Linear quadratic Nash game-based tracker for multiparameter singularly perturbed sampled-data systems: digital redesign approach |
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Authors: | Jason Sheng-Hong Tsai Zi-Yi Yang Shu-Mei Guo Leang-San Shieh Chia-Wei Chen |
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Affiliation: | 1. Department of Electrical Engineering , National Cheng Kung University , Tainan, 701, Taiwan, Republic of China shtsai@mail.ncku.edu.tw;3. Department of Electrical Engineering , National Cheng Kung University , Tainan, 701, Taiwan, Republic of China;4. Department of Computer Science and Information Engineering , National Cheng-Kung University , Tainan, 701, Taiwan, Republic of China;5. Department of Electrical and Computer Engineering , University of Houston , Houston, TX, 77204-4005, USA;6. Department of Mechanical and Automation Engineering , Kao Yuan University , Kaohsiung, 821, Republic of China |
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Abstract: | In this paper, a linear quadratic Nash game-based tracker for multiparameter singularly perturbed sample-data systems is developed. A generalized cross-coupled multiparameter algebraic Riccati equation (GCMARE) with two quadratic cost functions is solved by applying the LQR design methodology for the optimal tracker design. Firstly, the asymptotic expansions of the GCMARE are newly established, and the proposed algorithm is able to effectively solve the GCMARE with the quadratic convergence rate. Then, the low-gain digital controller with a high design performance is realized through the prediction-based digital redesign method. Finally, for further improving the tracking performance, the chaos-evolutionary-programming algorithm (CEPA) is utilized to optimally tune the parameters of the tracker. An example is presented to demonstrate the effectiveness of the proposed methodology. |
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Keywords: | Nash game Chaos evolutionary programming Digital redesign Optimal control Generalized cross-coupled multiparameter algebraic Riccati equation |
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