American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Stability and controllability of a wave equation with dynamical boundary control
  • MCRF Home
  • This Issue
  • Next Article
    Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension
June  2015, 5(2): 291-303. doi: 10.3934/mcrf.2015.5.291

A note on optimality conditions for optimal exit time problems

Luong V. Nguyen 1,

1. 

Università di Padova, Dipartimento di Matematica, via Trieste 63, 35121 Padova, Italy

Received  March 2014 Revised  July 2014 Published  April 2015

In this note, we obtain some optimality conditions for optimal control problems with exit time similar to those obtained in [Cannarsa, Pignotti and Sinestrari, Discrete Contin. Dynam. Systems 6 (2000), 975 - 997] without requiring an assumption on the Hamiltonian.
Keywords: semiconcave function, exit time problems., maximum principle, Value functions, optimality conditions.
Mathematics Subject Classification: Primary: 49K15, 93C15; Secondary: 49J5.
Citation: 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
References:
[1]

M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamiltonian-Jacobi-Bellman Equations,, Systems & Control: Foundations & Applications, (1997).  doi: 10.1007/978-0-8176-4755-1.  Google Scholar

[2]

P. Cannarsa, A. Marigonda and K. T. Nguyen, Optimality conditions and regularity results for time optimal control problems with differential inclusions,, J. Math. Anal. Appl., 427 (2015), 202.  doi: 10.1016/j.jmaa.2015.02.027.  Google Scholar

[3]

P. Cannarsa, C. Pignotti and C. Sinestrari, Semiconcavity for optimal control problems with exit time,, Discrete Contin. Dynam. Systems, 6 (2000), 975.  doi: 10.3934/dcds.2000.6.975.  Google Scholar

[4]

P. Cannarsa and C. Sinestrari, Convexity properties of the minimun time function,, Calc. Var. Partial Differential Equations, 3 (1995), 273.  doi: 10.1007/BF01189393.  Google Scholar

[5]

P. Cannarsa and C. Sinestrari, On a class of nonlinear time optimal control problems,, Discrete Contin. Dynam. Systems, 1 (1995), 285.  doi: 10.3934/dcds.1995.1.285.  Google Scholar

[6]

P. Cannarsa and C. Sinestrari, Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control,, Progress in Nonlinear Differential Equations and their Applications, (2004).   Google Scholar

[7]

H. Frankowska and L. V. Nguyen, Local regularity of the minimum time function,, J. Optim. Theory. Appl., 164 (2005), 68.  doi: 10.1007/s10957-014-0575-x.  Google Scholar

[8]

E. B. Lee and L. Markus, Foundations of Optimal Control Theory,, John Wiley & Sons, (1967).   Google Scholar

[9]

C. Pignotti, Rectifiability results for singular and conjugate points of optimal exit time problems,, J. Math. Anal. Appl., 270 (2002), 681.  doi: 10.1016/S0022-247X(02)00110-5.  Google Scholar

show all references

References:
[1]

M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamiltonian-Jacobi-Bellman Equations,, Systems & Control: Foundations & Applications, (1997).  doi: 10.1007/978-0-8176-4755-1.  Google Scholar

[2]

P. Cannarsa, A. Marigonda and K. T. Nguyen, Optimality conditions and regularity results for time optimal control problems with differential inclusions,, J. Math. Anal. Appl., 427 (2015), 202.  doi: 10.1016/j.jmaa.2015.02.027.  Google Scholar

[3]

P. Cannarsa, C. Pignotti and C. Sinestrari, Semiconcavity for optimal control problems with exit time,, Discrete Contin. Dynam. Systems, 6 (2000), 975.  doi: 10.3934/dcds.2000.6.975.  Google Scholar

[4]

P. Cannarsa and C. Sinestrari, Convexity properties of the minimun time function,, Calc. Var. Partial Differential Equations, 3 (1995), 273.  doi: 10.1007/BF01189393.  Google Scholar

[5]

P. Cannarsa and C. Sinestrari, On a class of nonlinear time optimal control problems,, Discrete Contin. Dynam. Systems, 1 (1995), 285.  doi: 10.3934/dcds.1995.1.285.  Google Scholar

[6]

P. Cannarsa and C. Sinestrari, Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control,, Progress in Nonlinear Differential Equations and their Applications, (2004).   Google Scholar

[7]

H. Frankowska and L. V. Nguyen, Local regularity of the minimum time function,, J. Optim. Theory. Appl., 164 (2005), 68.  doi: 10.1007/s10957-014-0575-x.  Google Scholar

[8]

E. B. Lee and L. Markus, Foundations of Optimal Control Theory,, John Wiley & Sons, (1967).   Google Scholar

[9]

C. Pignotti, Rectifiability results for singular and conjugate points of optimal exit time problems,, J. Math. Anal. Appl., 270 (2002), 681.  doi: 10.1016/S0022-247X(02)00110-5.  Google Scholar

[1]

Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020048
[2]

Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020045
[3]

Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248
[4]

Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020442
[5]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017
[6]

Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020046
[7]

Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077
[8]

Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020050
[9]

Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu. On the convexity for the range set of two quadratic functions. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020169
[10]

Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296
[11]

Yu Zhou, Xinfeng Dong, Yongzhuang Wei, Fengrong Zhang. A note on the Signal-to-noise ratio of $ (n, m) $-functions. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020117
[12]

Djamel Aaid, Amel Noui, Özen Özer. Piecewise quadratic bounding functions for finding real roots of polynomials. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 63-73. doi: 10.3934/naco.2020015
[13]

Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323
[14]

Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020443
[15]

Sihem Guerarra. Maximum and minimum ranks and inertias of the Hermitian parts of the least rank solution of the matrix equation AXB = C. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 75-86. doi: 10.3934/naco.2020016
[16]

João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138
[17]

Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020052
[18]

Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380
[19]

Monia Capanna, Jean C. Nakasato, Marcone C. Pereira, Julio D. Rossi. Homogenization for nonlocal problems with smooth kernels. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020385
[20]

Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020070

2019 Impact Factor: 0.857

Tools

Metrics

  • PDF downloads (65)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences