American Institute of Mathematical Sciences

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

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.  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

[1]

Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195
[2]

Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control & Related Fields, 2018, 8 (3&4) : 809-828. doi: 10.3934/mcrf.2018036
[3]

Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song, Yanping Ma. Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial & Management Optimization, 2018, 14 (2) : 653-671. doi: 10.3934/jimo.2017067
[4]

Shanjian Tang. A second-order maximum principle for singular optimal stochastic controls. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1581-1599. doi: 10.3934/dcdsb.2010.14.1581
[5]

Md. Haider Ali Biswas, Maria do Rosário de Pinho. A nonsmooth maximum principle for optimal control problems with state and mixed constraints - convex case. Conference Publications, 2011, 2011 (Special) : 174-183. doi: 10.3934/proc.2011.2011.174
[6]

Hans Josef Pesch. Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 161-173. doi: 10.3934/naco.2013.3.161
[7]

Andrei V. Dmitruk, Nikolai P. Osmolovskii. Proof of the maximum principle for a problem with state constraints by the v-change of time variable. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2189-2204. doi: 10.3934/dcdsb.2019090
[8]

Yi Wang, Dun Zhou. Transversality for time-periodic competitive-cooperative tridiagonal systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1821-1830. doi: 10.3934/dcdsb.2015.20.1821
[9]

Luong V. Nguyen. A note on optimality conditions for optimal exit time problems. Mathematical Control & Related Fields, 2015, 5 (2) : 291-303. doi: 10.3934/mcrf.2015.5.291
[10]

Piermarco Cannarsa, Cristina Pignotti, Carlo Sinestrari. Semiconcavity for optimal control problems with exit time. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 975-997. doi: 10.3934/dcds.2000.6.975
[11]

Giuseppe Maria Coclite, Mauro Garavello, Laura V. Spinolo. Optimal strategies for a time-dependent harvesting problem. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : 865-900. doi: 10.3934/dcdss.2018053
[12]

Piotr Kopacz. A note on time-optimal paths on perturbed spheroid. Journal of Geometric Mechanics, 2018, 10 (2) : 139-172. doi: 10.3934/jgm.2018005
[13]

Kim Dang Phung, Gengsheng Wang, Xu Zhang. On the existence of time optimal controls for linear evolution equations. Discrete & Continuous Dynamical Systems - B, 2007, 8 (4) : 925-941. doi: 10.3934/dcdsb.2007.8.925
[14]

N. Arada, J.-P. Raymond. Time optimal problems with Dirichlet boundary controls. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1549-1570. doi: 10.3934/dcds.2003.9.1549
[15]

Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185
[16]

Zuzana Chladná. Optimal time to intervene: The case of measles child immunization. Mathematical Biosciences & Engineering, 2018, 15 (1) : 323-335. doi: 10.3934/mbe.2018014
[17]

Piermarco Cannarsa, Carlo Sinestrari. On a class of nonlinear time optimal control problems. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 285-300. doi: 10.3934/dcds.1995.1.285
[18]

Shu Dai, Dong Li, Kun Zhao. Finite-time quenching of competing species with constrained boundary evaporation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1275-1290. doi: 10.3934/dcdsb.2013.18.1275
[19]

Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233
[20]

Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183

2018 Impact Factor: 1.292

Tools

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences