The maximum principle in infinite dimension

Previous Article
A note on boundary layer effects in periodic homogenization with Dirichlet boundary conditions
DCDS Home
This Issue
Next Article
Existence of bounded trajectories via upper and lower solutions

July 2000, 6(3): 557-574. doi: 10.3934/dcds.2000.6.557

The maximum principle in infinite dimension

1.	University of California, Department of Mathematics, Los Angeles, California 90095, United States

Received July 1999 Revised February 2000 Published April 2000

Abstract
Related Papers

We provide a counterexample to the maximum principle for the minimum norm problem and establish several relations between this problem and the time optimal problem. The system is linear, infinite dimensional, with point target and "full" control.

Keywords: time optimal problem, minimum norm problem., Linear control systems in Banach spaces.

Mathematics Subject Classification: Primary: 49J27, 49K27, 93E20, 93E2.

Citation: H. O. Fattorini. The maximum principle in infinite dimension. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 557-574. doi: 10.3934/dcds.2000.6.557

[1]	Andrei V. Dmitruk, Nikolai P. Osmolovski. Necessary conditions for a weak minimum in a general optimal control problem with integral equations on a variable time interval. Mathematical Control & Related Fields, 2017, 7 (4) : 507-535. doi: 10.3934/mcrf.2017019
[2]	Jiongmin Yong. A deterministic linear quadratic time-inconsistent optimal control problem. Mathematical Control & Related Fields, 2011, 1 (1) : 83-118. doi: 10.3934/mcrf.2011.1.83
[3]	Ugo Boscain, Yacine Chitour. On the minimum time problem for driftless left-invariant control systems on SO(3). Communications on Pure & Applied Analysis, 2002, 1 (3) : 285-312. doi: 10.3934/cpaa.2002.1.285
[4]	Tijana Levajković, Hermann Mena, Amjad Tuffaha. The stochastic linear quadratic optimal control problem in Hilbert spaces: A polynomial chaos approach. Evolution Equations & Control Theory, 2016, 5 (1) : 105-134. doi: 10.3934/eect.2016.5.105
[5]	Saeed Ketabchi, Hossein Moosaei, M. Parandegan, Hamidreza Navidi. Computing minimum norm solution of linear systems of equations by the generalized Newton method. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 113-119. doi: 10.3934/naco.2017008
[6]	Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1743-1767. doi: 10.3934/dcdsb.2018235
[7]	Hongyan Yan, Yun Sun, Yuanguo Zhu. A linear-quadratic control problem of uncertain discrete-time switched systems. Journal of Industrial & Management Optimization, 2017, 13 (1) : 267-282. doi: 10.3934/jimo.2016016
[8]	Viorel Barbu, Gabriela Marinoschi. An identification problem for a linear evolution equation in a banach space. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1-12. doi: 10.3934/dcdss.2020081
[9]	Monica Motta. Minimum time problem with impulsive and ordinary controls. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5781-5809. doi: 10.3934/dcds.2018252
[10]	Peter I. Kogut. On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2105-2133. doi: 10.3934/dcds.2014.34.2105
[11]	Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial & Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967
[12]	Giulia Cavagnari. Regularity results for a time-optimal control problem in the space of probability measures. Mathematical Control & Related Fields, 2017, 7 (2) : 213-233. doi: 10.3934/mcrf.2017007
[13]	Jingtao Shi, Juanjuan Xu, Huanshui Zhang. Stochastic recursive optimal control problem with time delay and applications. Mathematical Control & Related Fields, 2015, 5 (4) : 859-888. doi: 10.3934/mcrf.2015.5.859
[14]	Fabio Bagagiolo. An infinite horizon optimal control problem for some switching systems. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 443-462. doi: 10.3934/dcdsb.2001.1.443
[15]	Alfredo Lorenzi, Ioan I. Vrabie. An identification problem for a linear evolution equation in a Banach space and applications. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 671-691. doi: 10.3934/dcdss.2011.4.671
[16]	Jiamin Zhu, Emmanuel Trélat, Max Cerf. Planar tilting maneuver of a spacecraft: Singular arcs in the minimum time problem and chattering. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1347-1388. doi: 10.3934/dcdsb.2016.21.1347
[17]	Hongtruong Pham, Xiwen Lu. The inverse parallel machine scheduling problem with minimum total completion time. Journal of Industrial & Management Optimization, 2014, 10 (2) : 613-620. doi: 10.3934/jimo.2014.10.613
[18]	Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557
[19]	Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. An optimal control problem in HIV treatment. Conference Publications, 2013, 2013 (special) : 311-322. doi: 10.3934/proc.2013.2013.311
[20]	Donghui Yang, Jie Zhong. Optimal actuator location of the minimum norm controls for stochastic heat equations. Mathematical Control & Related Fields, 2018, 8 (3&4) : 1081-1095. doi: 10.3934/mcrf.2018046

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences