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Main Authors: Yan, Fei, Gao, Jie, Feng, Tao, Liu, Jianxing
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2407.13227
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author Yan, Fei
Gao, Jie
Feng, Tao
Liu, Jianxing
author_facet Yan, Fei
Gao, Jie
Feng, Tao
Liu, Jianxing
contents In this paper, the discrete-time modified algebraic Riccati equation (MARE) is solved when the system model is completely unavailable. To achieve this, firstly a brand new iterative method based on the standard discrete-time algebraic Riccati equation (DARE) and its input weighting matrix is proposed to solve the MARE. For the single-input case, the iteration can be initialized by an arbitrary positive input weighting if and only if the MARE has a stabilizing solution; nevertheless a pre-given input weighting matrix of a sufficiently large magnitude is used to perform the iteration for the multi-input case when the characteristic parameter belongs to a specified subset. Benefit from the developed specific iteration structure, the Q-learning (QL) algorithm can be employed to subtly solve the MARE where only the system input/output data is used thus the system model is not required. Finally, a numerical simulation example is given to verify the effectiveness of the theoretical results and the algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2407_13227
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Solving the Model Unavailable MARE using Q-Learning Algorithm
Yan, Fei
Gao, Jie
Feng, Tao
Liu, Jianxing
Systems and Control
In this paper, the discrete-time modified algebraic Riccati equation (MARE) is solved when the system model is completely unavailable. To achieve this, firstly a brand new iterative method based on the standard discrete-time algebraic Riccati equation (DARE) and its input weighting matrix is proposed to solve the MARE. For the single-input case, the iteration can be initialized by an arbitrary positive input weighting if and only if the MARE has a stabilizing solution; nevertheless a pre-given input weighting matrix of a sufficiently large magnitude is used to perform the iteration for the multi-input case when the characteristic parameter belongs to a specified subset. Benefit from the developed specific iteration structure, the Q-learning (QL) algorithm can be employed to subtly solve the MARE where only the system input/output data is used thus the system model is not required. Finally, a numerical simulation example is given to verify the effectiveness of the theoretical results and the algorithm.
title Solving the Model Unavailable MARE using Q-Learning Algorithm
topic Systems and Control
url https://arxiv.org/abs/2407.13227