Policy iteration for H∞ control of polynomial time‐varying systems

This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Theref...

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Bibliographic Details
Published in:IET control theory & applications Vol. 18; no. 10; pp. 1248 - 1261
Main Authors: Pakkhesal, Sajjad, Shamaghdari, Saeed
Format: Journal Article
Language:English
Published: Stevenage John Wiley & Sons, Inc 01.07.2024
Wiley
Subjects:
Algorithms
Approximation
Attenuation coefficients
Closed loop systems
Control systems design
Control theory
convex programming
Design
Dynamic programming
H-infinity control
H∞ control
Independent variables
Iterative algorithms
Neural networks
non‐linear control systems
Optimization
Optimization techniques
Partial differential equations
Polynomials
robust control
Semidefinite programming
Stability
System theory
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Summary:This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples. In this paper, the H∞ control problem is solved for polynomial time‐varying systems. A sum‐of‐squares‐based approximate dynamic programming method is proposed to solve this problem. The convergence and stability properties of the proposed algorithm are stated and proven.
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ISSN:1751-8644
1751-8652
DOI:10.1049/cth2.12661