基于Volterra模型的预测控制及应用

由于工业实践的需要,非线性预测控制近年来受到广泛地关注.Volterra模型是一类特殊的非线性模型,非常适合描述工业过程中的无记忆非线性对象.传统的基于Volterra模型的控制器合成法及迭代计算预测控制器法计算量大,且不便于处理控制约束.非线性模型预测控制求解是典型的非线性规划问题,序列二次规划(sequential quadratic program,SQP)算法是求解非线性规划问题常用方法之一.针对Volterra非线性模型预测控制求解问题,本文将滤子法与一种信赖域SQP算法相结合,提出一种改进SQP算法用于基于非线性Volterra模型的带控制约束的多步预测控制求解,并分析了所提方法的收敛性.工业实例仿真结果证实了所提方法的可行性与有效性.     

基于PSO的预测控制及在聚丙烯中的应用

输入输出受限非线性系统的预测控制问题,可以看作是一个难以直接求解的约束非线性优化问题。针对预测控制在解决此类优化问题时,存在易收敛到局部极小或者非可行解,对初始值敏感等缺点,提出了一种基于微粒群优化方法的非线性预测控制算法。采用微粒群优化算法（PSO）作为模型预测控制的滚动优化方法,在线实时求解最优控制律。将PSO与序贯二次规划（SQP）算法进行对比仿真实验,求解两个标准函数优化问题,结果表明PSO能够快速有效地求得全局最小点,而SQP则很容易陷入局部极小点。将该算法应用于丙烯聚合反应过程的温度控制中,仿真结果显示了该方法的有效性。     

基于SQP算法的SAR成像导引头三维弹道优化

弹载SAR平台轨迹的设计是研究弹载SAR成像算法的前提。为了在满足SAR成像条件的同时降低导弹打击时间,需要对SAR成像导引头的弹道进行优化。该问题属于非线性最优控制问题,本文采用序列二次规划(SQP)优化算法进行求解。首先以波束驻留时间最小为指标函数,导弹俯仰、偏航加速度为优化变量,建立了SAR成像导引头三维弹道优化模型,模型的约束包括SAR成像约束、过载约束和导弹飞行高度约束。然后,将原最优控制问题进行参数化,转换成非线性规划问题,利用SQP算法进行求解。参数化时,离散节点越多,得到的非线性规划问题规模越大,求解速度就越慢。仿真结果表明,SQP算法能够有效解决SAR成像导引头三维弹道优化问题,得到的解满足模型约束。     

求解二次规划逆问题的非单调信赖域算法

为了提高求解二次规划逆问题的速度,提出了针对求解该问题的非单调信赖域算法.为了降低问题的复杂度,将二次规划逆问题转换为决策变量相对较少的对偶问题,采用增广Lagrange法构造对偶问题的子问题,并通过引入光滑函数将子问题转换为无约束优化问题,利用非单调信赖域算法进行求解.数值实验结果表明,该算法的迭代次数比牛顿算法、Gauss回代交替方向法少,运行速度快.因此,对于大规模二次规划逆问题,该算法更加有效.     

自由时间最优控制问题的一种控制向量参数化方法

针对自由时间最优控制问题,提出一种控制向量参数化（CVP）方法.通过引入时间尺度因子,将自由时间最优控制问题转化为固定时间问题,并将终端时刻作为优化参数.基于CVP方法,最优控制问题被转化为一个非线性规划（NLP）问题.建立目标和约束函数的Hamiltonian函数,通过求解伴随方程获得目标和约束函数的梯度,采用序列二次规划（SQP）方法获得问题的数值解.对于控制有切换结构的优化问题,给出了一种网格精细化策略,以提高控制质量.补料分批反应器最优控制问题的仿真实验验证了所提出方法的有效性.     

基于列队竞争算法的多杂质水网络集成优化

对于多杂质的用水和水处理集成优化问题,建立了以总费用最小为目标的混合整数非线性规划(MINLP)模型,并提出了一种将列队竞争算法(Line-up competition algorithm,LCA)和序列二次规划(Sequential Quadratic Programming,SQP)法相结合的求解策略。其中,用LCA优化整数变量,而用SQP法优化连续变量,通过这两种方法的交替求解来逼近最优解。将所提出的计算方法对文献中的2个典型实例进行了求解,求解结果优于文献。实例计算表明,本文所提出的计算方法是有效的。     

一种双足机器人实时步态规划方法及相关数值算法

针对步行双足机器人实时步态规划问题,提出了一种改进的非线性模型预测控制（NMPC）方法．采用扩展的关节坐标,将单腿支撑相（SSP）和双腿支撑相（DSP）统一表示为一个非线性动力学模型．通过对SSP和DSP的3个阶段设定运动学和动力学虚拟约束,将复杂实时步态规划问题转化为4个以预测时域内控制量二次型为代价函数的NMPC问题．采用直接法将连续优化问题参数化为有限维优化问题,并采用惩罚函数法将状态变量约束转化为代价函数中的惩罚项,从而得到能够用渐进二次规划（SQP）求解的有限维静态优化问题．仿真结果表明,应用该方法对BIP机器人模型进行实时步态规划,实现了包含足部转动的动态步行,且机器人满足稳定性条件,不发生侧滑,从而证明了该方法的有效性和可实现性．     

多体动力学优化的并行SQP方法

并行计算的发展大大提高计算机的计算效率,降低计算时间.针对多体动力学的优化问题,分析了求解灵敏度的三种方法的并行性,建立了有限差分法与直接微分法的并行算法.同时采用并行Armijo线性搜索,构成了完整的并行序列二次规划(SQP)算法.将上述算法应用到曲柄滑块的优化中,并与串行SQP算法进行了比较,证实了并行SQP算法可以大大降低计算时间.上述研究为多体动力学优化提供了一种并行求解思路.     

