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Thursday, July 16, 2020 | History

4 edition of Optimal control of random sequences in problems with constraints found in the catalog.

Optimal control of random sequences in problems with constraints

by A. B. Piunovskiy

  • 170 Want to read
  • 19 Currently reading

Published by Kluwer in Dordrecht, Boston .
Written in English

    Subjects:
  • Control theory.,
  • Mathematical optimization.,
  • Stochastic processes.

  • Edition Notes

    Includes bibliographical references (p. 327-336) and index.

    Statementby A.B. Piunovskiy.
    SeriesMathematics and its applications ;, v. 410, Mathematics and its applications (Kluwer Academic Publishers) ;, v. 410.
    Classifications
    LC ClassificationsQA402.3 .P455 1997
    The Physical Object
    Paginationxi, 345 p. :
    Number of Pages345
    ID Numbers
    Open LibraryOL670667M
    ISBN 100792345711
    LC Control Number97016602

    Various applications of game theory to control problems and, in particular, to interception problems, are discussed. The fundamental concepts of probability theory and of random processes, needed for solving stochastic optimization problems, are stated in Chapters 10 and Much attention is given to MARKOV sequences and processes. Numerical solution of optimal control problems with explicit and implicit switches. Hans Georg Bock (bock ) Christian Kirches (s ) Andreas Meyer ( ) Andreas Potschka (ka ). Abstract: In this article, we present a unified framework for the numerical solution of optimal control problems.

    OPTIMAL TRAJECTORIES AND NEIGHBORING-OPTIMAL SOLUTIONS Statement of the Problem Cost Functions Parametric Optimization Conditions for Optimality Necessary Conditions for Optimality Sufficient Conditions for Optimality The Minimum Principle The Hamiltonn-Jacobi-Bellman Equation Constraints and Singular Control Terminal State 4/5(22). This paper is concerned with theconvergence of a sequence of discrete-time Markov decisionłinebreak processes (DTMDPs) with constraints, state-action dependent discount factors, and possibly unbounded łinebreak costs. Using the convex analytic approach under mild conditions, we prove that the optimal values and optimal policies of the original DTMDPs converge to those of the “limit” : Wu Xiao, Guo Xianping.

    the optimal control problems to which the above maximum principle is applicable. EXAMPLE 1 One area of application of optimality conditions for optimal control problems with mixed constraints is to the control of devices modelled by differential algebraic systems of equations (DAE systems). DAE models are widespread in the chemical processing. In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformulating a constrained optimal control problem into a global optimization problem. A differential flow is presented to deduce some optimality conditions for solving global Author: Dan Wu.


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Optimal control of random sequences in problems with constraints by A. B. Piunovskiy Download PDF EPUB FB2

The present book is devoted to the rather new area, that is, to the optimal control theory with functional constraints. This theory is close to the theory of multicriteria optimization. The compromise between the mathematical rigor and the big number of meaningful examples makes the book attractive for professional mathematicians and for.

Optimal Control of Random Sequences in Problems with Constraints (Mathematics and Its Applications (closed)) [A.B. Piunovskiy] on *FREE* shipping on qualifying offers. Controlled stochastic processes with discrete time form a very interest­ ing and meaningful field of research which attracts widespread attention.

At the same time these processes are used for solving of many Cited by: Get this from a library. Optimal control of random sequences in problems with constraints. [A B Piunovskiy] -- This volume is devoted to the investigation of general Borel models of stochastic optimal control, taking into consideration additional performance criteria which must satisfy the.

Optimal Control of Random Sequences in Problems with Constraints (Mathematics and Its Applications) [A.B. Piunovskiy] on *FREE* shipping on qualifying offers.

Controlled stochastic processes with discrete time form a very interest­ ing and meaningful field of research which attracts widespread attention. At the same time these processes are used for solving of many applied Cited by: Piunovskiy A.B.

() Optimal Control Problems with Constraints. In: Optimal Control of Random Sequences in Problems with Constraints. Mathematics and Its Applications, vol Cited by: 3. The optimal control of Markov chains is known long ago [23]. In the series of the recent works we developed the existing theory to non stationary case with constraints and obtained following.

