Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone

Abstract

This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.

General Dynamic Equivalent Modeling of Microgrid Based on Physical Background

“…The trajectory sensitivity of these two parameters will pass zero at the same time. Oppositely, if the output variable curves of the two parameters do not pass zero at the same time approximately, they are independent and can be identified using the dynamics of output variables of the system [31].…”

A two-phased and Ensemble scheme integrated Backpropagation algorithm

“…In [30], J.H. Perez-Cruz et al address the issue of trajectory tracking for a wide category of uncertain nonlinear systems with multiple inputs, each one subject to an unknown symmetric dead zone.…”

“…Moreover, it is necessary to mention that, there exist mainly two differences between our proposed TP-ES-BP algorithm and those algorithms proposed in references [28][29][30][31][32][33]: (1) TP-ES-BP algorithm is based on the two phase scheme and in the relation between the sum of squared error and an error threshold, while those algorithms proposed in [28][29][30][31][32][33] are based on a Lyapunov stability analysis;…”

“…(2) TP-ES-BP algorithm is thought in the pattern recognition issue while those algorithms proposed in [28][29][30][31][32][33] are thought in the identification issue.…”

Acquisition system and approximation of brain signals

“…In [6], a dynamic reconstruction model, which integrates the measurement information and physical evolution information of the objects of interest is presented. In [7][8][9][10], the estimation of some non-linear behaviours for the control of some non-linear systems with dead zone inputs are introduced. In [11], a gas chamber and four defect models were designed.…”