American Institute of Mathematical Sciences

Advanced
October  2000, 6(4): 803-808. doi: 10.3934/dcds.2000.6.803

A gradient flow approach for computing jump linear quadratic optimal feedback gains

K.H. Wong 1, , C. Myburgh 1, and  L. Omari 1,

1. 

Department of Computational and Applied Mathematics, University of The Witwatersrand, Johannesburg, South Africa, South Africa, South Africa

Received  October 1998 Revised  May 2000 Published  August 2000

A class of linear systems subject to sudden jumps in parameter values is considered. To solve this class of stochastic control problem, we try to find the best feedback control law depending both on the measurable output as well as the mode of the system. A gradient flow based algorithm is derived for this problem. It is shown that an optimal solution can be successfully computed by finding the limiting solution of an ordinary differential equation which is given in terms of the gradient flow associated with the cost function. Several important properties are obtained. A numerical example is solved.
Keywords: Lyapunov differential equations, feedback control., jump linear quadratic systems, Gradient flow.
Mathematics Subject Classification: 49N35, 49N10, 93E2.
Citation: K.H. Wong, C. Myburgh, L. Omari. A gradient flow approach for computing jump linear quadratic optimal feedback gains. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 803-808. doi: 10.3934/dcds.2000.6.803
[1]

Jun Moon. Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems. Mathematical Control and Related Fields, 2022, 12 (2) : 371-404. doi: 10.3934/mcrf.2021026
[2]

Jian Chen, Tao Zhang, Ziye Zhang, Chong Lin, Bing Chen. Stability and output feedback control for singular Markovian jump delayed systems. Mathematical Control and Related Fields, 2018, 8 (2) : 475-490. doi: 10.3934/mcrf.2018019
[3]

Qi Lü, Tianxiao Wang, Xu Zhang. Characterization of optimal feedback for stochastic linear quadratic control problems. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 11-. doi: 10.1186/s41546-017-0022-7
[4]

Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1103-1119. doi: 10.3934/dcdss.2018063
[5]

Russell Johnson, Carmen Núñez. Remarks on linear-quadratic dissipative control systems. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 889-914. doi: 10.3934/dcdsb.2015.20.889
[6]

Jianhui Huang, Xun Li, Jiongmin Yong. A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. Mathematical Control and Related Fields, 2015, 5 (1) : 97-139. doi: 10.3934/mcrf.2015.5.97
[7]

Yu Li, Kok Lay Teo, Shuhua Zhang. A new feedback form of open-loop Stackelberg strategy in a general linear-quadratic differential game. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022105
[8]

Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic mean-field-game of backward stochastic differential systems. Mathematical Control and Related Fields, 2018, 8 (3&4) : 653-678. doi: 10.3934/mcrf.2018028
[9]

Galina Kurina, Sahlar Meherrem. Decomposition of discrete linear-quadratic optimal control problems for switching systems. Conference Publications, 2015, 2015 (special) : 764-774. doi: 10.3934/proc.2015.0764
[10]

Ying Hu, Shanjian Tang. Mixed deterministic and random optimal control of linear stochastic systems with quadratic costs. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 1-. doi: 10.1186/s41546-018-0035-x
[11]

Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4099-4116. doi: 10.3934/dcdsb.2019052
[12]

Cătălin-George Lefter, Elena-Alexandra Melnig. Feedback stabilization with one simultaneous control for systems of parabolic equations. Mathematical Control and Related Fields, 2018, 8 (3&4) : 777-787. doi: 10.3934/mcrf.2018034
[13]

Sanmei Zhu, Jun-e Feng, Jianli Zhao. State feedback for set stabilization of Markovian jump Boolean control networks. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1591-1605. doi: 10.3934/dcdss.2020413
[14]

Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 939-956. doi: 10.3934/dcdsb.2018049
[15]

Nguyen Dinh Cong, Nguyen Thi Thuy Quynh. Coincidence of Lyapunov exponents and central exponents of linear Ito stochastic differential equations with nondegenerate stochastic term. Conference Publications, 2011, 2011 (Special) : 332-342. doi: 10.3934/proc.2011.2011.332
[16]

Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linear-quadratic optimal control problem with second-order linear ordinary differential equation of state variable. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 495-512. doi: 10.3934/naco.2020040
[17]

Janusz Mierczyński, Sylvia Novo, Rafael Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2235-2255. doi: 10.3934/cpaa.2020098
[18]

Xingwu Chen, Jaume Llibre, Weinian Zhang. Averaging approach to cyclicity of hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3953-3965. doi: 10.3934/dcdsb.2017203
[19]

Jaume Llibre. Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022034
[20]

Hongyan Yan, Yun Sun, Yuanguo Zhu. A linear-quadratic control problem of uncertain discrete-time switched systems. Journal of Industrial and Management Optimization, 2017, 13 (1) : 267-282. doi: 10.3934/jimo.2016016

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (63)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy