多车型回程车辆调度问题的ADP算法研究

采用近似动态规划(ADP)方法对钢铁物流运输过程中的车辆调度问题进行了分析, 设计了车辆和运输货物的状态向量空间、动作向量空间等, 充分考虑运输成本和能力约束, 建立状态转移函数、目标函数, 并对近似动态规划算法进行改进。在基于决策后状态的ADP算法的基础上, 采用Boltzmann探索策略对所有的状态空间进行遍历, 避免局部最优和低效问题。通过对比实验, 比较Q学习算法、基于决策后状态的ADP算法以及采用Boltzmann探索策略的ADP算法的实验结果, 证明了采用Boltzmann探索策略的ADP算法具有更快的收敛速度, 执行效率更高。     

非线性离散时间系统带ε误差限的自适应动态规划

为了获得非线性离散时间系统的最优控制策略,基于自适应动态规划的原理,提出了一种带误差限的自适应动态规划方法.对于一个任意的状态,用一个有限长度的控制序列近似最优控制序列,使性能指标与最优性能指标的误差在一个较小的范围内.选取一个非线性离散时间系统对算法的性能进行数值实验,结果验证了该算法的有效性,用较少的计算代价获得了近似最优的控制策略.     

基于乘子法的离散动态非凸大系统的递阶优化算法及其应用

本文针对一类时间上关联的离散动态非凸大规模优化问题,提出了一种将部分约束作为罚项从而将非凸优化问题转化为凸优化问题的方法,研究了它的递阶优化算法,讨论了算法的收敛性及实际应用情况。     

基于非线性规划的指数自回归模型的辨识

讨论了指数自回归模型的辨识问题，证明了该模型最小二乘估计的目标函数的非凸性，并给出了使该函数为凸的条件，最后给出了辨识该模型的算法及该算法的收敛性，并以数值例子加以说明。     

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。     

Doo-Sabin细分算法在动态模式下的推广

提出一种基于均匀三角多项式B样条的动态保凸细分算法，它可以看作Doo-Sabin细分算法在动态模式下的一个推广．其细分规则基于张量积曲面细分模式的几何意义，不仅可以生成旋转曲面等特殊曲面，而且可以根据参数来控制细分曲面的形状．最后运用传统的离散傅里叶技术和特征根方法证明了该细分算法的收敛性．     

l_p范数下具有等级约束的负载均衡问题

具有等级约束的负载均衡问题是不同类平行机排序问题的一个特殊情形。当目标函数为最小化机器负载向量的lp范数时,通过分析该问题的组合性质,利用目标函数的凸性得到了一个全范数2-近似的组合算法;当机器数为常数时,在固定lp范数下,构造一个辅助实例,分析输入实例和辅助实例的最优值之间的关系,利用动态规划算法求出辅助实例的最优解,进一步得到输入实例的一个近似解,其目标函数值与最优值无限接近。这些均在算法的时间复杂性方面改进了之前的结果。     

离散时间Hopfield网络的动力系统分析

离散时间的Hopfield网络模型是一个非线性动力系统．对网络的状态变量引入新的能量函数，利用凸函数次梯度性质可以得到网络状态能量单调减少的条件．对于神经元的连接权值且激活函数单调非减(不一定严格单调增加)的Hopfield网络，若神经元激活函数的增益大于权值矩阵的最小特征值，则全并行时渐进收敛；而当网络串行时，只要网络中每个神经元激活函数的增益与该神经元的自反馈连接权值的和大于零即可．同时，若神经元激活函数单调，网络连接权值对称，利用凸函数次梯度的性质，证明了离散时间的Hopfield网络模型全并行时收敛到周期不大于2的极限环．     

交通流模型参数的近似动态规划辨识方法

针对交通流模型的强非线性、不确定性等特点,提出了基于近似动态规划的交通流模型参数辨识算法.该算法具有自学习和自适应的特性,不依赖于被控对象的解析模型.严格的理论推导证明了这种参数辨识方案的收敛性,仿真结果验证了所提出算法的有效性.     

基于评价网络近似误差的自适应动态规划优化控制

为了求解有限时域最优控制问题,自适应动态规划(ADP)算法要求受控系统能一步控制到零。针对不能一步控制到零的非线性系统,提出一种改进的ADP算法,其初始代价函数由任意的有限时间容许序列构造。推导了算法的迭代过程并证明了算法的收敛性。当考虑评价网络的近似误差并满足假设条件时,迭代代价函数将收敛到最优代价函数的有界邻域。仿真例子验证了所提出方法的有效性。     

Solving Fixed Final Time Fractional Optimal Control Problems Using the Parametric Optimization Method

In this paper, the parametric optimization method is used to find optimal control laws for fractional systems. The proposed approach is based on the use for the fractional variational iteration method to convert the original optimal control problem into a nonlinear optimization one. The control variable is parameterized by unknown parameters to be determined, then its expression is substituted into the system state‐space model. The resulting fractional ordinary differential equations are solved by the fractional variational iteration method, which provides an approximate analytical expression of the closed‐form solution of the state equations. This solution is a function of time and the unknown parameters of the control law. By substituting this solution into the performance index, the original fractional optimal control problem reduces to a nonlinear optimization problem where the unknown parameters, introduced in the parameterization procedure, are the optimization variables. To solve the nonlinear optimization problem and find the optimal values of the control parameters, the Alienor global optimization method is used to achieve the global optimal values of the control law parameters. The proposed approach is illustrated by two application examples taken from the literature.     

