Solving a continuous nonlinear problem of optimal set partition with arrangement of subset centers in the case of a convex objective functional

A continuous nonlinear single-commodity problem of optimal partition of a set Ω in an n-measurable Euclidean space into disjoint subsets with arrangement of their centers is analyzed using equality and inequality constraints in the case of a convex objective functional. A method and algorithm are proposed to solve this problem. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 134–152, March–April 2008.     

Extremum Conditions for a Continuous Optimal Problem of Partitioning of a Set with a Nondifferentiable Objective Functional

Necessary and sufficient subdifferential extremum conditions are obtained based on the Dubovitskii-Milyutin scheme for a continuous multiproduct problem of optimal partitioning of a set into subsets with fixed centers under additional constraints.     

用双种群混合遗传算法求解最优QoS划分问题

在取决于性能的价格机制下,最优QoS划分用于沿路由路径最优化地分配QoS参数值,以使得通信总费用最小。提出了求解最优QoS划分问题(OPQ问题)的双种群混合遗传算法。该算法充分利用了遗传算法的全局搜索优势和模拟退火算法的局部搜索优势,并且两个相互独立的子群体周期性的交流最优染色体,进一步提高了性能。仿真结果表明了该算法的有效性。     

Stability of a combinatorial vector partition problem

The vector variant of the partition problem is considered. It is shown that the coincidence of the Pareto and Slater sets is the necessary and sufficient condition of stability of the problem with respect to its functional. __________ Translated from Kibernetika i Sistemny i Analiz, No. 3, pp. 177–181, May–June 2007.     

序列折半划分问题的形式化推导

形式化推导是在程序正确性证明理论下所进行的程序开发,最终得到完全正确的算法程序。针对序列折半划分问题,现有的形式化推导方法将推导与证明交替进行,推导过程繁琐且大多无法直接获得可执行程序。为解决上述问题,提出了一种新的序列折半划分问题的形式化推导方法。该方法基于分划递推的核心思想,应用规约变换技术对问题规约进行变换并严格保证一致性,使得在推导过程中无需交替证明,进而导出递推关系式并得到高可靠性抽象算法程序Apla,最终通过转换工具自动生成可执行程序。实现了从程序规约到具体可执行程序的完整程序求精过程。以2个序列算法为例,验证了该方法的有效性和可行性,对相关问题的形式化推导具有指导意义。     

在逐点状态约束下一个四阶线性系统的时间最优控制

在逐点状态约束下,最优控制问题的求解是很困难的,已有的最大值原理和形态规划理论很难用来求解在逐点状态约束下最优控制问题.本文讨论逐点状态约束下一个四阶线性系统的时间最优控制问题.我们采用转换的方法给出了最优时间与最优控制的具体表达式.     

Tissue P systems with cell separation: attacking the partition problem

Tissue P systems are distributed parallel and non-deterministic computing models in the framework of membrane computing, which are inspired by intercellular communication and cooperation between neurons. Recently, cell separation is introduced into tissue P systems, which enables systems to generate an exponential workspace in a polynomial time. In this work, the computational power of tissue P systems with cell separation is investigated. Specifically, a uniform family of tissue P systems with ce...     

Least-squares solutions of constrained inverse eigenproblem and associated optimal approximation problem

In this paper, the least-squares solutions of constrained inverse eigenvalue problem and the associated optimal approximation problem are considered. We get the general expression of the least-squares solutions of the constrained inverse eigenvalue problem, obtain the representation of the unique optimal approximation solution in the least-squares solutions set, and give the algorithm and corresponding computational examples.     

A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities

In this paper, we study a finite element method overcoming corner singularities for elliptic optimal control problem posed on a polygon. Based on a corner singularity decomposition of singular solution for the associated elliptic system, we derive an extraction formula for coefficients of singular parts, called stress intensity factors, and introduce a finite element discretization for regular parts of the solution pair. Furthermore, we analyze the finite element solutions in $L^2$ and $H^1$ norms. By numerical experiments, we confirm the efficiency and reliability of the proposed method.     

线性–非二次最优控制问题的一种解法

讨论了求解状态终端无约束线性–非二次最优控制问题的拟Riccati方程方法, 并据此提出了计算无约束线性–非二次问题之数值解的方法; 然后将这个方法与一种能近似地化有约束问题为无约束问题的惩罚方法结合起来, 给出了一种算法, 可以计算状态终端有约束的线性–非二次最优控制问题之近似解.     

