Optimal blowup/quenching time for controlled autonomous ordinary differential equations

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September 2015, 5(3): 517-527. doi: 10.3934/mcrf.2015.5.517

Optimal blowup/quenching time for controlled autonomous ordinary differential equations

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

Received July 2014 Revised November 2014 Published July 2015

Abstract
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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: optimal quenching time, Optimal blowup time, transversality condition., maximum principle.

Mathematics Subject Classification: Primary: 49J15; Secondary: 49K15, 34A3.

Citation: Hongwei Lou, Weihan Wang. Optimal blowup/quenching time for controlled autonomous ordinary differential equations. Mathematical Control & Related Fields, 2015, 5 (3) : 517-527. doi: 10.3934/mcrf.2015.5.517

References:

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

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References:

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

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