Neural Network-Based Event-Triggered State Feedback Control of Nonlinear Continuous-Time Systems

Abstract

This paper presents a novel approximation-based event-triggered control of multi-input multi-output uncertain nonlinear continuous-time systems in affine form. The controller is approximated using a linearly parameterized neural network (NN) in the context of event-based sampling. After revisiting the NN approximation property in the context of event-based sampling, an event-triggered condition is proposed using the Lyapunov technique to reduce the network resource utilization and to generate the required number of events for the NN approximation. In addition, a novel weight update law for aperiodic tuning of the NN weights at triggered instants is proposed to relax the knowledge of complete system dynamics and to reduce the computation when compared with the traditional NN-based control. Nonetheless, a nonzero positive lower bound for the inter-event times is guaranteed to avoid the accumulation of events or Zeno behavior. For analyzing the stability, the event-triggered system is modeled as a nonlinear impulsive dynamical system and the Lyapunov technique is used to show local ultimate boundedness of all signals. Furthermore, in order to overcome the unnecessary triggered events when the system states are inside the ultimate bound, a dead-zone operator is used to reset the event-trigger errors to zero. Finally, the analytical design is substantiated with numerical results.

About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

“…In contrast to linear systems, where one or infinite equilibrium states exist, a nonlinear system can contain one, none, a finite number, or infinite states of equilibrium. For the resolution of the set of equations in (22), both numerical or more complex methods can be utilized. Complex methods, as bioinspired algorithms (i.e., evolutionary computation techniques), can locate a large number of solutions, but its slower convergence is a clear disadvantage in comparison with numerical methods.…”

“…Complex methods, as bioinspired algorithms (i.e., evolutionary computation techniques), can locate a large number of solutions, but its slower convergence is a clear disadvantage in comparison with numerical methods. Then, in order to solve the set of nonlinear equations in (22), the use of numerical methods will be proposed, since they can offer a rapid convergence and precision in the obtained results [42,43]. In this sense, the Levenberg-Marquardt (L-M) method [44] with the extension proposed by Moré [45] will be performed.…”

“…Although this is the methodology that has been used in this article, the important thing in this case is to obtain as many solutions as possible, regardless of the method used to find them. Therefore, any other algorithm to solve (22) would be perfectly valid.…”

“…To solve the set of equations shown in (22), a minimization algorithm based on the same approach of L-M, adapted by Moré, has been used [44,45]. With this purpose, a dense mesh has been created to initialize the calculation process whose limits are directly related to the universe of discourse of the studied variables, applying increments of 0.05 and 0.1.…”

“…Proper selection and training of a basic structure such as a multilayer perceptron (MLP) can accurately reproduce the behaviour of a nonlinear system. This modelling technique can be used, both qualitatively and analytically [6,[22][23][24][25], taking into account that MLPs are universal approximators, either for a function [26][27][28][29] or its derivative [30,31]. Thus, although the system might be unknown, it is possible to obtain a NN model of its behaviour, representing its dynamics in the workspace studied.…”