基于序列二次规划的非线性不等式状态约束滤波算法

针对非线性不等式状态约束滤波问题,提出一种基于序列二次规划的迭代不敏卡尔曼滤波算法。在迭代不敏卡尔曼滤波的基础上,采用序列二次规划优化法求解非线性不等式约束条件下的最优解。通过对每一次迭代求解二次规划子问题来确定下降方向,重复该步骤直到求得原问题的解,利用效益函数对目标函数最小化和不等式约束条件进行权衡,以保证算法的收敛性,利用正定矩阵近似海森矩阵降低时间复杂度。对具有约束的航路跟踪系统进行实验仿真,结果表明,该算法在处理非线性不等式状态约束滤波问题时,能够有效地提高状态估计精度,获得较高的滤波精度,且时间复杂度较低。     

基于信赖域二次规划的非线性模型预测控制优化算法

针对非线性预测控制如何在有限时域内有效的求解非凸非线性规划这一关键问题, 本文采用序列二次规划方法, 将非线性规划转化为一系列二次子规划求解. 首先根据非线性规划联立方法将系统状态和控制量同时作为优化变量, 得到以控制量步长为优化变量, 只包含不等式约束的子二次规划问题, 并用它取代原SQP子规划, 减小了子问题的规模; 随后采用基于信赖域二次规划的方法求解子规划问题, 保证每次迭代的可行性; 同时采用一种能够保持SQP问题Hessian矩阵稀疏结构的更新方法, 也在一定程度上降低了算法的复杂程度.最后的仿真结果表明了该方法的有效性.     

基于多参数规划的显式模型预测系统设计的可行域扩张算法

基于约束线性优化控制问题的多参数二次规划求解方法, 提出设计显式模型预测控制系统的可行域逐步扩张算法. 首先建立一种求取优化控制问题输出不变集的迭代算法. 以该输出不变集作为多参数规划问题中状态区域约束限制的初始条件, 通过反复求解多参数规划问题和不断改变状态区域约束限制, 能够逐步扩大显式模型预测控制系统的无限时间可行区域, 直到可行域不再继续扩大. 算法收敛时设计得到的显式模型预测控制系统在其所有的状态分区上都是无限时间可行的. 通过数值仿真计算, 验证本文提出算法的有效性.     

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.     

永磁同步电机高效非线性模型预测控制

永磁电机控制器要求电机有很强的转速跟踪能力,并且要保证系统参数变化及负荷扰动下系统的鲁棒性. 永磁电机包含很多不确定因素,是强耦合的非线性系统,传统的线性控制器很难对其进行控制. 针对永磁电机的转速控制构造非线性模型预测控制方法. 非线性永磁电机模型通过输入-输出反馈线性化策略解耦成为新的线性系统. 为保证可行解的收敛性,提出一种迭代二次规划方法来处理由输入-输出反馈线性化导致的非线性约束. 仿真结果表明,控制器能有效降低计算负担,具有很好的动态控制性能,能抑制转矩脉动,并保证在参数变化和负荷扰动下控制系统的鲁棒性.     

一类控制受约束非线性系统的基于单网络贪婪迭代DHP算法的近似最优镇定

提出一种贪婪迭代DHP (Dual heuristic programming)算法, 解决了一类控制受约束非线性系统的近似最优镇定问题. 针对系统的控制约束, 首先引入一个非二次泛函把约束问题转换为无约束问题, 然后基于协状态函数提出一种贪婪迭代DHP算法以求解系统的HJB (Hamilton-Jacobi-Bellman)方程. 在算法的每个迭代步, 利用一个神经网络来近似系统的协状态函数, 而后根据协状态函数直接计算系统的最优控制策略, 从而消除了常规近似动态规划方法中的控制网络. 最后通过两个仿真例子证明了本文提出的最优控制方案的有效性和可行性.     

约束Hammerstein系统非线性预测控制及在聚丙烯牌号切换中的仿真研究

对状态和输入受约束的Hammerstein系统, 提出一种新的可保证闭环指数稳定的非线性模型预测控制策略. 基于线性子系统镇定的最优控制律, 滚动预测非线性代数方程的解算误差, 继而在线优化计算满足约束的预测控制量. 进一步, 得到闭环系统指数稳定的解算误差上界. 从而闭环系统不仅满足约束而且对解算误差具有鲁棒性. 最后以工业聚丙烯牌号切换控制为例, 仿真验证本文算法的有效性.     

