带不等式路径约束最优控制问题的惩罚函数法

控制变量参数化（Control variable parameterization,CVP）方法是目前求解流程工业中最优操作问题的主流数值方法,但如果问题中包含路径约束,特别是不等式路径约束时,CVP方法则需要考虑专门的处理手段.为了克服该缺点,本文提出一种基于L1精确惩罚函数的方法,能够有效处理关于控制变量、状态变量、甚至控制变量/状态变量复杂耦合形式下的不等式路径约束.此外,为了能使用基于梯度的成熟优化算法,本文还引进了最新出现的光滑化技巧对非光滑的惩罚项进行磨光.最终得到了能高效处理不等式路径约束的改进型CVP架构,并给出相应数值算法.经典的带不等式路径约束最优控制问题上的测试结果及与国外文献报道的比较研究表明:本文所提出的改进型CVP 架构及相应算法在精度和效率上兼有良好表现.     

热率约束下高超声速飞行器Gauss时间网格参数化轨迹规划

针对热率约束下高超声速飞行器(HV)再入轨迹规划, 提出一种结合光滑化不等式约束处理和非均匀Gauss离散时间网格的改进控制变量参数化(CVP)优化算法. 首先, 结合HV动力学方程和约束条件建立了HV再入轨迹优化问题; 然后, 采用光滑化函数对不等式路径约束进行处理并引入附加状态变量转化进微分方程中; 进一步, 在CVP算法框架下, 给出了基于Gauss分布的时间网格控制参数化策略, 以此改善HV攻角控制精度进而提升HV再入航程; 最后, 在通用航空器模型上进行仿真测试, 验证提出方法的性能并分析不同热率约束限值对最大航程规划的影响. 结果显示, 相较于均匀时间网格参数化CVP–S–P方法, 改进方法再入航程增加320.1 km(提升4.1%), 表明了改进算法的有效性; 同时, 基于本文方法仿真结果, 热率限值降低对HV最大航程减少有限, 当热率限值降低15%时, 最大航程损失仅3.16%, 展示了本文方法对HV热防护设计的理论价值.     

一种微处理机控制次优直流伺服系统

本文讨论用积分罚函数处理伺服系统控制变量不等式约束,研究了一种适合于微处理机 实现的次优综合方法,并给出了一个实例.数字仿真实验证明,这个综合方法是可行的.     

罚函数凸优化迭代算法及在无人机路径规划中的应用

针对无人机路径规划问题,建立了具有定常非线性系统、非仿射等式约束、非凸不等式约束的非凸控制问题模型,并对该模型进行了算法设计和求解。基于迭代寻优的求解思路,提出了凸优化迭代求解方法和罚函数优化策略。前者利用凹凸过程(CCCP)和泰勒公式对模型进行凸化处理,后者将经处理项作为惩罚项施加到目标函数中以解决初始点可行性限制。经证明该方法严格收敛到原问题的Karush-Kuhn-Tucker(KKT)点。仿真实验验证了罚函数凸优化迭代算法的可行性和优越性,表明该算法能够为无人机规划出一条满足条件的飞行路径。     

基于Oracle罚函数的自适应约束差分进化算法

为有效求解约束优化问题,减少算法参数,提出基于Oracle罚函数方法的自适应约束差分进化算法。为满足求解优化问题的常用标准,提出一种改进的Oracle罚函数方法。将改进的Oracle罚函数方法与三种自适应差分进化算法相结合,提出三种自适应约束差分进化算法。对11个典型测试函数的优化结果验证了Oracle罚函数方法与自适应差分进化算法结合的有效性。与参考文献中提出的算法的比较结果表明该方法具有良好的寻优性能,因此基于Oracle罚函数方法的自适应约束差分进化算法是一种有效约束优化方法。     

