双层预测控制中保证动态控制可行的稳态目标计算策略

在双层结构模型预测控制(Model predictive control, MPC)中, 稳态目标计算(Steady-state targets calculation, SSTC)层(上层)为动态控制(Dynamic control, DC)层(下层)提供操作变量、被控变量设定值和变量约束. 但是,上层可行域和下层吸引域间存在的不一致性可能使得上层给出的设定值无法实现. 本文为下层事先选取若干组放松的软约束, 并对每一组软约束都离线计算出相应的吸引域, 其中最大的一个吸引域包含稳态目标计算的可行域. 在控制过程中, 根据当前状态所属吸引域在线地决定在DC层采用的软约束组. 采用上述方法后, 对所有处于最大吸引域的初始状态, 在跟踪稳态目标的过程中, 下层优化问题都是可行的. 仿真算例证明了该方法的有效性.     

基于最小方差基准的软约束调整与经济性能协调

模型预测控制的经济性能主要通过减少关键工艺参数的方差,以及移动过程的操作点使其更接近约束边界来实现。另一方面,软约束边界需要经常的调整以有效地解决模型预测控制的优化不可行问题。在协调软约束调整与模型预测控制的经济性能的过程中,本文提出了将基于性能评估的最小方差引入到模型预测控制的稳态目标计算中,以保证模型预测控制能够更加合理地提高系统的经济性能。最后,以延迟焦化装置加热炉预测控制为例,讨论和分析了该方法的有效性。     

带有优先级的分层满意优化控制算法研究

满意控制作为预测控制的实用发展,是基于模型在线实现有约束多目标多自由度优化（CMMO）,并由操作者参与决策的一种实用控制方法。针对有约束多目标多自由度优化中输出变量逼进期望值时存在的优先级结构,将一般的用二次规划表示的满意优化控制问题转化为一个分两层进行的直接优先级优化的满意优化控制问题,使用宽容分层优化方法进行分层,使用变可行域优化方法进行每层的优化,最终决策者得到满意解。     

具有先应性最优通道传输的车载网络研究分析

为解决车载网络中频谱感知和动态频谱管理问题,改善车载网络中无线电频谱信道中有效感知和数据传输性能,提出了一种预测控制的认知无线电（CR）车载网络。对所有预测变量,设定点计算的约束变量或目标值的期望值;根据目标期望值,在基于模型预测控制（MPC）框架中,通过控制计算预测变量的概率,使用数学模型计算预测变量在现实系统中的概率;基于现实系统预测做出决策操作,并将操作结果进行反馈,通过反馈提高预测质量。仿真实验结果表明：与抢占式MAC方法和反应式信道分配方法相比,提出方法的控制消息能耗更低,次级用户节点需要感知的信道数量更少,信道利用率得到增强。因此,可实现一个高效的CR车载网络。     

带有优先级的分层满意优化控制算法研究

满意控制作为预测控制的实用发展,是基于模型在线实现有约束多目标多自由度优化(CMMO),并由操作者参与决策的一种实用控制方法.针对有约束多目标多自由度优化中输出变量逼进期望值时存在的优先级结构,将一般的用二次规划表示的满意优化控制问题转化为一个分两层进行的直接优先级优化的满意优化控制问题,使用宽容分层优化方法进行分层,使用变可行域优化方法进行每层的优化,最终决策者得到满意解.     

预测控制动态过程对控制目标可达性影响分析

预测控制作为应用最广泛的先进控制策略,在复杂的工业过程控制中占据重要地位。预测控制可行域的确定是系统实施控制的先决条件。为保证控制效果,系统输出变量要一直保证在可行域内,且要求在系统稳定的情况下可行域内均可达。在实际控制过程中,可行域内系统输出的稳态值与目标设定值存在稳态误差的情况时有发生。系统实际的可达区域与可行域存在差异。可行域的变化,势必对控制效果产生重要影响。因此,需要在系统稳态条件决定的可行域的基础上,分析预测控制的动态过程对系统可行域的影响。为避免影响,需要设定新的目标值以保证目标可达。本文将以映射的思想充分分析预测控制算法的动态过程,证明输出变量动态响应对系统可行性的影响,提出满足约束条件下充分可达的设定值选取规则。     

优先级多目标稳定化约束模型预测控制

针对目标函数的不同优先级问题, 提出一种约束多变量线性定常系统的稳定化多目标模型预测控制策略. 首先, 基于多目标优化理论给出多目标预测控制问题的字典序最优解结果, 并在此基础上考虑目标函数的优先级, 重 新将多目标预测控制问题定义为字典序多目标预测控制问题; 然后, 采用终端约束、终端罚函数和局部状态反馈律 等三要素, 证明多目标预测控制闭环系统是渐近稳定的; 最后, 通过一个仿真实例验证了所提出方法的有效性.

