Applying a finite-horizon numerical optimization method to a periodic optimal control problem

Authors:
Jeffrey Azzato;Jacek B. Krawczyk
Affiliations:
Faculty of Science, Victoria University of Wellington, PO Box 600, Wellington, New Zealand;Faculty of Commerce and Administration, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
Venue:
Automatica (Journal of IFAC)
Year:
2008

Citing 4
Cited 0

Numerical methods for stochastic control problems in continuous time

SIAM Journal on Control and Optimization
Numerical methods for stochastic control problems in continuous time

Numerical methods for stochastic control problems in continuous time
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Linear Programming Approach to Deterministic Long Run Average Problems of Optimal Control

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Abstract

Computing a numerical solution to a periodic optimal control problem can be difficult, especially when the period is unknown. A method of approximating a solution to a stochastic optimal control problem using Markov chains was developed in [Krawczyk, J. B. (2001). A Markovian approximated solution to a portfolio management problem. Information Technology for Economics and Management, 1, http://www.item.woiz.polsl.pl/issue/journal1.htm]. This paper describes the application of that method to a periodic optimal control problem formulated in [Gaitsgory, V. & Rossomakhine, S. (2006). Linear programming approach to deterministic long run average problems of optimal control. SIAM Journal on Control and Optimization, 44(6), 2006-2037]. As a result, approximately optimal feedback rules are computed that can control the system both on and off the optimal orbit.