Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

AMS Subj. Classification: 49J15, 49M15

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Neural Network Based Optimal Control with Constraints

In the present paper the problems of the optimal control of systems when constraints are imposed on the control is considered. The optimality conditions are given in the form of Pontryagin’s maximum principle. The obtained piecewise linear function is approximated by using feedforward neural network. A numerical example is given.

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

An Optimal Distributed Algorithm for All-Pairs Shortest-Path

In this paper the network problem of determining all-pairs shortest-path is examined. A distributed algorithm which runs in O(n) time on a network of n nodes is presented. The number of messages of the algorithm is O(e+n log n) where e is the number of communication links of the network. We prove that this algorithm is time optimal.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

Study of Queueing Behaviour in IP Buffers

It is unquestioned that the importance of IP network will further increase and that it will serve as a platform for more and more services, requiring different types and degrees of service quality. Modern architectures and protocols are being standardized, which aims at guaranteeing the quality of service delivered to users. In this paper, we investigate the queueing behaviour found in IP output buffers. This queueing increases because multiple streams of packets with different length are being multiplexed together. We develop balance equations for the state of the system, from which we derive packet loss and delay results. To analyze these types of behaviour, we study the discrete-time version of the “classical” queue model M/M/1/k called Geo/Gx/1/k, where Gx denotes a different packet length distribution defined on a range between a minimum and maximum value.