     

多变量预测控制系统稳态解的相容性与唯一性分析

多变量控制系统在结构形态上可以划分为方系统和非方系统, 非方系统可进一步划分为胖系统和瘦系统. 对瘦系统和胖系统, 预测控制系统分别可能出现输出静差和输入稳态值不确定问题. 本文从控制输入与被控输出稳态关系入手, 将上述问题归结为非齐次线性方程组的相容性与唯一性问题. 通过非齐次方程组解的判定定理分析了多变量预测控制系统稳态解出现相容性和唯一性问题的原因, 并由此给出了双层结构控制策略及解决方案. 上层稳态优化方法从理论上解决了瘦系统的相容性问题, 并从胖系统的无穷多个相容解中找到最优解. 下层集成控制输入目标的预测控制从根本上保证了胖系统控制输入稳态解的唯一性, 并实现了方系统与非方系统预测控制在算法描述上的统一. 仿真结果验证了本文提出的双层结构预测控制算法的有效性, 即多变量预测控制系统稳态解既是相容的又是唯一的.     

一类对称非线性系统的约束自校正控制器

针对MIMO随机广义Hammerstein模型,从实际工程对象的物理意义出发,分析了其不能描述＂对称非线性系统＂的问题。在模型中加入控制输入的符号函数,提出一可描述＂对称非线性系统＂的MIMO随机广义Hammerstein模型。在目标函数中加入控制输入的高次项和其符号函数提出一超二次型目标函数。对控制输入加入饱和限幅限制,给出了改进的MIMO随机广义Hammerstein模型的约束自校正控制器算法,适用于开环不稳定的＂非最小相位＂系统。提出一控制策略使算法无稳态偏差,且控制输入收敛于以原点为中心的变化域内。采用约束最优化的投影梯度法和无约束最优化的变尺度算法对目标函数寻优,证明了可行域内所有点均可作为投影梯度算法的初始可行点,并证明了线性不等式约束的任意紧约束组合时其可行域即为正则域。仿真研究表明了上述研究的合理性和有效性。     

性能维持的增广可行域Tube鲁棒经济模型预测控制

针对未知但有界扰动作用下的约束线性系统,提出一种性能维持的增广可行域Tube经济模型预测控制(tube economic model predictive control,TEMPC)策略.首先考虑经济性能优化目标和鲁棒稳定控制目标,构造TEMPC优化问题的隐式收缩约束,并对系统状态和控制约束进行紧缩Tube设计,给出增广可行域优化问题的数学描述;然后,引入线性分解增广名义终端状态和终端罚函数,扩大优化问题的初始可行域,在此基础上应用终端“三要素”和收缩原理,建立TEMPC策略的递推可行性和闭环系统关于最优经济平衡点有界稳定性的充分性条件,进而证明闭环性能在原初始可行域上的不变性;最后,通过对比仿真结果验证所提出策略的有效性和优越性.     

Analyzing the Simple Ranking and Selection Process for Constrained Evolutionary Optimization

Many optimization problems that involve practical applications have functional constraints,and some of these constraints are active,meaning that they prevent any solution from improving the objective function value to the one that is better than any solution lying beyond the constraint limits.Therefore,the optimal solution usually lies on the boundary of the feasible region.In order to converge faster when solving such problems,a new ranking and selection scheme is introduced which exploits this feature ...     

Discrete optimal control with multiple constraints I Constraint separation and transformation technique

The discrete optimal control problem with multiple inequality constraints on functions of the state and/or control variables is presented. A new transformation technique for dealing with problems in which the number of constraint functions does not exceed the number of control variables is derived. The application of this technique results in a set of control constrained system equations of the same dimensionality as the original system equations.This transformation technique is then extended by the introduction of the principle of constraint separation to cater for the more general problem in which the constraint functions outnumber the control variables. It is shown that the time interval may be split up into segments over which the number of dominant constraints does not exceed the number of control variables. The necessary conditions for extremals and the interpoint boundary conditions at the switchover points are derived and a numerical switching algorithm is presented. It is shown that the state and adjoint variables are single-valued at the switchover points and that all sub-optimal trajectories are feasible in that they will not violate the constraints imposed.Two practical examples are solved in which the constraint functions outnumber the control variables. The solution to the second example is compared with that obtained by using a penalty function approach.     

