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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

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, 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.
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), 102-123. 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), 305-330. 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), Art ID 127809, 13 pp. 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), 73-105. doi: 10.1137/090764232.  Google Scholar

[6]

H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations, ESAIM: COCV, 21 (2015), 815-834. 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), 289-314. doi: 10.3934/mcrf.2014.4.289.  Google Scholar

[8]

R. Vinter, Optimal Control, Birkhäuser, Springer, Boston, 2000.  Google Scholar

[9]

J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.  Google Scholar

[10]

K. Yosida, Functional Analysis, Springer-Verlag, 6th edition, 1980.  Google Scholar

show all references

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.  Google Scholar

[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.  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), Art ID 127809, 13 pp. 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), 73-105. doi: 10.1137/090764232.  Google Scholar

[6]

H. Lou and W. Wang, Optimal blowup time for controlled ordinary differential equations, ESAIM: COCV, 21 (2015), 815-834. 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), 289-314. doi: 10.3934/mcrf.2014.4.289.  Google Scholar

[8]

R. Vinter, Optimal Control, Birkhäuser, Springer, Boston, 2000.  Google Scholar

[9]

J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.  Google Scholar

[10]

K. Yosida, Functional Analysis, Springer-Verlag, 6th edition, 1980.  Google Scholar

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