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Advantages for controls imposed in a proper subset
1. | School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China |
2. | School of Mathematical Sciences, Fudan University, KLMNS, Shanghai, 200433, China |
References:
[1] |
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 1998. |
[2] |
H. O. Fattorini, Time-optimal control of solutions of operational differential equations. Journal of the Society for Industrial and Applied Mathematics Series A, 2 (1964), 54-59.
doi: 10.1137/0302005. |
[3] |
H. O. Fattorini, "Infinite-dimensional Optimization and Control Theory," Encyclopedia of Mathematics and its Applications, 62, Cambridge University Press, Cambridge, 1999. |
[4] |
Qing Han and Fanghua Lin, "Elliptic Partial Differential Equations," Courant Lecture Notes in Mathematics, 1, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 1997. |
[5] |
Steven G. Krantz, "Function Theory of Several Complex Variables," Pure and Applied Mathematics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1982. |
[6] |
F. H. Lin, A uniqueness theorem for parabolic equations, Communications on Pure and Applied Mathematics, 43 (1990), 127-136.
doi: 10.1002/cpa.3160430105. |
[7] |
Qi L and Gengsheng Wang, On the existence of time optimal controls with constraints of the rectangular type for heat equations, SIAM Journal on Control and Optimization, 49 (2011), 1124-1149.
doi: 10.1137/10081277X. |
[8] |
A. M. Micheletti, Perturbazione dello spettro dell'operatore di Laplace, in relazione ad una variazione del campo, (Italian) Ann. Scuola Norm. Sup. Pisa, 26 (1972), 151-169. |
[9] |
Victor J. Mizel and Thomas I. Seidman, An abstract bang-bang principle and time-optimal boundary control of the heat equation, SIAM Journal on Control and Optimization, 35 (1997), 1204-1216.
doi: 10.1137/S0363012996265470. |
[10] |
Jaime H. Ortega and Enrique Zuazua, Generic simplicity of the spectrum and stabilization for a plate equation, SIAM Journal on Control and Optimization, 39 (2000), 1585-1614 (electronic).
doi: 10.1137/S0363012900358483. |
[11] |
Kim Dang Phung and Gengsheng Wang, An observability estimate for parabolic equations from a measurable set in time and its applications, Journal of the European Mathematical Society, 15 (2013), 681-703.
doi: 10.4171/JEMS/371. |
[12] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes," Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt Interscience Publishers John Wiley & Sons, Inc, New York-London, 1962. |
[13] |
E. D. Sontag, "Mathematical Control Theory: Deterministic Finite-Dimensional Systems," Second edition, Texts in Applied Mathematics, 6, Springer-Verlag, New York, 1998. |
[14] |
K. Uhlenbeck, Generic properties of eigenfunctions, American Journal of Mathematics, 98 (1976), 1059-1078.
doi: 10.2307/2374041. |
[15] |
Gengsheng Wang, $L^\infty$-null controllability for the heat equation and its consequences for the time optimal control problem, SIAM Journal on Control and Optimization, 47 (2008), 1701-1720.
doi: 10.1137/060678191. |
show all references
References:
[1] |
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 1998. |
[2] |
H. O. Fattorini, Time-optimal control of solutions of operational differential equations. Journal of the Society for Industrial and Applied Mathematics Series A, 2 (1964), 54-59.
doi: 10.1137/0302005. |
[3] |
H. O. Fattorini, "Infinite-dimensional Optimization and Control Theory," Encyclopedia of Mathematics and its Applications, 62, Cambridge University Press, Cambridge, 1999. |
[4] |
Qing Han and Fanghua Lin, "Elliptic Partial Differential Equations," Courant Lecture Notes in Mathematics, 1, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 1997. |
[5] |
Steven G. Krantz, "Function Theory of Several Complex Variables," Pure and Applied Mathematics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1982. |
[6] |
F. H. Lin, A uniqueness theorem for parabolic equations, Communications on Pure and Applied Mathematics, 43 (1990), 127-136.
doi: 10.1002/cpa.3160430105. |
[7] |
Qi L and Gengsheng Wang, On the existence of time optimal controls with constraints of the rectangular type for heat equations, SIAM Journal on Control and Optimization, 49 (2011), 1124-1149.
doi: 10.1137/10081277X. |
[8] |
A. M. Micheletti, Perturbazione dello spettro dell'operatore di Laplace, in relazione ad una variazione del campo, (Italian) Ann. Scuola Norm. Sup. Pisa, 26 (1972), 151-169. |
[9] |
Victor J. Mizel and Thomas I. Seidman, An abstract bang-bang principle and time-optimal boundary control of the heat equation, SIAM Journal on Control and Optimization, 35 (1997), 1204-1216.
doi: 10.1137/S0363012996265470. |
[10] |
Jaime H. Ortega and Enrique Zuazua, Generic simplicity of the spectrum and stabilization for a plate equation, SIAM Journal on Control and Optimization, 39 (2000), 1585-1614 (electronic).
doi: 10.1137/S0363012900358483. |
[11] |
Kim Dang Phung and Gengsheng Wang, An observability estimate for parabolic equations from a measurable set in time and its applications, Journal of the European Mathematical Society, 15 (2013), 681-703.
doi: 10.4171/JEMS/371. |
[12] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes," Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt Interscience Publishers John Wiley & Sons, Inc, New York-London, 1962. |
[13] |
E. D. Sontag, "Mathematical Control Theory: Deterministic Finite-Dimensional Systems," Second edition, Texts in Applied Mathematics, 6, Springer-Verlag, New York, 1998. |
[14] |
K. Uhlenbeck, Generic properties of eigenfunctions, American Journal of Mathematics, 98 (1976), 1059-1078.
doi: 10.2307/2374041. |
[15] |
Gengsheng Wang, $L^\infty$-null controllability for the heat equation and its consequences for the time optimal control problem, SIAM Journal on Control and Optimization, 47 (2008), 1701-1720.
doi: 10.1137/060678191. |
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