解约束优化问题的一种新的罚函数模型

罚函数法是进化算法中解决约束优化问题最常用的方法之一,它通过对不可行解进行惩罚使得搜索逐步进入可行域.罚函数常定义为目标函数与惩罚项之和,其缺陷一方面在于此模型的罚因子难以控制,另一方面当目标函数值与惩罚项的函数值的差值很大时,此模型不能有效地区分可行解与不可行解,从而不能有效处理约束.为了克服这些缺点,首先引入了目标满意度函数与约束满意度函数,前者是根据目标函数对解的满意度给出的一个度量,而后者是根据约束违反度对解的满意度给出的一个度量.然后将两者有机结合,定义了一种新的罚函数,给出了一种新的罚函数模型.并且设置了自适应动态罚因子,其随着当前种群质量和进化代数的改变而改变.因此它很易于控制.进一步设计了新的杂交和变异算子,在此基础上提出了解决约束优化问题的一种新的进化算法.通过对6个常用标准测试函数所作的数据仿真实验表明,提出的算法是十分有效的.     

Self-organizing adaptive penalty strategy in constrained genetic search

This research aims to develop an effective and robust self-organizing adaptive penalty strategy for genetic algorithms to handle constrained optimization problems without the need to search for appropriate values of penalty factors for the given optimization problem. The proposed strategy is based on the idea that the constrained optimal design is almost always located at the boundary between feasible and infeasible domains. This adaptive penalty strategy automatically adjusts the value of the penalty parameter used for each of the constraints according to the ratio between the number of designs violating the specific constraint and the number of designs satisfying the constraint. The goal is to maintain equal numbers of designs on each side of the constraint boundary so that the chance of locating their offspring designs around the boundary is maximized. The new penalty function is self-defining and no parameters need to be adjusted for objective and constraint functions in any given problem. This penalty strategy is tested and compared with other known penalty function methods in mathematical and structural optimization problems, with favorable results.     

Constrained efficient global optimization with support vector machines

This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based ??probability of feasibility?? using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the ??expected improvement?? of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.     

Viscosity solutions and optimal control problems with integral constraints

We discuss optimal control problems with integral state-control constraints. We rewrite the problem in an equivalent form as an optimal control problem with state constraints for an extended system, and prove that the value function, although possibly discontinuous, is the unique viscosity solution of the constrained boundary value problem for the corresponding Hamilton–Jacobi equation. The state constraint is the epigraph of the minimal solution of a second Hamilton–Jacobi equation. Our framework applies, for instance, to systems with design uncertainties.     

An interior feasible direction method with constraint projections for linear programming

A new feasible direction method for linear programming problems is presented. The method is not boundary following. The method proceeds from a feasible interior point in a direction that improves the objective function until a point on a constraint surface is met. At this point searches are initiated in the hyperplane of constant function value by using projections of the bounding constraints until n bounding constraints are identified that yield a vertex as candidate solution. If the vertex is not feasible or feasible with a worse function value, the next iteration is started from the centre of the simplex defined by the identified points on the bounding constraint surfaces. Otherwise the feasible vertex is tested for optimality. If not optimal a perturbed point with improved function value on an edge emanating from the vertex is calculated from which the next iteration is started. The method has successfully been applied to many test problems.     

Regularity properties of solutions to linear quadratic optimal control problems with state constraints

We establish regularity properties of solutions of linear quadratic optimal control problems involving state inequality constraints. Under simply stated and directly verifiable hypotheses on the data, it is shown that if the state constraint has index k> 0 then the optimal control is k times differentiable; the kth derivative may be discontinuous but it is a function of bounded variation (and consequently it has left and right limits at each point in its domain). If on the other hand the state constraint has index k = 0 then the optimal control is continuous. The latter property is perhaps surprising because it implies that for the class of problems considered optimal state trajectories cannot abruptly change direction when they strike the boundary of the state constraint region. These findings are significant because they justify assumptions which underlie analysis of junction conditions (i.e. properties of state trajectories at contact points with the boundary of the state constraint set) provided elsewhere in the literature.     

基于收缩约束模型预测控制的无人车辆路径跟踪

针对存在有界扰动的非线性无人驾驶车辆避障过程中最优路径规划跟踪问题,提出一种基于预测时域内系统输入输出收缩约束(PIOCC)的模型预测控制(MPC)方法.首先在构建目标函数时,为扩大可行性解的范围引入软约束思想,将最优规划路径的跟随问题转化为对模型预测控制优化问题的求解;其次为避免短预测时域造成闭环系统发散而导致在约束条件限定下出现无可行性解的情况,采用预测时域内系统输入输出收缩约束的方法,设计模型预测控制器;再次基于Lyapunov稳定性理论证明所设计的模型预测闭环控制系统是渐近稳定的;最后通过仿真实例验证了所提出基于PIOCC的控制策略在解决扩大可行解范围和避免闭环系统发散问题时的有效性,实现了无人驾驶车辆在路径跟踪时具有良好的快速性和稳定性.