出了控制器的滚动最优控制律,该控制律可以无静差地跟踪常数设定值.文中给出并证明了SGPC闭环控制系统的稳定性充分条件.数值仿真表明,该SGPC控制器可以保证闭环系统无稳态误差,并且适用于具有近似相消零极点的被控对象.     

Proportioning with second-order information for model predictive control

We propose an algorithm for the effective solution of quadratic programming (QP) problems arising from model predictive control (MPC). MPC is a modern multivariable control method which gives the solution for a QP problem at each sample instant. Our algorithm combines the active-set strategy with the proportioning test to decide when to leave the actual active set. For the minimization in the face, we use a direct solver implemented by the Cholesky factors updates. The performance of the algorithm is illustrated by numerical experiments, and the results are compared with the state-of-the-art solvers on benchmarks from MPC.     

Fast suboptimal predictive control with guaranteed stability

Efficient algorithms for constrained minimization of infinite horizon predictive control costs are presented. Control laws with guaranteed stability and asymptotic tracking are derived on the basis of appropriately chosen one-dimensional and ellipsoidal constraint set approximations. These achieve comparable performance with existing QP-based control laws with significant reductions in computational burden.     

快速递推广义预测控制

本文利用反向递推方法对广义预测控制的准则函数进行变换，得出一种递推的快速ＧＰＳ算法。     

Linear programming and model predictive control

The practicality of model predictive control (MPC) is partially limited by the ability to solve optimization problems in real time. This requirement limits the viability of MPC as a control strategy for large scale processes. One strategy for improving the computational performance is to formulate MPC using a linear program. While the linear programming formulation seems appealing from a numerical standpoint, the controller does not necessarily yield good closed-loop performance. In this work, we explore MPC with an l₁ performance criterion. We demonstrate how the non-smoothness of the objective function may yield either dead-beat or idle control performance.     

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.     

Interpolation methods in model predictive control: an overview

Interpolation methods are one means of tackling the classical performance versus feasibility compromise in model predictive control (MPC). However, although some details are available in various conferences, very little has appeared in the published journals and also there is no paper pulling all the various algorithms together. Hence this article seeks to give a brief but insightful survey of existing proposals along with their strengths and weaknesses, before proposing useful avenues for future studies.     

一种约束输入的广义预测控制新算法

提出一种约束输入的广义预测控制新算法（GPCIC），该算法不必求逆矩阵，占用内存小，计算速度快，仿真结果表明，该算法具有良好的控制性能。     

对角CARIMA模型多变量自适应约束广义预测控制

为了简化约束存在时多变量广义预测控制算法的设计与实现,依据对角CARIMA模型的结构特点,将多输入多输出对象的参数辨识和模型预报问题转化为一系列多输入单输出子对象的参数辨识和模型预报问题.推导了输入输出的约束形式及优化求解过程.简化了多变量对象的参数辨识、模型预报、目标函数和约束条件系数矩阵的计算.在由DCS控制的非线性液位装置上的对比实验结果表明了该方法的有效性.     

Fast economic model predictive control based on NLP-sensitivities

This study adapts the advanced step NMPC framework to Economic NMPC. Here, sufficient conditions for nominal stability are derived for NMPC controllers that incorporate economic stage costs with appropriate regularization. To guarantee these conditions, we derive a constructive strategy to calculate the regularization term directly. Moreover, we extend the sensitivity components in the advanced step NMPC framework to consider a rigorous path-following algorithm. This approach accounts for active set changes and allows much weaker constraint qualifications. Moreover, using an ℓ₁ formulation of the NMPC problem satisfies these constraint qualifications and allows more reliable solution of the moving horizon optimization problem, even in the presence of noise. Finally, all of these concepts are demonstrated on a detailed case study with a continuously stirred tank reactor.     

Efficient algorithms for trading off feasibility and performance in predictive control

This article introduces two simple modifications to conventional predictive control algorithms with the aim of enlarging the feasible regions without increasing computational complexity. It is shown that despite the relatively large feasibility gains, the loss in performance may be far smaller than expected and thus the algorithms give mechanisms for achieving low computational loads with good feasibility and good performance while using a simple algorithm set-up. Both algorithms have standard convergence and feasibility guarantees.     

An improved approach for constrained robust model predictive control

In this paper, we present a new technique to address constrained robust model predictive control. The main advantage of this new approach with respect to other well-known techniques is the reduced conservativeness. Specifically, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.     

无穷时域的连续时间广义预测控制

将无穷时域的性能指标引入连续时间的广义预测控制,通过施加新的终端等式约束,把包含无穷时域性能指标的优化问题转化成可解的二次规划问题.利用后退时域性能指标的单调性,给出了保证连续时间广义预测控制闭环稳定性的条件.仿真例子验证了该算法的有效性.     

对角CARIMA模型多变量广义预测控制改进算法

为了增强多变量广义预测控制算法(MGPC)的实用性,对其实现形式进行了进一步的简化.利用对角CARIMA模型的结构特点,先对系统中单个输出变量期望值的自由响应部分进行分解推导,将其表达成自由响应项系数与系统输入输出变量已知值乘积的形式,得到此输出变量的预测表达式,然后将系统所有输出变量的预测表达式代入目标函数中,得到的控制增量等于控制器系数与参考轨迹、过程输入输出历史数据的乘积.控制器系数只与模型参数及设计参数有关,求解控制量时不再需要进行模型输出预报,控制器结构简单,实现容易.对比实验结果表明了该方法保持了常规MGPC方法的优秀控制性能.     

多变量预测控制结构分解的图论方法

预测控制算法的计算复杂度主要由变量个数和控制时域决定, 而大型复杂系统中变量个数较多将导致计 算量大的问题, 尤其在有约束预测控制的优化求解中增加较重的计算负担. 本文针对此问题利用邻接矩阵、可达矩 阵和关联矩阵梳理系统传递函数模型中变量之间的关联, 将有关联的控制变量划分为一个子系统, 进而将一个大系 统分解成若干独立子系统, 即可将一个高维度的优化求解问题分解成多个维度较低的子优化问题, 降低计算复杂度 以达到减少计算量的目的. 最后将其应用在多变量有约束的双层结构预测控制算法中, 通过仿真进行验证.