无穷时域上常微分方程的最优控制问题

Abstract

Abstract:

This paper studies an infinite horizon optimal control problem governed by a kind of controlled linear ordinary differential equations. Corresponding to certain controls, the solutions of the equation may blow up at a finite time. It differs from the most infinite horizon optimal control problems in past publications. The purpose of this study is to develop a new method to establish Pontryagin Maximum Principle of optimal controls for such problem.

Key words: optimal control, ordinary differential equations, Pontryagin Maximum Principle

CLC Number:

O231.2

Xingyang Yu. Infinite Horizon Optimal Control Problem for Ordinary Differential Equations[J].Acta mathematica scientia,Series A, 2026, 46(5): 1884-1899.

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References 19

[1]	Aseev S M, Kryazhimskiy A V. The Pontryagin maximum prinicple and transversality conditions for a class of optimal control problems with infinite time horizons. SIAM Journal on Control and Optimization, 2004, 43: 1094-1119 doi: 10.1137/S0363012903427518
[2]	Aseev S M, Kryazhimskiy A V. The Pontryagin maximum principle and problems of optimal economic growth. Proc Steklov Inst Math, 2007, 257: 1-255 doi: 10.1134/S0081543807020010
[3]	Barbu V. Analysis and Control of Nonlinear Infinite Dimensional System. New York: Academic Press, 1993
[4]	Barbu V, Optimal Control of Variational Inequalities. London: Res Notes Math, 1984
[5]	Carlson D A, Haurie A B, Leizarowitz A. Infinite Horizon Optimal Control. Deterministic and Stochastic Systems. Berlin: Springer-Verlag, 1991
[6]	Casas E, Kunisch K. Infinite horizon optimal control problems for a class of semilinear parabolic equations. SIAM Journal on Control and Optimization, 2022, 60: 2070-2094 doi: 10.1137/21M1464816
[7]	Casas E, Kunisch K. Infinite horizon optimal control problems with discount factor on the state. SIAM Journal on Control and Optimization, 2023, 61: 1438-1459 doi: 10.1137/22M1490296
[8]	Casas E, Kunisch K. Infinite horizon optimal control for a general class of semilinear parabolic equations. Applied Mathematics and Optimization, 2023, 99(47): Art 36
[9]	Casas E, Yong J. Maximum principle for state-constrained optimal control problems governed by quasilinear equations. Differential Integral Equations, 1996, 130: 179-200
[10]	De La Vega C. Necessary conditions for infinite-horizon Volterra optimal control problems with time delay. IMA Journal of Mathematical Control and Information, 2009, 26(1): 1-22 doi: 10.1093/imamci/dnm026
[11]	Fattorini H O, Murphy T. Optimal problems for nonlinear parabolic boundary control systems. SIAM Journal on Control and Optimization, 1994, 32(6): 1577-1596 doi: 10.1137/S0363012992237959
[12]	Halkin H. Necessary conditions for optimal control problems with infinite horizons. Econometrica, 1974, 42(2): 267-272 doi: 10.2307/1911976
[13]	Li X J, Yong J M. Optimal Control Theory for Infinite Dimensional Systems. Boston: Cambridge MA, 1995
[14]	Pontryagin L S, Boltyanskii V G, Gamkrelidze R V, et al. The Mathematical Theory of Optimal Processes. New York: Wiley, 1962
[15]	Seierstad A. Necessary conditions for nonsmooth, infinite-horizon, optimal control problems. Journal of Optimization Theory and Applications, 1999, 103(1): 201-229 doi: 10.1023/A:1021733719020
[16]	Tauchnitz N. The Pontryagin maximum principle for nonlinear optimal control problems with infinite horizon. Journal of Optimization Theory and Applications, 2015, 167(1): 27-48 doi: 10.1007/s10957-015-0723-y
[17]	Wang G S. Optimal controls of 3-dimensional Navier-Stokes equations with state constraint. SIAM Journal on Control and Optimization, 2002, 41(2): 583-606 doi: 10.1137/S0363012901385769
[18]	Wang G S, Wang L J. State-constrained optimal control governed by non-well-posed parabolic differential equations. SIAM Journal on Control and Optimization, 2002, 40(5): 1517-1539 doi: 10.1137/S0363012900377006
[19]	Ye J J. Nonsmooth maximum principle for infinite-horizon problems. Journal of Optimization Theory and Applications, 1993, 76(3): 485-500 doi: 10.1007/BF00939379

Infinite Horizon Optimal Control Problem for Ordinary Differential Equations

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