多引力场小推力引力借力轨道设计与优化

采用序贯法设计优化小推力引力借力轨道(low-thrust gravity-assist,LTGA)时,设计步骤复杂且优化结果最优性条件难以保证.本文提出一种多引力场LTGA问题联立求解框架.首先对多引力场环境和探测器动力学模型进行统一描述和处理.设计初始化策略,利用Radau伪谱法将发射窗口、借力顺序、初始轨道搜索以及轨道优化联立求解,简化设计步骤.利用hp自适应网格精细化策略保证优化结果最优性条件.该联立框架用于求解地木转移任务,得到地球–火星–地球–木星的转移方案.本文提出的联立求解框架,简化了设计步骤,保证了优化结果的最优性条件,得到比序贯求解更优的转移方案.     

自主泊车的全联立动态优化方法

本文提出联立框架下的自主泊车动态优化方法.不同于通常采用的几何方法,该联立方法对障碍环境和车辆模型进行统一的描述和处理.提出基于互补约束的数学规划方法(MPCC)与R函数方法描述泊车过程的避障条件约束,并联立车辆的运动学、动力学、相关物理约束建立行车系统模型;在此基础上以运动学相关的最短时间为优化目标,构造泊车轨迹动态优化命题;基于有限元正交配置离散化方法实现该动态问题的精确求解,得到具有时间信息的、可直接用于指导车辆操作的泊车轨迹.多种泊车位情形下的数值试验验证了本文方法的有效性.     

改进的嵌套分区算法求解旅行商问题

嵌套分区算法是近年来提出的一种求解大规模优化问题的新型全局优化方法。介绍了嵌套分区算法（NPM）的基本思想,将其应用于求解旅行商问题。分析确定了嵌套分区算法各个算子的策略,提出了一种改进的嵌套分区算法。该算法采用加权抽样法求得初始最可能域,用全局数组记录下每个区域的历史最优解,用3-opt局部搜索算法改进每个区域解的质量。对TSPLIB中部分实例仿真结果表明,所提出的结合3-opt算法的改进嵌套分区算法在求解 TSP问题时可以获得高质量的解。     

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。     

基于嵌套分区算法的立体仓库货位分配优化

根据小型立体化仓库运营特点,基于顺序单目标优化思想,提出一种新的仓库货位分配策略。将考虑存储能耗、货架稳定性、运行效率的多目标仓库货位优化问题,转化为单目标优化,建立了仓库货位优化数学模型。根据数学模型特点,采用嵌套分区算法进行优化求解。通过算例分析证明该分配策略与优化方法,可有效处理多目标仓库库位优化问题,优化效果显著。     

双种群灰狼优化算法的物流配送中心选址策略

针对物流配送中心选址模型具有多约束和非线性的特点,导致难以求解的问题.提出一种改进灰狼优化算法的求解策略.文章通过引入交叉变异策略,改进了传统灰狼算法在迭代后期易早熟收敛的问题;通过加入双种群寻优策略,丰富了灰狼算法的种群多样性,提高了算法的收敛速度.将改进后的灰狼算法针对物流配送中心选址模型进行求解,实验结果表明,该改进灰狼优化算法具有较高的全局搜索能力,针对物流配送中心选址模型具有较高的搜索精度,很大程度的提高了物流配送效率.     

基于包络切换的四旋翼吊挂无人机避障轨迹优化研究

考虑非圆避障区域以及吊挂载荷摆动导致的包络圆切换,开展四旋翼吊挂无人机避障飞行轨迹优化研究.首先,通过互补约束对拉紧-松弛系绳进行统一描述,建立了吊挂四旋翼无人机系统的整体动力学模型;而后,采用R函数建立了不同包络圆情形下的统一避障约束方程,使用碰撞检测算法计算包络圆与障碍物的距离,并通过非线性最优控制方法建立了吊挂无人机避障轨迹优化数学模型;继而利用Legendre-Gauss-Radau伪谱法将开环非线性最优控制问题离散为非线性规划问题,通过数值求解得到了吊挂无人机的最优运动轨迹.最后,通过数值仿真算例验证了所提出的轨迹优化算法的有效性.     

Optimal control of the aeration system based on a simplified ASM1 model apply to Wastewater treatment plant

本文建立了基于ASM1模型的曝气系统简化数学模型,在此基础上提出了以曝气能量消耗最小为目标函数的曝气系统优化控制问题.采用联立配置法进行优化问题的求解,把非线性微分代数方程组的DAE系统转化为非线性代数方程组,将动态优化问题转化为非线性规划问题,最后调用IPOPT解法器求解.在动态入水的条件下进行曝气池的优化控制仿真,其结果显示比传统定值PID控制可节约近40％的能耗.     

基于并行分区搜索的多模态多目标优化及其应用

基于分区搜索的多模态多目标优化属于一种决策空间分解策略,因此它具有天然的并行性.为提高求解效率,提出了一种并行分区搜索(Parallel Zoning Search,PZS)方法来辅助多模态多目标进化算法.在PZS中,首先将多模态多目标优化问题的整个决策空间划分为多个子空间,然后利用并行计算技术来实现选定的多模态多目标...     

