2025/01/06 by Torbjörn Wigren, Wigren, Torbjörn, Ruoqi Zhang +3
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Experimental Learning in Engineering #FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2501.03049
openalex publication_date 2025/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper derives analytical expressions for the asymptotic average updating direction of the adaptive moment generation (ADAM) algorithm when applied to recursive identification of nonlinear systems. It is proved that the standard hyper-parameter setting results in the same asymptotic average updating direction as a diagonally power normalized stochastic gradient algorithm. With the internal filtering turned off, the asymptotic average updating direction is instead equivalent to that of a sign-sign stochastic gradient algorithm. Global convergence to an invariant set follows, where a subset of parameters contain those that give a correct input-output description of the system. The paper also exploits a nonlinear dynamic model to embed structure in recurrent neural networks. A Monte-Carlo simulation study validates the results.