动态罚函数法求解约束优化问题

针对罚函数法在求解约束优化问题时罚系数不易选取的问题,提出一种基于动态罚函数的差分进化算法。利用罚函数法将约束优化问题转化为无约束优化问题。为平衡种群的目标函数和约束违反程度,结合[ε]约束法设计了一种动态罚系数策略,其中罚系数随着种群质量和进化代数的改变而改变。采用差分进化算法更新种群直到搜索到最优解。对IEEE CEC 2010和IEEE CEC 2017两组基准测试集进行仿真实验,结果表明提出的算法具有较强的寻优性能。     

动态优化问题的瞬态自适应麻雀搜索算法求解

动态优化普遍存在于工业过程控制领域,是实现系统稳态与产值最大化的重要手段,应用并发展更加高效的动态优化方法逐渐成为了当前研究的热点。鉴于此,提出一种基于瞬态自适应麻雀搜索算法（TASSA）的动态优化问题求解方案。首先,分析了原始麻雀搜索算法的缺陷,为了提升全局勘探能力,引入瞬态搜索策略指导加入者的寻优过程;其次,采用随迭代而变化的惯性权重调节具体的搜索方式,增强了算法的动态适应能力,并通过九组基准函数的数值测试确认了改进策略的有效性。最后,采用时域等分的方式,在控制变量参数化（CVP）的框架下利用TASSA对三组典型的动态优化问题进行求解,对比不同文献中的方法,所提算法取得了更精确的结果。     

采用不可微精确罚函数的约束优化演化算法

针对多数已有的采用罚函数的约束优化遗传算法存在优化效果差的问题 ,提出了一种新的求解约束优化问题的演化算法 .借助不可微精确罚函数把约束问题转化为单个无约束问题来处理 .采用混合杂交和间歇变异来提高算法的搜索能力 .数值实验结果表明了新算法的优化效果远远优于已有的几种采用罚函数的遗传算法     

一种关于目标罚参数的精确罚函数法

罚函数法是一种将约束优化问题转化为无约束问题的重要方法.对于一般的约束优化问题,通过加入新参数,给出了一种改进的精确罚函数和这种罚函数的精确罚定理证明,提出了求解这种罚函数的算法.实验表明该算法是有效的.     

含K类函数和附加控制量的自适应L2励磁控制

为了简化常规非线性自适应L_2增益控制计算和加快控制系统状态变量的稳定收敛速度,通过引入附加控制变量和K类函数,克服了每次虚拟函数设计时都要考虑γ–耗散不等式的不足,保证了L_2增益控制能力随误差变量的增加而增强,给出了一种含附加控制变量和K类函数的非线性自适应L_2增益控制的通式,并以具体军用电站谐波励磁系统为对象,进行了仿真实验.仿真结果表明,相对于传统L_2增益控制,该方法可提高状态变量的收敛速度,并可加强军用电站励磁系统的动态稳定性.     

Control variable parameterisation with penalty approach for hypersonic vehicle reentry optimisation

An efficient trajectory optimisation approach combining the classical control variable parameterisation (CVP) with a novel smooth technology and two penalty strategies is developed to solve the trajectory optimal control problems. Since it is difficult to deal with path constraints in CVP method, the novel smooth technology is firstly employed to transform the complex constraints into one smooth constraint. Then, two penalty strategies are proposed to tackle the converted path and terminal constraints to decrease the computational complexity and improve the constraints satisfaction. Finally, a nonlinear programming problem, which approximates the original trajectory optimisation problem, is obtained. Error analysis shows that the proposed method has good convergence property. A general hypersonic cruise vehicle trajectory optimisation example is employed to test the performance of the proposed method. Numerical results show that the path and terminal conditions are well satisfied and better trajectory profiles are obtained, showing the effectiveness of the proposed method.     

Dynamic optimization of dual-mode hybrid systems with state-dependent switching conditions

This paper presents a computational approach for optimizing a class of hybrid systems in which the state dynamics switch between two distinct modes. The times at which the mode transitions occur cannot be specified directly, but are instead governed by a state-dependent switching condition. The control variables, which should be chosen optimally by the system designer, consist of a set of continuous-time input signals. By introducing an auxiliary binary-valued control function to represent the system's current mode, we show that any dual-mode hybrid system with state-dependent switching conditions can be transformed into a standard dynamic system subject to path constraints. We then develop a computational algorithm, based on control parameterization, the time-scaling transformation, and an exact penalty method, for determining the optimal piecewise constant input signals for the original hybrid system. A numerical example on cancer chemotherapy is included to demonstrate the effectiveness of the proposed algorithm.     