面向自由飞行目标捕获的四旋翼最优轨迹规划

自由飞行目标物捕获作为动态任务，在其被执行的过程中，四旋翼不仅要规划出一条时间最优的追踪轨迹，而且还要根据目标物的位置反馈信息实时对轨迹进行重新规划，以实现在最短的时间内追上目标物.针对这一问题，提出了诱导时间最优MPC （model predictive control）算法用于四旋翼的轨迹规划.该算法通过宽松约束条件下时间最优轨迹的引导，利用MPC的滚动优化策略，可以在每个控制周期内用反馈信息实时求解时间最优的追踪轨迹.为了躲避追踪路径中的障碍物，本文还提出了一种用动态线性约束表示障碍物的方法，以提高障碍物约束下轨迹求解的效率.结合诱导时间最优MPC的算法，可以在线实时地求解出具有障碍物避碰能力的时间最优轨迹.仿真结果表明了本文提出算法的有效性，其高效的计算效率也能满足实际系统对算法实时性的要求.     

离散时间最优控制—–评论动态规划

阐述离散时间最优控制的特点.对比3种求解离散时间最优控制的解法,即:1)用非线性规划求解离散时间最优控制;2)用无约束优化求解离散时间最优控制;3)动态规划及其数值解.1)和2)都适用于多维静态优化,计算效率较高,是高级方法.在名义上,3)为动态优化.实际上,3)为一维分段无约束静态优化,计算效率较低,是初级方法.本文并用数字实例进一步阐明动态规划及其数值解在求解方面较差,故动态规划及其数值解已失去实用价值.在求解离散时间最优控制问题方面,无法与非线性规划求解相匹敌.     

基于强化学习的部分线性离散时间系统的最优输出调节

针对同时具有线性外部干扰与非线性不确定性下的离散时间部分线性系统的最优输出调节问题, 提出了仅利用在线数据的基于强化学习的数据驱动控制方法. 首先, 该问题可拆分为一个受约束的静态优化问题和一个动态规划问题, 第一个问题可以解出调节器方程的解. 第二个问题可以确定出控制器的最优反馈增益. 然后, 运用小增益定理证明了存在非线性不确定性离散时间部分线性系统的最优输出调节问题的稳定性. 针对传统的控制方法需要准确的系统模型参数用来解决这两个优化问题, 提出了一种数据驱动离线策略更新算法, 该算法仅使用在线数据找到动态规划问题的解. 然后, 基于动态规划问题的解, 利用在线数据为静态优化问题提供了最优解. 最后, 仿真结果验证了该方法的有效性.     

Solving the Dynamic Optimal Set Partitioning Problem with Arrangement of Centers of Subsets

A mathematical model is presented for the dynamic problem of optimal partitioning of a set from a space Rⁿ with arrangement of centers of subsets under joint constraints on the partition and phase variable. A method is described that solves this problem and synthesizes the essentials of the theory of continuous partitioning problems and optimal control theory for dynamic systems. A numerical algorithm for solving the problem and an analysis of the results of computational experiments are presented.     

From human to humanoid locomotion—an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.     

A Neural Network Approach for Solving Optimal Control Problems with Inequality Constraints and Some Applications

In this paper, a class of nonlinear optimal control problems with inequality constraints is considered. Based on Karush–Kuhn–Tucker optimality conditions of nonlinear optimization problems and by constructing an error function, we define an unconstrained minimization problem. In the minimization problem, we use trial solutions for the state, Lagrange multipliers, and control functions where these trial solutions are constructed by using two-layered perceptron. We then minimize the error function using a dynamic optimization method where weights and biases associated with all neurons are unknown. The stability and convergence analysis of the dynamic optimization scheme is also studied. Substituting the optimal values of the weights and biases in the trial solutions, we obtain the optimal solution of the original problem. Several examples are given to show the efficiency of the method. We also provide two applicable examples in robotic engineering.     

基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

Computational Method for a Class of Switched System Optimal Control Problems

We consider an optimal control problem with dynamics that switch between several subsystems of nonlinear differential equations. Each subsystem is assumed to satisfy a linear growth condition. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantaneous changes-called ldquostate jumpsrdquo-are influenced by a set of control parameters that, together with the subsystem switching times, are decision variables to be selected optimally. We show that an approximate solution for this optimal control problem can be computed by solving a sequence of conventional dynamic optimization problems. Existing optimization techniques can be used to solve each problem in this sequence. A convergence result is also given to justify this approach.     

精确求解一类动态规划问题的神经网络

根据一类动态规划问题（ＤＦＤＰ）的特点，提出一种能够精确求解此问题的神经网络（ＬＤＰＮＮ）。ＬＤＰＮＮ具有结构简单、易于硬件实现、求解速度快并且能够求得精确最优解等优点，特别适合于大规模动态规划问题的求解。在复杂系统的实时优化与控制等方面具有广阔的应用前景。     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

Solutions to a class of nonstandard stochastic control problemswith active learning

The author formulates and solves a dynamic stochastic optimization problem of a nonstandard type, whose optimal solution features active learning. The proof of optimality and the derivation of the corresponding control policies is an indirect one, which relates the original single-person optimization problem to a sequence of nested zero-sum stochastic games. Existence of saddle points for these games implies the existence of optimal policies for the original control problem, which, in turn, can be obtained from the solution of a nonlinear deterministic, optimal control problem. The author also studies the problem of existence of stationary optimal policies when the time horizon is infinite and the objective function is discounted