An Infinite Horizon Linear Quadratic Problem with Unbounded Controls in Hilbert Space

Han Zhong Wu; Xun Jing Li

doi:10.1007/s101140100123

An Infinite Horizon Linear Quadratic Problem with Unbounded Controls in Hilbert Space

Acta Mathematica Sinica English Series ◽

10.1007/s101140100123 ◽

2001 ◽

Vol 17 (3) ◽

pp. 527-540

Author(s):

Han Zhong Wu ◽

Xun Jing Li

Keyword(s):

Hilbert Space ◽

Infinite Horizon ◽

Linear Quadratic ◽

Quadratic Problem ◽

Unbounded Controls

An Infinite Horizon Linear Quadratic Problem with Unbounded Controls in Hilbert Space

Acta Mathematica Sinica ◽

10.1007/pl00011629 ◽

2001 ◽

Vol 17 (3) ◽

pp. 527-540

Author(s):

Han Zhong Wu ◽

Xun Jing Li

Keyword(s):

Hilbert Space ◽

Infinite Horizon ◽

Linear Quadratic ◽

Quadratic Problem ◽

Unbounded Controls

Augmented state space approach for solving infinite-horizon linear-quadratic problem in discrete-time systems with mulitple time-delays

2015 19th International Conference on System Theory, Control and Computing (ICSTCC) ◽

10.1109/icstcc.2015.7321364 ◽

2015 ◽

Author(s):

Przemyslaw Ignaciuk

Keyword(s):

Discrete Time ◽

Time Delays ◽

Infinite Horizon ◽

Linear Quadratic ◽

Quadratic Problem ◽

State Space Approach ◽

Discrete Time Systems ◽

Augmented State ◽

Time Systems ◽

Space Approach

The value-function of an infinite-horizon linear-quadratic problem

Applied Mathematics Letters ◽

10.1016/s0893-9659(02)00146-5 ◽

2003 ◽

Vol 16 (1) ◽

pp. 71-78 ◽

Cited By ~ 15

Author(s):

J. Blot ◽

P. Michel

Keyword(s):

Value Function ◽

Infinite Horizon ◽

Linear Quadratic ◽

Quadratic Problem ◽

The Value Function

Singular linear-quadratic problem with a terminal condition

10.1063/5.0041692 ◽

2021 ◽

Author(s):

A. N. Sesekin ◽

A. A. Frolova

Keyword(s):

Terminal Condition ◽

Linear Quadratic ◽

Quadratic Problem

Infinite horizon linear quadratic gene regulation in fluctuating environments

2012 IEEE 51st IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2012.6426841 ◽

2012 ◽

Cited By ~ 1

Author(s):

Farshad R. Pour Safaei ◽

Joao P. Hespanha ◽

Stephen R. Proulx

Keyword(s):

Gene Regulation ◽

Infinite Horizon ◽

Linear Quadratic ◽

Fluctuating Environments

Infinite horizon multiobjective optimal control of stochastic cooperative linear-quadratic dynamic difference games

Journal of the Franklin Institute ◽

10.1016/j.jfranklin.2021.08.022 ◽

2021 ◽

Author(s):

Chenchen Peng ◽

Weihai Zhang ◽

Limin Ma

Keyword(s):

Optimal Control ◽

Infinite Horizon ◽

Linear Quadratic ◽

Multiobjective Optimal Control

An indirect pseudospectral method for the solution of linear-quadratic optimal control problems with infinite horizon

Optimization ◽

10.1080/02331934.2015.1014481 ◽

2015 ◽

Vol 65 (3) ◽

pp. 609-633 ◽

Cited By ~ 8

Author(s):

S. Pickenhain ◽

A. Burtchen ◽

K. Kolo ◽

V. Lykina

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Infinite Horizon ◽

Pseudospectral Method ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Quadratic Optimal Control

Asymptotic Solution of a Singularly Perturbed Linear-Quadratic Problem in Critical Case with Cheap Control

Journal of Optimization Theory and Applications ◽

10.1007/s10957-017-1156-6 ◽

2017 ◽

Vol 175 (2) ◽

pp. 324-340 ◽

Cited By ~ 2

Author(s):

Nguyen Thi Hoai

Keyword(s):

Asymptotic Solution ◽

Critical Case ◽

Singularly Perturbed ◽

Linear Quadratic ◽

Quadratic Problem ◽

Cheap Control

An alternate numerical solution to the linear quadratic problem

IEEE Transactions on Automatic Control ◽

10.1109/9.273368 ◽

1994 ◽

Vol 39 (1) ◽

pp. 198-202 ◽

Cited By ~ 48

Author(s):

P.L.D. Peres ◽

J.C. Geromel

Keyword(s):

Numerical Solution ◽

Linear Quadratic ◽

Quadratic Problem

On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2014-0053 ◽

2014 ◽

Vol 24 (4) ◽

pp. 723-733

Author(s):

K.Maciej Przyłuski

Keyword(s):

Minimum Energy ◽

Sufficient Conditions ◽

Control Problems ◽

Linear Quadratic Control ◽

Linear Quadratic ◽

Minimum Norm Solution ◽

Quadratic Problem ◽

Infinite Dimensional ◽

Necessary And Sufficient ◽

Quadratic Control Problems

Abstract In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.