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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 article is devoted to the stabilization via adaptive feedback for a class of uncertain coupled reaction–diffusion dynamics in the actuation path of an ordinary differential equation (ODE) system. The system under investigation, a class of coupled parabolic partial differential equation (PDE)–ODE systems, is more representative since the dynamics in actuation path (i.e., the PDE subsystem) are coupled rather than uncoupled parabolic equations and hence includes those in the related literature as special cases. Moreover, serious parametric uncertainties are present in both PDE and ODE subsystems, which bring obstacles to the traditional methods on this issue. To solve the control problem, an infinite-dimensional backstepping transformation with time-varying matrix-valued kernel functions is adopted to change the original system into a new one. Then, an adaptive state-feedback controller is designed for the new system, which guarantees that all the closed-loop system states are bounded while regulating the original system states to zero. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the control design with prescribed performance for uncertain nonlinear systems. Different from the existing literature, the systems under investigation possess unknown control directions and nonparametric uncertainties. Even so, the control objective to be achieved is still refined, not only to ensure the basic performance on stabilization, but also to guarantee certain prescribed performance required in real applications. Motivated by the funnel control method, a time-varying stabilizing scheme is developed for the systems, to effectively handle the serious uncertainties and to successfully guarantee the states to converge to zero with a prescribed rate. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis methods/tools to stochastic convergence and stochastic adaptive output-feedback control. As the first contribution, a general stochastic convergence theorem is proposed for stochastic nonlinear systems. The theorem doesn't necessarily involve a positive-definite function of the system states with negative-semidefinite infinitesimal, essentially different from stochastic LaSalle's theorem (see e.g., [1]), and hence can provide more opportunities to achieve stochastic convergence. Moreover, as a direct extension of the convergence theorem, a general version of stochastic Barb ă lat's lemma is obtained, which requires the concerned stochastic process to be almost surely integrable, rather than absolutely integrable in the sense of expectation, unlike in [2]. As the second contribution, supported by the general stochastic convergence theorem, an adaptive output-feedback control strategy is established for the global stabilization of a class of stochastic nonlinear systems with severe parametric uncertainties coupled to unmeasurable states. Its feasibility analysis takes substantial effort, and is largely based on the general stochastic convergence theorem. Particularly, for the resulting closed-loop system, certain stochastic boundedness and integrability are shown by the celebrated nonnegative semimartingale convergence theorem, and furthermore, the desired stochastic convergence is achieved via the general stochastic convergence theorem. [ABSTRACT FROM PUBLISHER]