General Lyapunov Stability and Its Application to Time-Varying Convex Optimization
文献类型：期刊论文
| 作者 | Zhibao Song; Ping Li |
| 刊名 | IEEE/CAA Journal of Automatica Sinica
 |
| 出版日期 | 2024 |
| 卷号 | 11期号:11页码:2316-2326 |
| 关键词 | Fixed-time stability nonlinear system predefined-time stability time-varying (TV) convex optimization |
| ISSN号 | 2329-9266 |
| DOI | 10.1109/JAS.2024.124374 |
| 英文摘要 | In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settling-time function is exhibited for fixed-time stability, and it is still extraneous to the initial conditions. This can be applied to obtain less conservative convergence time of the practical systems without the information of the initial conditions. As an application, the given fixed-time stability theorem is used to resolve time-varying (TV) convex optimization problem. By the Newton’s method, two classes of new dynamical systems are constructed to guarantee that the solution of the dynamic system can track to the optimal trajectory of the unconstrained and equality constrained TV convex optimization problems in fixed time, respectively. Without the exact knowledge of the time derivative of the cost function gradient, a fixed-time dynamical non-smooth system is established to overcome the issue of robust TV convex optimization. Two examples are provided to illustrate the effectiveness of the proposed TV convex optimization algorithms. Subsequently, the fixed-time stability theory is extended to the theories of predefined-time/practical predefined-time stability whose bound of convergence time can be arbitrarily given in advance, without tuning the system parameters. Under which, TV convex optimization problem is solved. The previous two examples are used to demonstrate the validity of the predefined-time TV convex optimization algorithms. |
| 源URL | [http://ir.ia.ac.cn/handle/173211/59455]  |
| 专题 | 自动化研究所_学术期刊_IEEE/CAA Journal of Automatica Sinica |
| 推荐引用方式 GB/T 7714 | Zhibao Song,Ping Li. General Lyapunov Stability and Its Application to Time-Varying Convex Optimization[J]. IEEE/CAA Journal of Automatica Sinica,2024,11(11):2316-2326. |
| APA | Zhibao Song,&Ping Li.(2024).General Lyapunov Stability and Its Application to Time-Varying Convex Optimization.IEEE/CAA Journal of Automatica Sinica,11(11),2316-2326. |
| MLA | Zhibao Song,et al."General Lyapunov Stability and Its Application to Time-Varying Convex Optimization".IEEE/CAA Journal of Automatica Sinica 11.11(2024):2316-2326. |
入库方式： OAI收割
来源：自动化研究所
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