ESN-Observer-Based Adaptive Stabilization Control for Delayed Nonlinear Systems with Unknown Control Gain

Shuxian Lun (), Zhaoyi Lv, Xiaodong Lu () and Ming Li
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Shuxian Lun: School of Control Science and Engineering, Bohai University, Jinzhou 121013, China
Zhaoyi Lv: School of Control Science and Engineering, Bohai University, Jinzhou 121013, China
Xiaodong Lu: School of Control Science and Engineering, Bohai University, Jinzhou 121013, China
Ming Li: School of Control Science and Engineering, Bohai University, Jinzhou 121013, China

Mathematics, 2023, vol. 11, issue 13, 1-21

Abstract: This paper investigates the observer-based adaptive stabilization control problem for a class of time-delay nonlinear systems with unknown control gain using an echo state network (ESN). In order to handle unknown functions, a new recurrent neural network (RNN) approximation method called ESN is utilized. It improves accuracy, reduces computing cost, and is simple to train. To address the issue of unknown control gain, the Nussbaum function is used, and the Lyapunov–Krasovskii functionals are used to address the delay term. The backstepping strategy and command filtering methodology are then used to create an adaptive stabilization controller. All of the closed-loop system’s signals are predicted to be confined by the Lyapunov stability theory. Finally, a simulation example is used to demonstrate the effectiveness of the suggested control mechanism.

Keywords: echo state network (ESN); stabilization control; unknown control gain; time-delay nonlinear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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