Solving the Model Unavailable MARE using Q-Learning Algorithm
<|reference_start|>Solving the Model Unavailable MARE using Q-Learning Algorithm: 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.<|reference_end|>
@article{yan2024solving,
    title={Solving the Model Unavailable MARE using Q-Learning Algorithm},
    author={Fei Yan, Jie Gao, Tao Feng, Jianxing Liu},
    journal={arXiv preprint arXiv:2407.13227},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13227},
    primaryClass={eess.SY cs.SY}
}