Symplectic algorithms with mesh refinement for a hypersensitive optimal control problem

A symplectic algorithm with nonuniform grids is proposed for solving the hypersensitive optimal control problem using the density function. The proposed method satisfies the first-order necessary conditions for the optimal control problem that can preserve the structure of the original Hamiltonian systems. Furthermore, the explicit Jacobi matrix with sparse symmetric character is derived to speed up the convergence rate of the resulting nonlinear equations. Numerical simulations highlight the features of the proposed method and show that the symplectic algorithm with nonuniform grids is more computationally efficient and accuracy compared with uniform grid implementations. Besides, the symplectic algorithm has obvious advantages on optimality and convergence accuracy compared with the direct collocation methods using the same density function for mesh refinement.     

A system decomposition approach to the design of functional observers

This paper reports a system decomposition that allows the construction of a minimum-order functional observer using a state observer design approach. The system decomposition translates the functional observer design problem to that of a state observer for a smaller decomposed subsystem. Functional observability indices are introduced, and a closed-form expression for the minimum order required for a functional observer is derived in terms of those functional observability indices.     

The problem of LQG optimal control via a limited capacity communication channel

The paper addresses a LQG optimal control problem involving bit-rate communication capacity constraints. A discrete-time partially observed system perturbed by white noises is studied. Unlike the classic LQG control theory, the control signal must be first encoded, then transmitted to the actuators over a digital communication channel with a given bandwidth, and finally decoded. Both the control law and the algorithms of encoding and decoding should be designed to archive the best performance. The optimal control strategy is obtained. It is shown that where the estimator-coder separation principle holds, the controller-coder one fails to be true.     

Solution of continuous problems of optimal covering with spheres using optimal set-partition theory

The paper considers a continuous problem of optimal c-sphere covering of a compact set from Ω from E _n with a given number of spheres of minimum radius and a problem of covering a set with the minimum number of spheres of given radius. Algorithms are proposed and substantiated to solve the problems using optimal set-partition theory and Shor’s r-algorithm. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 98–117, May–June 2009.     

A smoothing approach for the optimal parameter selection problem with continuous inequality constraint

In this paper, we consider a class of optimal parameter selection problems with continuous inequality constraints. By introducing a smoothing parameter, we formulate a sequence of KKT (Karush-Kuhn-Tucker) systems of this problem and then transform it into a system of constrained nonlinear equations. Then, the first- and second-order gradients formulae of the cost functional and the constraints are derived. On this basis, a smoothing projected Newton-type algorithm is developed to solving this system of nonlinear equations. To illustrate the effectiveness of the proposed method, some numerical results are solved and presented.     

Regional optimal control problem of a class of infinite-dimensional bi-linear systems

The purpose of this paper is to study regional optimal control of an infinite-dimensional bi-linear system, excited by unbounded or bounded controls. Then we prove the existence of an optimal control that minimises a functional cost and we give the characterisation of such a control. Also we give the condition that ensures the uniqueness of the optimal control. The obtained results lead to an algorithm that we illustrate by simulations for a bi-dimensional diffusion system excited by a zone actuator.     

A graph-theoretic optimal control problem for terminating discrete event processes

Most of the results to date in discrete event supervisory control assume a zero-or-infinity structure for the cost of controlling a discrete event system, in the sense that it costs nothing to disable controllable events while uncontrollable events cannot be disabled (i.e., their disablement entails infinite cost). In several applications however, a more refined structure of the control cost becomes necessary in order to quantify the tradeoffs between candidate supervisors. In this paper, we formulate and solve a new optimal control problem for a class of discrete event systems. We assume that the system can be modeled as a finite acylic directed graph, i.e., the system process has a finite set of event trajectories and thus is terminating. The optimal control problem explicitly considers the cost of control in the objective function. In general terms, this problem involves a tradeoff between the cost of system evolution, which is quantified in terms of a path cost on the event trajectories generated by the system, and the cost of impacting on the external environment, which is quantified as a dynamic cost on control. We also seek a least restrictive solution. An algorithm based on dynamic programming is developed for the solution of this problem. This algorithm is based on a graph-theoretic formulation of the problem. The use of dynamic programming allows for the efficient construction of an optimal subgraph (i.e., optimal supervisor) of the given graph (i.e., discrete event system) with respect to the cost structure imposed. We show that this algorithm is of polynomial complexity in the number of vertices of the graph of the system.Research supported in part by the National Science Foundation under grant ECS-9057967 with additional support from GE and DEC.     

A simulation‐based algorithm for optimal pricing policy under demand uncertainty

We propose a simulation‐based algorithm for computing the optimal pricing policy for a product under uncertain demand dynamics. We consider a parameterized stochastic differential equation (SDE) model for the uncertain demand dynamics of the product over the planning horizon. In particular, we consider a dynamic model that is an extension of the Bass model. The performance of our algorithm is compared to that of a myopic pricing policy and is shown to give better results. Two significant advantages with our algorithm are as follows: (a) it does not require information on the system model parameters if the SDE system state is known via either a simulation device or real data, and (b) as it works efficiently even for high‐dimensional parameters, it uses the efficient smoothed functional gradient estimator.