Optimal blowup/quenching time for controlled autonomous ordinary differential equations

Hongwei Lou; Weihan  Wang

doi:10.3934/mcrf.2015.5.517

Article Contents

2015, Volume 5, Issue 3: 517-527. Doi: 10.3934/mcrf.2015.5.517

This issue Previous Article Controlled reflected mean-field backward stochastic differential equations coupled with value function and related PDEs Next Article Transposition method for backward stochastic evolution equations revisited, and its application

Optimal blowup/quenching time for controlled autonomous ordinary differential equations

Hongwei Lou^1, and
Weihan Wang^2,

1.
School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433
2.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: June 30, 2014

Revised: October 31, 2014

Published: August 2015

Abstract Related Papers Cited by

Abstract

Blowup/Quenching time optimal control problems for controlled autonomous ordinary differential equations are considered. The main results are maximum principles for these time optimal control problems, including the transversality conditions.

Keywords:

Mathematics Subject Classification: Primary: 49J15; Secondary: 49K15, 34A34.

Citation:

Related Papers

Cited by

References

[1]	E. N. Barron and W. Liu, Optimal control of the blowup time, SIAM J. Control Optim., 34 (1996), 102-123.doi: 10.1137/S0363012993245021.
[2]	S. Kaplan, On the growth of solutions of quasi-linear parabolic equations, Comm. Pure Appl. Math., 16 (1963), 305-330.doi: 10.1002/cpa.3160160307.
[3]	H. Kawarada, On solutions of initial-boundary problem for $u_t=u_{x x}+1/(1-u)$, Publ. Res. Inst. Math. Sci., 10 (1974/1975), 729-736. doi: 10.2977/prims/1195191889.
[4]	P. Lin, Quenching time optimal control for some ordinary differential equations, J. Appl. Math., (2014), Art ID 127809, 13 pp.doi: 10.1155/2014/127809.
[5]	P. Lin and G. Wang, Blowup time optimal control for ordinary differential equations, SIAM J. Control Optim., 49 (2011), 73-105.doi: 10.1137/090764232.
[6]	H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations, ESAIM: COCV, 21 (2015), 815-834.
[7]	H. Lou, J. Wen and Y. Xu, Time optimal control problems for some non-smooth systems, Math. Control Relat. Fields, 4 (2014), 289-314.doi: 10.3934/mcrf.2014.4.289.
[8]	R. Vinter, Optimal Control, Birkhäuser, Springer, Boston, 2000.
[9]	J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.
[10]	K. Yosida, Functional Analysis, Springer-Verlag, 6th edition, 1980.