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Linear programming approach to discrete time optimal control problems with time discounting

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posted on 28.03.2022, 12:09 authored by Alex Parkinson
The linear programming (LP) approach to control systems is based on the fact that the occupational measures generated by admissible controls and the corresponding solutions of a nonlinear system satisfy certain linear equations representing the system’s dynamics in an integral form. The idea of such linearization was explored extensively in relation to various deterministic and stochastic problems of optimal control of systems that evolve in continuous time. However, no results based on this idea for deterministic discrete time control systems is available in the literature. The thesis aims at the development of LP based techniques for analysis and solution of a deterministic discrete time optimal control problem with time discounting criteria. To this end, we reformulate the optimal control problem as that of optimization problem on the set of discounted occupational measures and we show that the optimal value of the latter is equal to the optimal value of a certain infinite dimensional (ID) LP problem. We then show that this IDLP problem can be approximated by semi-infinite linear programming problems and subsequently by finite-dimensional (“standard”) LP problems. We also indicate a way how a near optimal control of the underlying nonlinear optimal control problem can be constructed on the basis of the solution of an approximating finite-dimensional LP problem.

History

Table of Contents

1. Introduction -- 2. Occupational measure formulation and duality results -- 3. Equality of the optimal values of the optimal control and IDLP problems -- 4. Finite dimensional approximations -- 5. Future research directions.

Notes

Theoretical thesis. Bibliography: pages 29-30

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics

Department, Centre or School

Department of Mathematics

Year of Award

2016

Principal Supervisor

Vladimir Gaitsgory

Rights

Copyright Alex Parkinson 2016. Copyright disclaimer: http://mq.edu.au/library/copyright

Language

English

Extent

1 online resource (x, 30 pages) colour illustrations

Former Identifiers

mq:70185 http://hdl.handle.net/1959.14/1261090