Data-driven policy iteration algorithm for optimal control of continuous-time Itô stochastic systems with Markovian jumps

This studies the infinite horizon optimal control problem for a class of continuous-time systems subjected to multiplicative noises and Markovian jumps by using a data-driven policy iteration algorithm. The optimal control problem is equivalent to solve a stochastic coupled algebraic Riccatic equati...

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Vydané v:IET control theory & applications Ročník 10; číslo 12; s. 1431 - 1439
Hlavní autori: Song, Jun, He, Shuping, Liu, Fei, Niu, Yugang, Ding, Zhengtao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: The Institution of Engineering and Technology 08.08.2016
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ISSN:1751-8644, 1751-8652
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Abstract This studies the infinite horizon optimal control problem for a class of continuous-time systems subjected to multiplicative noises and Markovian jumps by using a data-driven policy iteration algorithm. The optimal control problem is equivalent to solve a stochastic coupled algebraic Riccatic equation (CARE). An off-line iteration algorithm is first established to converge the solutions of the stochastic CARE, which is generalised from an implicit iterative algorithm. By applying subsystems transformation (ST) technique, the off-line iterative algorithm is decoupled into N parallel Kleinman's iterative equations. To learn the solution of the stochastic CARE from N decomposed linear subsystems data, an ST-based data-driven policy iteration algorithm is proposed and the convergence is proved. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed two iterative algorithms.
AbstractList This studies the infinite horizon optimal control problem for a class of continuous‐time systems subjected to multiplicative noises and Markovian jumps by using a data‐driven policy iteration algorithm. The optimal control problem is equivalent to solve a stochastic coupled algebraic Riccatic equation (CARE). An off‐line iteration algorithm is first established to converge the solutions of the stochastic CARE, which is generalised from an implicit iterative algorithm. By applying subsystems transformation (ST) technique, the off‐line iterative algorithm is decoupled into N parallel Kleinman's iterative equations. To learn the solution of the stochastic CARE from N decomposed linear subsystems data, an ST‐based data‐driven policy iteration algorithm is proposed and the convergence is proved. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed two iterative algorithms.
Author Ding, Zhengtao
Song, Jun
Liu, Fei
Niu, Yugang
He, Shuping
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  email: shuping.he@ahu.edu.cn
  organization: 2School of Electrical Engineering and Automation, Anhui University, Hefei 230601, People's Republic of China
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  organization: 3Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi 214122, People's Republic of China
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  givenname: Yugang
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  organization: 1Key Laboratory of Advanced Control and Optimization for Chemical Process (East China University of Science and Technology), Ministry of Education, Shanghai 200237, People's Republic of China
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  givenname: Zhengtao
  surname: Ding
  fullname: Ding, Zhengtao
  organization: 4Control Systems Center, School of Electrical and Electronic Engineering, University of Manchester, Sackville Street Building, Manchester M13 9PL, UK
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Issue 12
Keywords iterative methods
stochastic coupled algebraic Riccatic equation
multiplicative noises
subsystems transformation technique
parallel Kleinman iterative equations
transforms
optimal control
offline iteration algorithm
convergence of numerical methods
ST-based data-driven policy iteration algorithm
Riccati equations
infinite horizon optimal control problem
continuous-time Itô stochastic systems
stochastic systems
Markov processes
Markovian jumps
continuous time systems
implicit iterative algorithm
stochastic CARE
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SSID ssj0055645
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Snippet This studies the infinite horizon optimal control problem for a class of continuous-time systems subjected to multiplicative noises and Markovian jumps by...
This studies the infinite horizon optimal control problem for a class of continuous‐time systems subjected to multiplicative noises and Markovian jumps by...
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SubjectTerms Algorithms
continuous time systems
continuous‐time Itô stochastic systems
convergence of numerical methods
implicit iterative algorithm
infinite horizon optimal control problem
Iterative algorithms
Iterative methods
Markov processes
Markovian jumps
Mathematical analysis
Mathematical models
multiplicative noises
offline iteration algorithm
Optimal control
parallel Kleinman iterative equations
Policies
Riccati equations
Special Issue: Data-driven Control, and Data-Based System Modelling, Monitoring, and Control
stochastic CARE
stochastic coupled algebraic Riccatic equation
stochastic systems
Stochasticity
ST‐based data‐driven policy iteration algorithm
subsystems transformation technique
transforms
Title Data-driven policy iteration algorithm for optimal control of continuous-time Itô stochastic systems with Markovian jumps
URI http://digital-library.theiet.org/content/journals/10.1049/iet-cta.2015.0973
https://onlinelibrary.wiley.com/doi/abs/10.1049%2Fiet-cta.2015.0973
https://www.proquest.com/docview/1845820083
Volume 10
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