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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

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.
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. [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. [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. [4] P. Lin, Quenching time optimal control for some ordinary differential equations,, J. Appl. Math., (2014). 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. doi: 10.1137/090764232. [6] H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations,, ESAIM: COCV, 21 (2015), 815. [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. [8] R. Vinter, Optimal Control,, Birkhäuser, (2000). [9] J. Warga, Optimal Control of Differential and Functional Equations,, Academic Press, (1972). [10] K. Yosida, Functional Analysis,, Springer-Verlag, (1980).

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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. [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. [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. [4] P. Lin, Quenching time optimal control for some ordinary differential equations,, J. Appl. Math., (2014). 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. doi: 10.1137/090764232. [6] H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations,, ESAIM: COCV, 21 (2015), 815. [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. [8] R. Vinter, Optimal Control,, Birkhäuser, (2000). [9] J. Warga, Optimal Control of Differential and Functional Equations,, Academic Press, (1972). [10] K. Yosida, Functional Analysis,, Springer-Verlag, (1980).
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