Global output‐feedback stabilization for nonlinear systems with unknown relative degree

Abstract

Summary This paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper.

Global practical tracking for nonlinear systems with unknown input powers using dual high‐gain‐based adaptive feedback

“…Up to now, adaptive control has been widely adopted in engineering applications, such as flexible-joint robots, autonomous aerial vehicles and electromechanical systems (see, eg, other works [1][2][3] and references therein). Despite numerous strategies for various uncertainties (parametric unknowns, 4,5 unknown control direction, 6,7 unknown relative degree, 8,9 and so on), adaptive control still deserves further investigation to recognize its essence and capability, and to cover more types of uncertainties.…”

Differentiator-Based Output-Feedback Controller for Uncertain Nonautonomous Nonlinear Systems With Unknown Relative Degree

“…In [26], an automatic identification algorithm for a relative degree with a known upper limit is proposed. In [27], a controller based on two switching algorithms is proposed for global output-feedback stabilization for nonlinear systems with an unknown relative degree. However, [11], [26] consider affinein-the-control nonlinear systems; in [26], there is no rigorous stability proof of the closed-loop system including a switching scheme between controllers that have different orders.…”

“…However, [11], [26] consider affinein-the-control nonlinear systems; in [26], there is no rigorous stability proof of the closed-loop system including a switching scheme between controllers that have different orders. The system considered in [27] is more restrictive than that of [11] and [26], since it is a linear-in-the-control autonomous nonlinear system whose nonlinearities are the functions of the system output only. That is, none of the current results can be applied to more general nonaffine and nonautonomous nonlinear systems.…”

“…The proposed control scheme is based on the input filter and higher-order switching differentiator (HOSD) [19] with over dimension under the assumption that the relative degree's maximum value is available. The main contributions of the proposed control algorithm can be summarized as follows: 1) Compared to the previous controllers in [11], [26], [27], the nonlinear system considered in this paper is a relatively broader class of nonaffine-in-the-control nonautonomous nonlinear systems. To the authors' knowledge, there has been no research examining controller for the considered general nonlinear systems with the unknown relative degree.…”