Stability Analysis of Recurrent-Neural-Based Controllers Using Dissipativity Domain

Reza Jafari ()
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Reza Jafari: Computer Science, Virginia Tech University, Falls Church, VA 22043, USA

Mathematics, 2023, vol. 11, issue 14, 1-18

Abstract: This paper proposes a method for the stability analysis of dynamic neural networks. The stability analysis of dynamic neural networks is a challenging task due to internal feedback connections. In this research work, we propose an algorithm based on the Reduction of Dissipativity Domain (RODD) algorithm. The RODD algorithm is a numerical technique for the detection of the stability of nonlinear dynamic systems. The method works by using an approximation of the reachable set. This paper proposes linear and quadratic approximations of reachable sets. RODD-LB uses a linear approximation, RODD-EB uses a quadratic approximation, and the RODD-Hybrid algorithm uses a combination of the linear and quadratic approximations. The accuracy and convergence of these algorithms were derived through numerical dynamic systems.

Keywords: recurrent neural network; stability analysis; dissipativity domain; reachable set; linear and quadratic approximation of reachable set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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