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Nowadays, control-dependent stochastic noise is ruled out in adaptive control, whereas such noise can be encountered in financial, aerospace, and biomechanical models. The status is due to the presence of adaptive control in the diffusion term. The diffusion coefficient, heavily dependent on the adaptive signal (with unexpected size), undermines stochastic stability via its quadratic form which cannot be suppressed merely by the control itself in the drift term. This compels us to exploit the positive role of the diffusion term, entailing new sophisticated analysis in the nonlinear and adaptive context. This article aims to enlarge the applicability of adaptive control, and especially, seek adaptive stabilization via dynamic gain in the context of control-dependent stochastic noise. Specifically, basic theorems on stochastic convergence are proposed, particularly revealing the intrinsic relation between the system convergence and the gain evolution by exploiting the underlying positive role of the diffusion term. Then, a distinctive martingale-based analysis pattern for adaptive control is established, recognizing the inapplicability of classical Lyapunov/LaSalle theorems. In this way, for a specific class of uncertain nonlinear systems, global stabilization with almost sure asymptotic/exponential convergence is achieved by incorporating typical dynamic gains in the presence of control-dependent stochastic noise.

This article investigates global practical output tracking via adaptive output feedback for a class of uncertain nonlinear systems. Remarkably, the control problem under investigation is in the context of unknown control directions and output feedback, which severely restricts the system nonlinearities. Nevertheless, the growth on the unknown system nonlinearities in this article is extended from polynomial (of output) to arbitrary function, and meanwhile no further a priori information is required on the reference signal to be tracked. Specifically, sufficiently smooth pseudosign and pseudo-dead-zone functions are introduced acting as substitutions of sign and dead-zone functions in the literature, respectively. Typically, based on the pseudo-dead-zone function, a delicate estimate on the unknown system nonlinearities is established and a novel Lyapunov function is proposed. This, together with the elegant system performance analysis, is quite critical to remove the polynomial constraint and overcome the technical obstacle stemming from the essential extension. Additionally owing to the two refined functions, the use of smooth domination/treatment is moderately avoided in control design that enables the established control strategy to be tighter and less conservative. It turns out that under the proposed adaptive output-feedback controller, all the closed-loop system states are globally bounded, while the system tracking error enters a prescribed λ neighborhood of the origin in finite time and remains inside thereafter. A simulation example illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered tracking for a class of uncertain nonlinear systems. Essentially different from the related works, the nonlinear systems allow serious (parametric) uncertainties, while no further a priori information, excepting some coarse information, is required on the reference signal to be tracked. This makes event-triggered control more challenging, partially because the sampling error cannot be precisely bounded any more. As main contributions of this paper, new adaptive event-triggered tracking schemes are proposed for the systems in two event-triggering architectures with different roles of the event-triggering mechanism on the information transmitting and control computing/updating. Much importantly, a dynamic gain is incorporated in either scheme not only to counteract the serious uncertainties, but also to overcome the bad influence of the sampling error. Based on the dynamic gain, two adaptive event-triggered controllers are designed with distinct event-triggering mechanisms, respectively. Particularly, to ensure application flexibility, one of the triggering mechanisms is rendered relatively independent of the controller signal. The designed event-triggered controllers are shown to achieve the practical tracking for the systems, that is, the prespecified arbitrary tracking accuracy can be guaranteed (a comparable objective to that via continuous-time control), while avoiding infinitely fast sampling/execution. [ABSTRACT FROM AUTHOR]