Numerical solution to optimal feedback control by dynamic programming approach: A local approximation algorithm

This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.     

Finite element approximation for a class of parameter estimation problems

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.     

L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given.     

均值-方差模型下DC型养老金的随机最优控制

从DB型养老金转向DC型养老金已被越来越多的国家所考虑. 以均值-方差为目标研究 风险资产符合CEV模型的DC型养老金最优投资问题. 利用随机控制建立了养老金最优投资的HJB方程, 通过Legendre变换和对偶理论求得养老金的最优投资策略, 最后推导出均值-方差下 DC型养老金最优投资的有效前沿.     

Sample average approximation method for a class of stochastic variational inequality problems

This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu (2008), by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.     

突击作战干扰时机决策

干扰时机的确定是进行干扰决策的前提和基础。通过对问题分析,制定了两套干扰时机决策方案。为实现攻击机的飞行控制最优规划,综合考虑攻击机飞行性能、威胁约束以及边界约束,建立了最优航迹控制模型。引入主要应用于航天控制的勒让德伪谱法(Legendre pseudospectral method, LPM),将最优控制问题转化为非线性规划(nonlinear programming, NLP)问题,在此基础上设计了干扰时机解算流程。通过对基于c代码的可行序列二次规划(c code feasible sequential quadratic programming, CFSQP)算法的改进,有效减少了优化变量的数量,使其能对NLP问题快速寻优。仿真结果表明,所提出的干扰时机决策方案能有效地获得最优干扰开始和结束时刻。     

Legendre transform-dual solution for investment and consumption problem under the Vasicek model

This paper studies an investment and consumption problem with stochastic interest rate,where interest rate is governed by the Vasicek model.The financial market is composed of one riskfree asset and one risky asset,in which stock price dynamics is assumed to be generally correlated with interest rate dynamics.The aim is to maximize expected utility of consumption and terminal wealth in the finite horizon.Legendre transform is used to deal with this investment and consumption problem and the explicit solutions of the optimal investment and consumption strategies with power and logarithm preference are achieved.Finally,the authors add a numerical example to analyze the effect of market parameters on the optimal investment and consumption strategy and provide some economic implications.     

Numerical Solutions for Optimal Control of Stochastic Kolmogorov Systems

This work is concerned with controlled stochastic Kolmogorov systems. Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control, this paper is devoted to designing numerical methods for approximation. Different from the existing literature on numerical methods for stochastic controls, the Kolmogorov systems take values in the first quadrant. That is, each component of the state is nonnegative. The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent) the controlled diffusion. The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works. Convergence of the numerical scheme is proved under suitable conditions.     

直接鲁棒自适应模糊控制

针对一类不确定非线性系统 ,基于监督控制方案并利用第二类模糊系统的逼近能力 ,提出了一种直接鲁棒自适应模糊控制器设计的新方案。该方案通过引入最优逼近误差的自适应补偿项来消除建模误差的影响 ,从而在稳定性分析中取消了要求逼近误差平方可积或逼近误差的上确界已知的条件。理论分析证明了闭环控制系统是全局稳定的 ,跟踪误差收敛到零。仿真结果表明了该方法的有效性。     

Phased MIMO雷达恒模正交波形优化设计 Phased-MIMO雷达恒模正交波形优化设计

由于受到发射机功率和波形能量的限制,现代雷达系统一般选择恒模波形来实现发射功率的最大化利用。针对Phased MIMO雷达子阵单元之间的恒模正交波形优化设计问题,基于矩阵谱逼近的思想,本文提出了一种新的波形设计框架。首先假设输出信干比的需求得到划分的子阵数目,根据最大信噪比准则对子阵单元进行波束形成,提高了雷达系统的抗干扰性能,其次采用迭代矩阵谱逼近算法(iterative matrix spectral approximation algorithm, IMSAA)对子阵单元之间的正交波形进行优化设计,相对于multi-CAN算法,该算法能够获得更好的相关性能,而且运算效率较高,最终实现了恒模波形的优化设计。仿真结果证明了算法的有效性。     

HIGH-ACCURACY FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEM

1 IntroductionOptimal design or control is playing an increasingly importal role in engineering designwork. Efficient numerical methods are among the keys to successful application of optimalcontrol in practical work. With its wide range of application in scielltific and engineeringnumerical simulation, finite element approximation of optimal control problems plays a veryimportant role in numerical method of these problems. There have been eXtensive studies inthis respect, see, for example, […     