Approximation Algorithms for Low-Distortion Embeddings into Low-Dimensional Spaces Global Solution to the Three-Dimensional Compressible Flow of Liquid CrystalsCited by:   Framework for Optimal Control Modeling Dynamic Systems Optimal Control Objectives Overview of the Book Problems References 2.

THE MATHEMATICS OF CONTROL AND ESTIMATION "Scalars, Vectors, and Matrices "Scalars Vectors Matrices Inner and Outer Products "Vector Lengths, Norms, and Weighted Norms "Brand: Dover Publications.

A Geometric Approach to the Optimal Control of Nonholonomic Mechanical Systems Anthony Bloch, Leonardo Colombo, Rohit Gupta, and David Martín de Diego Abstract In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems.

In partic-Cited by: 8. "An excellent introduction to optimal control and estimation theory and its relationship with LQG design invaluable as a reference for those already familiar with the subject." highly regarded graduate-level text provides a comprehensive introduction to optimal control theory for stochastic systems, emphasizing application of its basic concepts to real problems.4/5(21).

An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov chain with a finite state space. The constraints are given as a set of inequalities. Numerical solution of optimal control problems with state constraints by sequential quadratic programming in function space Citation for published version (APA): Machielsen, K.

Numerical solution of optimal control problems with state constraints by sequential quadratic programming in function by: In this paper we describe an optimization algorithm for the computation of solutions to optimal control problems with control, state, and terminal constraints. Inequality and equality constraints are dealt with by means of feasible directions and exact penalty approaches, respectively.

We establish a general convergence property of the algorithm which makes no reference to the existence of Cited by: Optimal control and estimation Robert F.

Stengel Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems. (ii) How can we characterize an optimal control mathematically. (iii) How can we construct an optimal control.

These turn out to be sometimes subtle problems, as the following collection of examples illustrates. EXAMPLES EXAMPLE 1: CONTROL OF PRODUCTION AND CONSUMPTION. Suppose we own, say, a factory whose output we can control.

Let us begin toFile Size: KB. approach to necessary conditions in optimal control. The results constitute, from sev-eral points of view, the current state of the art for standard optimal control problems. Although the issue of mixed constraints is broached, it is not completely developed.

The purpose of this article is to do so. The principal result, Theorem below, is a. the system. The control or control function is an operation that controls the recording, processing, or transmission of data.

These two functions drive how the system works and how the desired control is found. With these definitions, a basic optimal control problem can be defined. This basic problem will be referred to as our standard problem. Necessary and sufficient optimality conditions in mathematical programming problems.

Our paper is devoted special, but widely occurred in applications, class of nonlinear discrete optimal control problems with control-state constraints, allowing linearization of the original problem by parametrization a subset of control functions.

This leads to optimal control of problems formulated in other terms of information. A large section of the mathematical theory of optimal control is dedicated to problems where the description of insufficient quantities has a statistical character (the so-called theory of stochastic optimal control).

Random Variables, Sequences, and Processes 86 Scalar Random Variables 86 Constraints and Singular Control Terminal State Equality Constraints Problems Neighboring-Optimal Control Evaluation of the Variational Cost Function.

A demonstration of a computation for optimal control problems with state variable constraint through a successive approximation procedure. A previous procedure for an optimal control problem has been developed with the use of terminal and in-flight constraints. The problem, stated in this paper is equivalent to the earlier one.Pergamon Press Ltd.

AN OPTIMAL CONTROL PROBLEM WITH MIXED CONSTRAINTS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS* A. M. TER-KRIKOROV Moscow (Received 13 August ) MANY optimal control problems with mixed constraints, for systems with distributed parameters, are reducible to a functional optimization problem; the latter is studied by methods of Cited by: 1.Some linear problems of optimal control theory 61 To obtain a comparison with the classical Pontryagin maximum principle, we consider an elementary problem without phase constraints, Problem I'.

To find max x*(T)a under the constraints dxdt=x'AJ^n', a:*(0)=a*, a'>0, u'D-^b'.Cited by: 4.