A boundary value problem for a non-linear difference equation

• Autorzy: Lefebvre Mario

Identyfikatory

DOI

10.24425/acs.2023.148883

• Języki publikacji: EN

Abstrakty

EN

A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.

Słowa kluczowe

EN

higher-order difference equations; optimal control; dynamic programming; first-passage time; homing problem

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 4
• Strony: 829--837
• Opis fizyczny: Bibliogr. 10 poz., tab., wzory

Twórcy

autor

Lefebvre Mario

• Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centreville, Montréal, Canada H3C 3A7, Canada

Bibliografia

• [1] M. Kounta and N.J. Dawson: Linear quadratic Gaussian homing for Markov processes with regime switching and applications to controlled population growth/decay. Methodology and Computing in Applied Probability, 23 (2021), 1155-1172. DOI: 10.1007/s11009-020-09800-2.
• [2] J. Kuhn: The risk-sensitive homing problem. Journal of Applied Probability, 22 (1985), 796-803. DOI: 10.2307/3213947.
• [3] M. Lefebvre: Minimizing or maximizing the first-passage time to a time-dependent boundary. Optimization, 71(2), (2022), 387-401. DOI: 10.1080/02331934.2021.1914039.
• [4] M. Lefebvre: The homing problem for autoregressive processes. IMA Journal of Mathematical Control and Information, 39(1), (2022), 322-344. DOI: 10.1093/imamci/dnab047.
• [5] M. Lefebvre and M. Kounta: Discrete homing problems. Archives of Control Sciences, 23(1), (2013), 5-18. DOI: 10.2478/v10170-011-0039-6.
• [6] C. Makasu: Risk-sensitive control for a class of homing problems. Automatica, 45(10), (2009), 2454-2455. DOI: 10.1016/j.automatica.2009.06.015.
• [7] S. Stević, M.A. Alghamdi, A. Alotaibi and E.M. Elsayed: On a class of solvable higher-order difference equations. Filomat, 31(2), (2017), 461-477. DOI: 10.2298/FIL1702461S.
• [8] Z. Wang and Z. Zhou: Boundary value problem for a second-order difference equation with resonance. Complexity, 2020 (2020). DOI: 10.1155/2020/7527030.
• [9] P. Whittle: Optimization over Time, I. Wiley, Chichester, 1982.
• [10] P. Whittle: Risk-sensitive Optimal Control. Wiley, Chichester, 1990.