基于伪谱法的滑翔轨迹多级迭代优化策略

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补序列二次规划算法在求解大规模非线性规划问题过程中,出现的初值敏感、收敛速度减慢等问题。通过与传统方法求解出的状态量与控制量仿真飞行状态进行对比,证明了多级迭代优化策略的有效性和高效性,该策略在实际工程应用中取得了良好效果。     

机械臂最优运动规划问题的混合求解

提出一种基于GA和SQP求解机械臂最优运动规划问题的混合算法．首先采用B样条函数逼近关节运动轨迹，将最优控制问题转化为有约束的非线性规划问题，然后引入基于种群的GA算法，给出全局最优解的初始估计；最后利用序列二次规划(SQP)得到高精度全局最优解．仿真结果表明该方法优于单纯的GA或SQP方法。     

基于SQP/GA混合优化算法的双容水箱非线性预测控制

为了计算控制序列，非线性模型预测控制可以转换为一个带约束的非线性优化过程．本文分析了三种约束处理方案，根据遗传算法的特点，将等式约束用于状态量计算，在搜索空间降维的同时消除遗传算法难以求解的等式约束．对双容水箱进行遗传算法和序列二次规划仿真试验和实际控制，结果表明遗传算法对控制量的优化效果优于序列二次规划．为克服遗传算法耗时较长、优化结果存在随机抖动的缺点，结合序列二次规划提出一种混合优化算法，仿真和实控结果表明其可行性和有效性．     

基于FPGA的非线性预测控制器设计

对于非线性程度较高的复杂对象,非线性模型预测控制（NonlinearModelPredictiveControl,NMPC）是一种有效的控制策略。为了实现对这类对象的有效控制,设计了一种基于FPGA（FieldProgrammableGateArray）的非线性预测控制器,该嵌入式控制器具有灵活性和高适应性等特点,能够应用于工业现场控制。为了满足工业控制的可行性和实时性要求,提出了一种序贯二次规划（SQP）算法的改进算法,在FPGA有限的计算资源下,保证每个采样间隔内都能得到NMPC优化问题的可行解。经仿真实验证明,采用非线性预测控制器在计算速度和精度上都能达到较好的性能。     

Explicit output-feedback nonlinear predictive control based on black-box models

Nonlinear model predictive control (NMPC) algorithms are based on various nonlinear models. A number of on-line optimization approaches for output-feedback NMPC based on various black-box models can be found in the literature. However, NMPC involving on-line optimization is computationally very demanding. On the other hand, an explicit solution to the NMPC problem would allow efficient on-line computations as well as verifiability of the implementation. This paper applies an approximate multi-parametric nonlinear programming approach to explicitly solve output-feedback NMPC problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system. The verification of the NMPC controller performance is based on simulation experiments.     

Nonlinear model predictive control for models in quasi‐linear parameter varying form

This article presents a nonlinear model predictive control (NMPC) approach based on quasi‐linear parameter varying (quasi‐LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi‐LPV representations of the system using velocity‐based linearization is presented in two examples.     

Nonlinear model predictive control using trust-region derivative-free optimization

Gradient-based optimization may not be suited if the objective and constraint functions in a nonlinear model predictive control (NMPC) optimization problem are not differentiable. Some well-known derivative-free optimization (DFO)-algorithms are investigated, and a novel warm-start modification to the Wedge DFO-algorithm is proposed. Together with a gradient-based SQP-algorithm these are applied to the NMPC problem and compared in a single-shooting NMPC formulation to a subsea oil–gas separation process. The findings are that DFO is significantly more robust against the numerical issues, compared to a gradient-based SQP tested. Moreover, the warm-start modification reduces the computational complexity.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

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.     

Latent‐variable Nonlinear Model Predictive Control Strategy for a pH Neutralization Process

Linear model predictive control (MPC) is a widely‐used control strategy in chemical processes. Its extension to nonlinear MPC (NMPC) has drawn increasing attention since many process systems are inherently nonlinear. When implementing the NMPC based on a nonlinear predictive model, a nonlinear dynamic optimization problem must be calculated. For the sake of solving this optimization problem efficiently, a latent‐variable dynamic optimization approach is proposed. Two kinds of constraint formulations, original variable constraint and Hotelling T² statistic constraint, are also discussed. The proposed method is illustrated in a pH neutralization process. The results demonstrate that the latent‐variable dynamic optimization based the NMPC strategy is efficient and has good control performance.     

High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.     

A new SQP approach for nonlinear complementarity problems

Sequential quadratic programming (SQP) methods have been extensively studied to handle nonlinear programming problems. In this paper, a new SQP approach is employed to tackle nonlinear complementarity problems (NCPs). At each iterate, NCP conditions are divided into two parts. The inequalities and equations in NCP conditions, which are violated in the current iterate, are treated as the objective function, and the others act as constraints, which avoids finding a feasible initial point and feasible iterate points. NCP conditions are consequently transformed into a feasible nonlinear programming subproblem at each step. New SQP techniques are therefore successful in handling NCPs.