Error analysis of solutions of second-order boundary value problems obtained with residual correction method

Based on the maximum principle of differential equations and with the aid of asymptotic iteration technique, this paper tries to establish monotonic relation of second-order obstacle boundary value problems with their approximate solutions to eventually obtain the upper and lower approximate solutions of the exact solution. To obtain numerical solutions, the cubic spline approximation method is applied to discretize equations, and then according to the ‘residual correction method’ proposed in this paper, residual correction values are added into discretized grid points to translate once complex inequalities’ constraint mathematical programming problems into simple equational iteration problems. The numerical results also show that such method has the characteristic of correcting residual values to symmetrical values for such problems, as a result, the mean approximate solutions obtained even with a considerably small quantity of grid points still quite approximate the exact solution. Furthermore, the error range of approximate solutions can be identified very easily by using the obtained upper and lower approximate solutions, even if the exact solution is unknown.     

State-space constrained optimal control problems with control variables appearing linearly

This paper deals with the state-space constrained optimal control problems with control variables appearing linearly by the concept of decomposition. To solve this continuous optimal control problem, we first discretize the time and replace the system of differential equations by difference equations. For this resulting discrete optimal control problem, fixing the value of state variables reduces the given problem to a finite number of independent linear programming problems which are parameterized by the value of state variables. From this point of view, after para. meterizing by the value of state variables, we outer-linearize the resulting itifimal valuo functions in the minimond and apply the relaxation strategy to the new constraints arising as a consequence of outer-linearization. An algorithm is proposed which requires baek-and-forth iteration between a master problem and a finite number of linear programming subproblems. Finite convergence of this algorithm follows directly from the finite number of constraints of the master problem.     

含状态和输入时滞的离散时间系统的近似最优跟踪控制

针对状 态和控制输入均含有时滞的离散时间系统, 提出最优跟踪控制的设计方法. 通 过引入一种新的状态向量, 将含有状态和控制输入时滞的离散时间系统转化为 含有虚拟扰动项的无时滞离散时间系统. 根据最优控制理论, 构造离散Riccati矩阵方 程和离散Stein矩阵方程的序列, 并证明该解序列一致收敛于变换后的离散时间系统的最优跟 踪控制策略. 利用最优控制的逐次逼近设计方法, 得到最优跟踪控制的近似 解, 并给出求解最优跟踪控制律的算法. 仿真算例表明了所提出最优跟踪控制 方法的有效性.     

Continuous State Dynamic Programming via Nonexpansive Approximation

This paper studies fitted value iteration for continuous state numerical dynamic programming using nonexpansive function approximators. A number of approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm.      

飞行器上升段轨迹的优化设计

针对飞行器上升段轨迹优化求解困难的问题,提出一种基于正交配点的优化求解方法。该方法以第二类切比雪夫正交多项式的零点作为系统控制变量和状态变量的离散点,利用拉格朗日插值多项式对状态和控制变量进行拟合。通过对多项式的求导将动力学微分方程约束转化为代数约束,从而把无限维的最优控制问题转化为一个有限维的非线性规划(Nonlinear Programming,NLP)问题。随后,利用序列二次规划(Sequential Quadratic Program-ming,SQP)方法求解转化后的NLP问题,获得最优的飞行轨迹。最后,飞行器上的仿真结果验证了所提方法的有效性。研究成果可为飞行器的制导控制提供可行的飞行轨迹,有一定的工程应用价值。     

具有π-导数模糊微分方程的近似解

在模糊值函数具有π-导数意义下研究一阶模糊微分方程的模糊初值问题,将模糊微分方程转化成同解的常微分方程,利用变分迭代算法给出方程的近似解,给出了具体算例。     

Discrete-sample curve fitting using chebyshev polynomials and the approximate determination of optimal trajectories via dynamic programming

Some useful properties of the Chebyshev polynomials are derived. By virtue of their discrete orthogonality, a truncated Chebyshev polynomials series is used to approximate a function whose discrete samples are the only available data. If minimization of the sum of the discrete squared error is used as the criterion, subject to some constraints on initial conditions and/or terminal conditions, the coefficients of the polynomials are easy to obtain. The simplicity of computing the coefficients of the polynomials from the discrete values of the function to be approximated is utilized to the approximate determination of optimal trajectories via dynamic programming using the technique of polynomial approximation. This allows use of the functional equation approach to solve multi-dimensional variational problems.     

The bounded energy optimal control for a class of distributed parameter systems†

The bounded energy optimal control for one-dimensional linear stationary distributed parameter system is solved here. The criterion function is a quadratic functional of the output.

Obtaining the optimal control involves the computation of the solution of a certain non-linear integral equation. The method of solving this integral equation is approximating the kernel of the integral operator by a sequence of degenerate kernels. It is shown that the sequence of approximate solutions of the approximate integral equations converges to the optimal solution; and that the sequence of approximate values of the criterion, converges to the optimal value of the criterion.     

含扩散项不可靠生产系统最优生产控制的数值求解

针对含扩散项不可靠随机生产系统最优生产控制的优化命题, 采用数值解方法来求解该优化命题最优控制所满足的模态耦合的非线性偏微分HJB方程. 首先构造Markov链来近似生产系统状态演化, 并基于局部一致性原理, 把求解连续时间随机控制问题转化为求解离散时间的Markov决策过程问题, 然后采用数值迭代和策略迭代算法来实现最优控制数值求解过程. 文末仿真结果验证了该方法的正确性和有效性.