Robust adaptive neural network control with supervisory controller

The problem of direct adaptive neural network control for a class of uncertain nonlinear systems with unknown constant control gain is studied in this paper. Based on the supervisory control strategy and the approximation capability of multilayer neural networks (MNNs), a novel design scheme of direct adaptive neural network controller is proposed.The adaptive law of the adjustable parameter vector and the matrix of weights in the neural networks and the gain of sliding mode control term to adaptively compensate for the residual and the approximation error of MNNs is determined by using a Lyapunov method. The approach does not require the optimal approximation error to be square-integrable or the supremum of the optimal approximation error to be known. By theoretical analysis, the closed-loop control system is proven to be globally stable in the sense that all signals involved are bounded, with tracking error converging to zero.Simulation results demonstrate the effectiveness of the approach.     

基于Shifted Legendre正交多项式的迭代学习控制方法

考虑用迭代学习控制方法来解决一类线性时变连续系统的终端控制问题。运用ShiftedLegendre正交多项式的展开技术,利用其正交性和边值条件,将线性时变系统的微分方程转化为代数方程,避免了在判断误差收敛条件的过程中求解线性时变系统状态转移矩阵。并采用高阶学习律来求控制输入的ShiftedLegendre系数向量,仿真实例验证了该方法的有效性。     

基于滚动时域控制的再入轨迹跟踪制导律

为了提高再入制导的实时性和鲁棒性,设计一种标准轨迹跟踪制导方法。首先将参考轨迹的跟踪问题转化为轨迹状态调节问题,进一步转化为一个线性时变系统的最优控制问题;然后采用滚动时域控制结合基于间接Legendre伪谱法的最优反馈控制算法设计出一种易于在线实现的制导律。基于上述工作完成了亚轨道飞行器（suborbital reusable launch vehicle, SRLV）返回制导过程的3自由度数值仿真研究工作。数值算例说明,该制导方法在初始点状态存在较大范围偏差和气动参数存在较大误差的情况下具有良好的鲁棒性。     

养老基金管理的常方差弹性模型及Legendre 变换2对偶解法

文章主要为待遇预定制养老基金的管理建立常方差弹性(CEV)模型,给出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,应用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的投资比例,以及养老金缴费水平,最终实现养老基金管理的最优资产配置和最低缴费水平.     

Optimal control using microscopic models for a pollutant elimination problem

Optimal control problem with partial derivative equation (PDE) constraint is a numerical-wise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman (HJB) equation approximation. For solving the problem, only an HJB equation (a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.     

基于伪谱法的欠驱动航天器实时最优控制算法设计

针对欠驱动刚性航天器提出了时间最优的闭环状态反馈控制算法。首先,利用直接Legendre 伪谱法规划出航天器开环的姿态机动轨迹,并验证了所得最优控制输入的可行性。然后,以航天器实际运行轨迹与开环轨迹间的偏差为变量构造偏差方程,并提出了基于间接Legendre 伪谱法的最优姿态稳定控制算法。最后,采用实时重规划策略实现了稳定控制器状态的反馈,从而完成了对参考轨迹的闭环跟踪。仿真结果表明所提算法运算量小,计算速度快,可以实时获取解析形式的控制输入修正量,而且对初始姿态存在扰动的情况具有一定的鲁棒性,运算精度较高。     

一种新的基于小波变换的图像融合方法

提出了一种新的基于小波变换的多光谱与高分辨率图像融合方法。该方法通过强度因子有效地将高分辨率图像经小波分解的低频分量信息融合到多光谱图像经小波分解的低频分量中去 ,使得经过小波反变换的融合图像较大程度地保留了多光谱图像的光谱信息和高分辨率图像的空间分辨率。给出了该方法的融合结果 ,并与小波变换法 (WT方法 )进行了比较 ,证明了该图像融合方法的正确性和有效性     

Geometric error control in the parabola-blending linear interpolator

This paper considers geometric error control in the parabola-blending linear interpolation method （Zhang, et al., 2011）. Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result. By computing the geometric error directly without accumulating the approximation error and chord error, the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.     

Optimal control of multisolution ordinary differential equations in the absence of convexity

<正> In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.