Output-Feedback Adaptive Neural Control for Stochastic Nonlinear Time-Varying Delay Systems With Unknown Control Directions

Abstract

This paper presents an adaptive output-feedback neural network (NN) control scheme for a class of stochastic nonlinear time-varying delay systems with unknown control directions. To make the controller design feasible, the unknown control coefficients are grouped together and the original system is transformed into a new system using a linear state transformation technique. Then, the Nussbaum function technique is incorporated into the backstepping recursive design technique to solve the problem of unknown control directions. Furthermore, under the assumption that the time-varying delays exist in the system output, only one NN is employed to compensate for all unknown nonlinear terms depending on the delayed output. Moreover, by estimating the maximum of NN parameters instead of the parameters themselves, the NN parameters to be estimated are greatly decreased and the online learning time is also dramatically decreased. It is shown that all the signals of the closed-loop system are bounded in probability. The effectiveness of the proposed scheme is demonstrated by the simulation results.

Command filter based globally stable adaptive neural control for cooperative path following of multiple underactuated autonomous underwater vehicles with partial knowledge of the reference speed

“…Before introducing our control design method, let us first recall the approximation property of the NNs [11][12][13][14][36][37][38][39][40][41][42][43][44][45] . The NNs take the form of W T σ ( ξ ) where W ∈ R ×m is called weight matrix, with being the number of NN nodes; and σ (ξ ) ∈ R is a vector valued function defined in R , with ξ ∈ R q being the NN input vector.…”

Single-approximation-based adaptive control of a class of nonlinear time-delay systems

“…In addition,Ŵ is bounded by the bounded constant W Ã . Because z i andŴ are bounded, x i and u are bounded from (12), (18), (19), (25), and (29). Finally, all signals of the closed-loop system are uniformly bounded.…”

“…Specifically, adaptive control approaches using the backstepping technique have been proposed for nonlinear strictfeedback systems with time delays [12][13][14][15][16][17][18][19] and without time delays [20][21][22][23]. In [13][14][15][16][17][18][19], adaptive approximationbased backstepping controllers were presented for nonlinear time-delay systems in strict-feedback form. However, the repeated differentiation of virtual controllers occurs in the backstepping algorithm.…”

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

“…In addition, time‐delays pose a challenging issue not only in observers design problem but also in controller design theory. The topic of stability of nonlinear time‐delay systems has received huge attention in the past decade …”