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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).

show all references

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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