A Novel Solution to the Time-Varying Lyapunov Equation: The Integral Dynamic Learning Network

作者：Zhijun Zhang, Lihang Ye, Lunan Zheng, Yamei Luo · 发表于：IEEE Transactions on Systems Man and Cybernetics Systems · 年份：2023 · DOI：10.1109/tsmc.2023.3285757 · 被引用次数：22 · 研究领域：Neural Networks and Applications、Neural Networks Stability and Synchronization、Advanced Memory and Neural Computing

In this article, a novel approach of utilizing an integral dynamic learning network (IDLN) is presented for addressing a general time-varying Lyapunov matrix equation (TVLME). First, a cost function is defined by designing a variable unbounded vector/matrix-type error function. The goal is to make the cost function approximate to zero. Second, an integral neural dynamic equation with an odd activation function that is monotonically increasing is designed and applied to guarantee that the error function can converge to zero. Third, a novel IDLN with a recurrent topological structure is exploited to find the time-varying theoretical solution. The proposed IDLN with strong robustness to bounded noise with unknown amplitude regardless of the value of hyperparameters, can be implemented through electronic circuits as a method of parallel computing and achieve global convergence from any initial state. In addition, for better convergence rates, the novel linear-arcsine-type and softsign-arcsine-type activation functions are designed and utilized to the proposed IDLN. The effectiveness, stability, and practicability of the proposed IDLN are verified by comparative computer simulations and the application to the analysis of voltage stability in a single-machine infinite bus system.