Finite-time convergent zeroing neural network for solving time-varying algebraic Riccati equations |
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| Institution: | 1. Hangzhou Dianzi University, School of Mechanical Engineering, Er Hao Da Jie 1158, Xiasha, Hangzhou 310018, China;2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan;3. Data Recovery Key Laboratory of Sichun Province, Neijing Normal Univ., Neijiang 641100, China;4. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece;5. Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece;6. University of Ni?, Faculty of Sciences and Mathematics, Vi?egradska 33, 18000 Ni?, Serbia;1. Faculty of Sciences and Mathematics, University of Ni?, Ni? 18000, Serbia;2. School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China;1. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China;2. Guangdong Key Laboratory of Modern Control Technology, Guangzhou 510070, China;3. Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, Guangzhou 510006, China |
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| Abstract: | Various forms of the algebraic Riccati equation (ARE) have been widely used to investigate the stability of nonlinear systems in the control field. In this paper, the time-varying ARE (TV-ARE) and linear time-varying (LTV) systems stabilization problems are investigated by employing the zeroing neural networks (ZNNs). In order to solve the TV-ARE problem, two models are developed, the ZNNTV-ARE model which follows the principles of the original ZNN method, and the FTZNNTV-ARE model which follows the finite-time ZNN (FTZNN) dynamical evolution. In addition, two hybrid ZNN models are proposed for the LTV systems stabilization, which combines the ZNNTV-ARE and FTZNNTV-ARE design rules. Note that instead of the infinite exponential convergence specific to the ZNNTV-ARE design, the structure of the proposed FTZNNTV-ARE dynamic is based on a new evolution formula which is able to converge to a theoretical solution in finite time. Furthermore, we are only interested in real symmetric solutions of TV-ARE, so the ZNNTV-ARE and FTZNNTV-ARE models are designed to produce such solutions. Numerical findings, one of which includes an application to LTV systems stabilization, confirm the effectiveness of the introduced dynamical evolutions. |
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