基于改进微粒群优化的学习路径优化控制方法

对学生学习的路径控制在智能化教学系统中是一个重要的问题。该文以知识空间理论为基础建立了学习状态空间,通过改进的微粒群算法对该学习状态空间的学习路径进行最优化控制,并利用死亡惩罚函数法把约束最优化学习路径问题转化成了无约束的最优化学习路径控制问题,引入交换子和交换序的概念对微粒群算法进行改进。在结果分析中,通过动态参数法,即动态变化交换子保留概率的方法提高微粒群的收敛效果,达到了最优化学习路径控制的目的。     

Cohort intelligence algorithm for discrete and mixed variable engineering problems

Abstract

In this study, the performance of an emerging socio inspired metaheuristic optimization technique referred to as Cohort Intelligence (CI) algorithm is evaluated on discrete and mixed variable nonlinear constrained optimization problems. The investigated problems are mainly adopted from discrete structural optimization and mixed variable mechanical engineering design domains. For handling the discrete solution variables, a round off integer sampling approach is proposed. Furthermore, in order to deal with the nonlinear constraints, a penalty function method is incorporated. The obtained results are promising and computationally more efficient when compared to the other existing optimization techniques including a Multi Random Start Local Search algorithm. The associated advantages and disadvantages of CI algorithm are also discussed evaluating the effect of its two parameters namely the number of candidates, and sampling space reduction factor.     

基于滚动时域的无人机动态航迹规划

针对带有动力学约束的多旋翼无人机航迹规划问题,提出了一种基于滚动时域控制和快速粒子群优化(RHC-FPSO)方法。该方法引入了基于VORONOI图的代价图方法说明从航迹端点到达目标点的距离估计。根据滚动时域和人工势场法的思想,将路径规划问题转化为优化问题,以最小距离和其他性能指标为代价函数。设计评价函数准则,按照评价准则使用变权重粒子群优化算法求解。针对无人机靠近危险区飞行的问题,将斥力场引入到代价函数中,提升其安全性。仿真实验结果显示,使用文中方法可以有效地在满足约束条件下穿过障碍物区域,以及在复杂环境下可以动态计算。     

Exact solutions to some minimum time problems with inequality state constraints

A heuristic method is developed for generating exact solutions to certain minimum time problems, with inequality state and control constraints. The control equation is linear and autonomous, with scalar-valued control. The state constraints are also linear inequalities. Assuming knowledge of a finite sequence, in which state and/or control constraints become active along an optimal path, the maximum principle is reduced to a set of equations and inequalities in a finite number of unknowns. A solution to the equations and inequalities determines both the solution path and a proof of its optimality. Certain types of constraint sequences lead to overdetermined equation systems, and this fact is interpreted in terms of the qualitative behavior of solutions to these problems. Two path-planning problems are solved, as illustrations of the solution technique.     

Time/fuel optimal control of constrained linear discrete systems

A unified approach to solving three common optimal control problems is presented, for linear systems under general constraints. The problems are: (1) the time optimal control problem; (2) the fuel optimal control problem in fixed time; (3) the time optimal control problem with a fuel constraint. A special purpose linear programming algorithm is used. State variable constraints are efficiently handled by a cutting plane algorithm. An example of a sixth order system with two inputs and two state variable constraints illustrates the method as implemented on a personal computer.     

An exact penalty function algorithm for control problems with state and control constraints

This paper describes an exact penalty function algorithm for solving control problems with state, control, and terminal constraints and establishes its convergence properties. A convex optimal control problem is defined whose solution yields a search direction which satisfies the control constraints and reduces a first-order estimate of the exact penalty function. Step length is determined using an Armijo-like procedure. An adaptive procedure for adjusting the penalty parameter completes the algorithm.     

Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .