Abstract
This paper addresses the problem of adaptive output-feedback control for more general class of stochastic time-varying delay nonlinear systems with unknown control coefficients and perturbations. By using Lyapunov–Krasovskii functional, backstepping and tuning function technique, a novel adaptive neural network (NN) output-feedback controller is constructed with fewer learning parameters. The designed controller guarantees that all the signals in the closed-loop system are 4-moment (or mean square) semi-globally uniformly ultimately bounded (SGUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed control scheme.
Highlights
In order to obtain global stability, some restrictions such as matching conditions, extended matching conditions or growth conditions are often imposed on system nonlinearities
To handle the above restrictions, neural networks (NNs) are gradually into people’s vision due to their ability to adaptively compensate for nonlinear functions
In the past two decades, based on the theoretical results of stochastic stability in [6, 7, 11] and NNs in [14, 16, 23], radial basis function neural network (RBF NN) approximation approach has been successfully used for various classes of stochastic nonlinear systems, see [1, 8, 12, 13, 15, 17, 27] and the references therein
Summary
In order to obtain global stability, some restrictions such as matching conditions, extended matching conditions or growth conditions are often imposed on system nonlinearities. The output-feedback control problems were presented in [2] and [10] for stochastic nonlinear systems with time-varying delays existing both in the drift and diffusion terms, but the considered time-delays only depended on measurable output. For more general classes of stochastic nonlinear systems with time-varying delays depending on unmeasurable states, NN tracking problems were solved in [24, 26]. The lasted reference [25] solved the adaptive NN output-feedback control problem for a class of stochastic time-varying delay nonlinear systems without considering perturbations. How to design an adaptive output-feedback controller for a class of stochastic nonlinear time-delay systems with both unknown control directions and perturbations?. (ii) An adaptive NN output-feedback controller is constructed for more general class of stochastic time-varying delay nonlinear systems.
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