This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network's (NN's) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.
This paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure-feedback nonlinear systems with time-varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time-varying delays. Based on a novel combination of the Razumikhin-Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed-loop signals are shown to be 4-Moment semi-globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes.On the other hand, stochastic disturbances often exist in many practical systems, such that the control problem for stochastic time-delay nonlinear systems has also received more and more attentions in recent years. Some nonlinear control design methods such as Sontag's stabilization formula, Lyapunov methods and backstepping techniques were extended to the case of stochastic nonlinear systems [22][23][24][25][26][27][28][29]. The main obstacle in the Lyapunov design for stochastic systems is that the I t O o stochastic differentiation involves not only the gradient but also the higher order Hessian term [30]. Nevertheless, the control problem for stochastic time-delay strict-feedback systems has also received increasing attentions, and many interesting control schemes [31][32][33][34][35][36][37] have been proposed by using the backstepping technique. In [31], the output-feedback control problem was addressed for a class of uncertain stochastic nonlinear strict-feedback systems with constant delay, their results require the system function to be known. In [32][33][34], the output-feedback control problem was presented for some classes of uncertain stochastic nonlinear strict-feedback systems with time-varying delays, where the unknown system function need to be satisfied the matching condition. When the system functions are unknown, the problem of adaptive neural control has been investigated for uncertain stochastic nonlinear strict-feedback systems with unknown constant time-delays or unknown timevarying delays in [35,36]. In [37], the problem of adaptive output-feedback control was addressed for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using NN. In comparison with many research results in the stochastic strict-feedback nonlinear time-delay systems, not enough attention has been paid to the stochastic pure-feedback nonlinear systems with time-varying delays.The Lyapunov-Krasovskii method [31][32][33][34][35]37] and the Lyapunov-Razumikhin method [36,38,39] are often employed in the stability analysis and robust control problem for stochastic nonlinear time-delay systems. The Lyapuno...
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