Abstract :
In order to conveniently analyze the stability of recurrent neural networks (RNNs) and successfully synthesize the controllers for nonlinear systems, similar to the nominal model in linear robust control theory, the novel neural network model, named delayed standard neural network model (DSNNM) is presented, which is the interconnection of a linear dynamic system and a bounded static delayed (or nondelayed) nonlinear operator. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability for the continuous-time DSNNMs (CDSNNMs) and discrete-time DSNNMs (DDSNNMs) are derived, whose conditions are formulated as linear matrix inequalities (LMIs). Based on the stability analysis, some state-feedback control laws for the DSNNM with input and output are designed to stabilize the closed-loop systems. Most RNNs and neurocontrol nonlinear systems with (or without) time delays can be transformed into the DSNNMs to be stability-analyzed or stabilization-synthesized in a unified way. In this paper, the DSNNMs are applied to analyzing the stability of the continuous-time and discrete-time RNNs with or without time delays, and synthesizing the state-feedback controllers for the chaotic neural-network-system and discrete-time nonlinear system. It turns out that the DSNNM makes the stability conditions of the RNNs easily verified, and provides a new idea for the synthesis of the controllers for the nonlinear systems.
Keywords :
Lyapunov methods; asymptotic stability; chaos; closed loop systems; continuous time systems; control system synthesis; delays; discrete time systems; feedback; linear matrix inequalities; linear systems; neurocontrollers; nonlinear control systems; nonlinear dynamical systems; recurrent neural nets; robust control; LMI; Lyapunov functionals; bounded static delayed nonlinear operator; chaotic neural-network-system; closed-loop system; continuous-time DSNNM; control system synthesis; delayed standard neural network models; discrete-time DSNNM; discrete-time nonlinear system; global asymptotic stability; global exponential stability; linear dynamic system; linear matrix inequalities; linear robust control theory; neurocontrol nonlinear systems; recurrent neural networks; state-feedback control; time delays; Asymptotic stability; Control system synthesis; Delay effects; Network synthesis; Neural networks; Nonlinear control systems; Nonlinear systems; Recurrent neural networks; Robust stability; Stability analysis; Delayed standard neural network model (DSNNM); generalized eigenvalue problem (GEVP); linear matrix inequality (LMI); nonlinear system; recurrent neural network (RNN); stability; Algorithms; Computer Simulation; Models, Theoretical; Neural Networks (Computer); Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Time Factors;