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.     

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SVM和PSO的新型非线性模型预测控制

对于具有强非线性或复杂非线性约束的系统,通过非线性模型的线性化和二次规划优化实现非线性模型预测控制,难以取得满意的结果。提出了一种基于支持向量机模型和粒子群优化的非线性模型预测控制系统的算法。仿真实例表明了支持向量机模型的泛化能力和粒子群优化的寻优速度及能力,证明了将其运用于非线性模型预测控制中的可行性。     

Predictive control based on neural network models with I/O feedback linearization

This paper presents an approach for the constrained non-linear predictive control problem based on the input-output feedback linearization (IOFL) of a general non-linear system modelled by a discrete-time affine neural network model. Using the resulting linear system in the formulation of the original non-linear predictive control problem enables to restate the optimization problem as the minimization of a quadratic function, which solution can be found using reliable and fast quadratic programming (QP) routines. However, the presence of a non-linear feedback linearizing controller maps the original linear input constraints onto non-linear and state dependent constraints on the controller output, which invalidates a direct application of QP routines. In order to cope with this problem and still be able to use QP routines, an approximate method is proposed which simultaneously guarantees a feasible solution without constraints violation over the complete prediction horizon within a finite number of steps, while allowing only for a small performance degradation.     

A New Optimal Force Distribution Scheme of Multiple Cooperating Robots Using Dual Method

A new optimal force distribution scheme of multiple cooperating robots is proposed, in which the duality theory of nonlinear programming (NLP) is combined with the quadratic programming (QP) approach. The optimal force distribution problem is formulated as a QP problem with both linear and quadratic constraints, and its solution is obtained by an efficient algorithm. The use of the quadratic constraints is important in that it considerably reduces the number of constraints, thus enabling the Dual method of NLP to be used in the solution algorithm. Moreover, it can treat norm constraints without approximation, such as bound of the norm of the force exerted by each robot. The proposed scheme is more efficient in terms of speed than any other method. Numerical examples of two PUMA robot task using the proposed method and a well-known fast method are compared, and the results indicate the capability of real time application of our method.     

Comment on “Stability of linear stationary systems with time delay”

Quadratic programming (QP) has previously been applied to the computation of optimal controls for linear systems with quadratic cost criteria. This paper extends the application of QP to non-linear problems through quasi-linearization and the solution of a sequence of linear-quadratic sub-problems whose solutions converge to the solution of the original non-linear problem. The method is called quasi-linearization-quadratic programming or Q-QP.

The principal advantage of the Q-QP method lies in the ease with which optimal controls can be computed when saturation constraints are imposed on the control signals and terminal constraints are imposed on the state vector. Use of a bounded-variable QP algorithm permits solution of constrained problems with a negligible increase in computing time over the corresponding unconstrained problems. Numerical examples show how the method can be applied to certain problems with non-analytic objective functions and illustrate the facility of the method on problems with constraints. The Q-QP method is shown to be competitive with other methods in computation time for unconstrained problems and to be essentially unaffected in speed for problems having saturation and terminal constraints     

An approximated scalar sign function approach to optimal anti-windup digital controller design for continuous-time nonlinear systems with input constraints

This article presents an approximated scalar sign function-based digital design methodology to develop an optimal anti-windup digital controller for analogue nonlinear systems with input constraints. The approximated scalar sign function, a mathematically smooth nonlinear function, is utilised to represent the constrained input functions, which are often expressed by mathematically non-smooth nonlinear functions. Then, an optimal linearisation technique is applied to the resulting nonlinear system (with smooth nonlinear input functions) for finding an optimal linear model, which has the exact dynamics of the original nonlinear system at the operating point of interest. This optimal linear model is used to design an optimal anti-windup LQR, and an iterative procedure is developed to systematically adjust the weighting matrices in the performance index as the actuator saturation occurs. Hence, the designed optimal anti-windup controller would lie within the desired saturation range. In addition, the designed optimal analogue controller is digitally implemented using the prediction-based digital redesign technique for the effective digital control of stable and unstable multivariable nonlinear systems with input constraints.     

