Inverse optimal noise‐to‐state stabilization of stochastic recurrent neural networks driven by noise of unknown covariance

Abstract

In this paper, we extend our previous research results regarding the stabilization of recurrent neural networks from the concept of input-to-state stability to noise-to-state stability, and present a new approach to achieve noise-to-state stabilization in probability for stochastic recurrent neural networks driven by the noise of unknown covariance. This approach is developed by using the Lyapunov technique, inverse optimality, differential game theory, and the Hamilton-Jacobi-Isaacs equation. Numerical examples demonstrate the effectiveness of the proposed approach.

Risk sensitive optimal synchronization of coupled stochastic neural networks with chaotic phenomena

“…It is known that the noise is an unavoidable factor that should be taken into consideration during the implementation of artificial neural networks. Therefore, in the past few years, the study of stochastic neural networks has started to attract the attention from the research community [10][11][12]. In the society of control engineering, there is a strong motivation for designing optimal systems because such systems automatically have many desirable properties, such as, stability, robustness, reduced sensitivity, etc.…”

Control óptimo inverso para sistemas no lineales en tiempo continuo

“…A partir de esto es bien conocida la dificultad para resolver la ecuación de Hamilton-Jacobi-Bellman (HJB) que constituye la génesis del control óptimo. Los principales resultados obtenidos corresponden con aproximaciones numéricas que explotan las bondades de los sistemas de cómputo actuales, lo cual sin embargo no es viable para implementación de sistemas de control en tiempo real, como PP: [13][14][15][16][17][18] Control óptimo inverso para sistemas no lineales en tiempo continuo problems in control theory. Methods: A general description of the optimal control problem is performed, followed by the justification of an inverse optimal approach.…”

“…A través de este enfoque es posible resolver explícitamente la ecuación HJB mediante la definición de una función de control de Lyapunov con una forma predeterminada. Resultados recientes encontrados en la literatura al respecto del control óptimo inverso incluyen [3,6,8,9,15]. El análisis de dicha técnica de control es por tanto el objetivo principal del presente artículo.…”

Inverse optimal control for discrete‐time nonlinear systems via passivation

“…The main characteristic of the inverse problem is that the meaningful cost functional is a posteriori determined for the stabilizing feedback control law. We refer the reader to for inverse optimal control of continuous‐time linear systems and to and references therein for the nonlinear continuous‐time case. The inverse optimal control has been treated for delay systems in and for adaptive control in .…”