Adaptive Recurrent Neural Network Enhanced Variable Structure Control for Nonlinear Discrete Mimo Systems

Abstract

The stability and performance of robust control for a nonlinear complex dynamic system deteriorates due to large uncertainties. To address this, a discrete variable structure control (DVSC) outside of a convex set is designed to force the operating point into a convergent set, which is verified by Lyapunov stability theory. Due to the dynamic features of the lumped uncertainties, they are learned on-line by a recurrent neural network (RNN) in a specific convex set containing the convergent set of the DVSC. Between this convergent set and the convex set, a switching mechanism determines whether a learning RNN for the lumped uncertainties is executed. An adaptive recurrent-neural-network enhanced discrete variable structure control is then established to improve both transient and steady performances. Simulations, including compared examples and application to the trajectory tracking of a mobile robot, validate the effectiveness and robustness of the proposed control.

Analysis and control of spatial limit sets and spatial chaos appearance in mimo cascade connected nonlinear systems

“…Modelling and simulation of the MIMO cascade connected nonlinear system (19) and nonlinear discrete system (21) is obtained using program package Matlab. Simulation results prove the existence of spatial limit sets and spatial chaos in system (19) for the same parameter values l 2 and the same initial conditions for which the limit sets and chaos exists in system (21).…”

“…The spatial limit set is obtained for parameter value l 2 = À 0.7in the cascade system (19), Fig. 7a.…”

“…Applying the modified Pyragas method of spatial chaos control, given in Fig. 5a and described with the set of equations (16) for K = 0.85, the spatial limit set of MIMO cascade connected nonlinear system (19), Fig. 7a, becomes stable focus, as shown in Fig.…”

“…Reduction of parameter l 2 value of uncontrolled MIMO system (19) moves the parameter value from the part of the parametric plane where spatial limit sets appear to the part where spatial chaos appears. For l 2 = À 0.85 spatial chaos appears in system (19), Fig. 8a.…”

“…8c. Applying the modified Pyragas method (16), for K = 0.85 spatial chaos for MIMO cascade connected nonlinear system (19) shown in Fig. 8a becomes stable focus, as shown in Fig.…”