An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity

In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported.     

When does QP yield the exact solution to constrained NMPC?

It is well known that the optimal control sequence for a linear system with a quadratic cost and linear inequality constraints over a finite optimisation horizon can be computed by means of a quadratic programme (QP). The aim of this article is to investigate when the optimal control sequence for a non-linear single-input single-output system also can be computed via QP. Our main contribution is to show that the optimal control sequence for non-linear systems, with a quadratic cost and linear inequality constraints can be computed in exact form via QP provided the optimisation horizon is no larger than a critical quantity that we name the ‘input–output linear horizon’. The results do not require any linearisation technique and are applicable to general non-linear systems, provided their input–output linear horizon is larger than their relative degree.     

CLF-CBF-QP新形式下非线性系统的安全攸关控制与优化

利用二次规划(QP)结合控制Lyapunov函数(CLF)和控制障碍函数(CBF)形成非线性系统的一种安全攸关控 制策略, 称为CLF-CBF-QP, 其在实现控制目标和确保安全之间起到协调作用. 然而, 一旦引入附加的约束, 如输入 约束, QP求解可能变得不可行. 另外, 当考虑系统本身的体积或环境中存在快速移动的障碍物时, 动态系统与障碍 物发生碰撞的可能性会极大地提高. 因此, 本文首先从控制输入空间和状态空间的角度分别分析QP求解可行性以 及CLF和CBF中参数对QP求解可行性和系统性能的影响, 并提出一种CLF-CBF-QP新形式来提高优化问题的可解 性; 其次, 在考虑动态系统本身的体积且环境中存在动态障碍物时, 设计一种CBF新形式使其仍能保证系统的安全 性; 最后, 通过线性平面四旋翼在存在动态或静态障碍物的环境中进行轨迹跟踪来验证所提出方法的有效性.     

Solving the stochastic support vector regression with probabilistic constraints by a high-performance neural network model

This paper offers a recurrent neural network to support vector machine (SVM) learning in stochastic support vector regression with probabilistic constraints. The SVM is first converted into an equivalent quadratic programming (QP) formulation in linear and nonlinear cases. An artificial neural network for SVM learning is then proposed. The presented neural network framework guarantees obtaining the optimal solution of the SVM problem. The existence and convergence of the trajectories of the network are studied. The Lyapunov stability for the considered neural network is also shown. The efficiency of the proposed method is shown by three illustrative examples.

     

Dinkelbach NCUT: An Efficient Framework for Solving Normalized Cuts Problems with Priors and Convex Constraints

In this paper, we propose a novel framework, called Dinkelbach NCUT (DNCUT), which efficiently solves the normalized graph cut (NCUT) problem under general, convex constraints, as well as, under given priors on the nodes of the graph. Current NCUT methods use generalized eigen-decomposition, which poses computational issues especially for large graphs, and can only handle linear equality constraints. By using an augmented graph and the iterative Dinkelbach method for fractional programming (FP), we formulate the DNCUT framework to efficiently solve the NCUT problem under general convex constraints and given data priors. In this framework, the initial problem is converted into a sequence of simpler sub-problems (i.e. convex, quadratic programs (QP’s) subject to convex constraints). The complexity of finding a global solution for each sub-problem depends on the complexity of the constraints, the convexity of the cost function, and the chosen initialization. However, we derive an initialization, which guarantees that each sub-problem is a convex QP that can be solved by available convex programming techniques. We apply this framework to the special case of linear constraints, where the solution is obtained by solving a sequence of sparse linear systems using the conjugate gradient method. We validate DNCUT by performing binary segmentation on real images both with and without linear/nonlinear constraints, as well as, multi-class segmentation. When possible, we compare DNCUT to other NCUT methods, in terms of segmentation performance and computational efficiency. Even though the new formulation is applied to the problem of spectral graph-based, low-level image segmentation, it can be directly applied to other applications (e.g. clustering).