Quantum Optimal Control Problems with a Sparsity Cost Functional

In this article, the investigation of a class of quantum optimal control problems with L¹ sparsity cost functionals is presented. The focus is on quantum systems modeled by Schrödinger-type equations with a bilinear control structure as it appears in many applications in nuclear magnetic resonance spectroscopy, quantum imaging, quantum computing, and in chemical and photochemical processes. In these problems, the choice of L¹ control spaces promotes sparse optimal control functions that are conveniently produced by laboratory pulse shapers. The characterization of L¹ quantum optimal controls and an efficient numerical semi-smooth Newton solution procedure are discussed.     

三维水平井轨道设计模糊最优控制模型

建立了三维水平井井眼轨道设计模糊非线性多目标最优控制模型 ,利用模糊集理论把该模型转化为非线性规划问题 ,并把该模型应用到水平井的实际生产中 ,得到满意的结果 .     

直接配置法求解连续铸钢过程中的最优控制问题

利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 .     

Dynamic Programming Method for Constrained Discrete-Time Optimal Control

A dynamic programming method is presented for solving constrained, discrete-time, optimal control problems. The method is based on an efficient algorithm for solving the subproblems of sequential quadratic programming. By using an interior-point method to accommodate inequality constraints, a modification of an existing algorithm for equality constrained problems can be used iteratively to solve the subproblems. Two test problems and two application problems are presented. The application examples include a rest-to-rest maneuver of a flexible structure and a constrained brachistochrone problem.     

Stability Analysis of Optimal Control Systems via Liapunov Method

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A Globally Convergent and Efficient Method for Unconstrained Discrete-Time Optimal Control

Shift schemes are commonly used in non-convex situations when solving unconstrained discrete-time optimal control problems by the differential dynamic programming (DDP) method. However, the existing shift schemes are inefficient when the shift becomes too large. In this paper, a new method of combining the DDP method with a shift scheme and the steepest descent method is proposed to cope with non-convex situations. Under certain assumptions, the proposed method is globally convergent and has q-quadratic local conve rgence. Extensive numerical experiments on many test problems in the literature are reported. These numerical results illustrate the robustness and efficiency of the proposed method.     

Inexact Iterative Bregman Method for Optimal Control Problems

In this article, we investigate an inexact iterative regularization method based on generalized Bregman distances of an optimal control problem with control constraints. We show robustness and convergence of the inexact Bregman method under a regularity assumption, which is a combination of a source condition and a regularity assumption on the active sets. We also take the discretization error into account. Numerical results are presented to demonstrate the algorithm.     

Parametric Sensitivity Analysis of Perturbed PDE Optimal Control Problems with State and Control Constraints

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control.The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods.Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.Communicated by H. J. Pesch     

Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems

We consider first nonlinear systems of the formx=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.     

带环境污染的与年龄相关的非线性种群动力系统的最优控制

研究带环境污染的与年龄相关的非线性种群动力系统的最优控制问题,利用不动点定理得出系统非负解的存在性和唯一性,利用极大化序列及紧性证明最优控制的存在性,利用法锥方法得到控制问题的最优条件.     

油田开发措施配置的最优控制建模及求解

为了解决油田开发后期各种措施的规划问题,本文提出了一个最优控制数学模型,并讨论了其求解方法,将其应用于油田后期的开发措施配置,并通过油田实例应用证明了这一方法的实用性.     

求线性规划对偶问题最优解的一种方法

线性规划对偶问题的最优解有重要的经济意义,中给出了一种较为简捷的求对偶问题最优解的方法。     

2-Regularity and 2-Normality Conditions in Discrete Optimal Control Problems

The paper is devoted to general optimal control problems for discrete-time systems with equality type of constraints on end points and control. We derive first-order necessary optimality conditions that are meaningful under the new nontriviality condition.     

Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems

In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.     

On Quantitative Stability in Optimization and Optimal Control

We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.     

随机递归最优控制和混合最优控制问题

对随机递归最优控制问题即代价函数由特定倒向随机微分方程解来描述和递归混合最优控制问题即控制者还需 决定最优停止时刻, 得到了最优控制的存在性结果. 在一类等价概率测度集中,还给出了递归最优值函数的最小和最大数学期望.     

Optimal Control of a Stochastic Assembly Production Line

The system under consideration comprises n workstations in parallel and one assembly workstation. The workstations are either reliable or unreliable and the product demand is random. The n different type parts are processed first in the parallel workstations and then are joined in the assembly workstation. By minimizing the expected discounted cost, it is shown that the optimal control policy is of the bang–bang type and can be described by a set of switching manifolds. The structural properties of the optimal policy, such as monotonicity and asymptotic behavior, are investigated. These structural properties are very useful to find the optimal policy in large-size systems. Three numerical examples are given to demonstrate the results.     

Optimal scheduling of inspection times in a production process with a finite planning horizon

Inspection models applicable to a finite planning horizon are developed for the following lifetime distributions: uniform, exponential, and Weibull distribution. For a given lifetime distribution, maximization of profit is used as the sole optimization criterion for determining an optimal planning horizon over which a system may be operated as well as ideal inspection times. Illustrative examples (focusing on the uniform and Weibull distributions and using Mathematica programs) are given. For some situations, evenly spreading inspections over the entire planning horizon are seen to result in the attainment of desirable profit levels over a shorter planning horizon. Scope for further research is given as well. Copyright © 2016 John Wiley & Sons, Ltd.     

A Domain Embedding Method Using the Optimal Distributed Control and a Fast Algorithm

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast algorithm developed by Daripa et al. [3,7,10–12]. The arbitrary domains can be simply or multiply connected and the proposed method can be applied, in principle, to a large number of elliptic problems. Numerical results obtained for Dirichlet problems associated with the Poisson equation in simply and multiply connected domains are presented. The computed solutions are found to be in good agreement with the exact solutions with moderate number of grid points in the domain.     

最优控制问题参数化研究—基于勒让德正交多项式逼近

使用勒让德正交多项式逼近方法,将Lagrange型最优控制问题转化为非线性规划问题.采用序列二次规划方法对此非线性规划问题的求解,并对多项式逼近和非线性规划求解后得到的解是否收敛给出了证明和实例分析.