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arXiv · 2407.13227

Solving the Model Unavailable MARE using Q-Learning Algorithm

Fei Yan·Jie Gao·Tao Feng·Jianxing Liu
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Abstract

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.

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Fei Yan, Jie Gao, Tao Feng, Jianxing Liu. 2024-07-18. Solving the Model Unavailable MARE using Q-Learning Algorithm. https://arxiv.org/abs/2407.13227

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