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

• Published in: Automatica (Oxford) Vol. 44; no. 6; pp. 1642 - 1651
• Main Authors: Azzato, Jeffrey, Krawczyk, Jacek B.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.06.2008; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Dynamic systems; Exact sciences and technology; Information systems. Data bases; Markov chain approximation; Memory organisation. Data processing; Numerical optimization; Optimal control; Periodic control; Software; Markov chain approximation; Numerical optimization; Dynamic systems; Periodic control; Markov process; Orbit; Linear programming; HTTP; Dynamical system; Periodic solution; Modeling; Information technology; Optimization; Markov chain; Finite horizon; Optimal control; Stochastic control; Economic information; Deterministic approach; Portfolio management
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2007.12.022

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.