An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

Abstract

In this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding-mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding-mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input-to-state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding-mode observer.

Output global oscillatory synchronisation of heterogeneous systems

“…Finite-time convergence of d i using observer structure similar to the proposed one can also be found in the literature, cf. Ríos et al (2018). These useful properties are reflected in the following assumption:…”

Adaptive Estimation for Uncertain Nonlinear Systems: A Sliding-Mode Observer Approach

“…The functions φ : R n × R m → R n and G : R ≥0 ×R n ×R m → R n×q are also known and they ensure uniqueness and existence of solutions for system (1) for all admissible disturbances. It is important to highlight that in [16] the functions φ(x, u) and G(t, x, u) were considered depending only on the measurable output y. The aim of this paper is to provide estimations of the state and parameter vectors, i.e.…”

“…The following stability properties for system (3) are introduced (for more details see [16], [17], [18], [19] and [20]). Definition 1.…”

“…In this paper a nonlinear adaptive sliding-mode observer is proposed, based on a nonlinear parameter identification algorithm, for uncertain nonlinear systems. The proposed nonlinear adaptive observer is an extension of the one presented by [16]. This extension tries to increase the class of nonlinear systems for which the adaptive observer can be applied allowing to have a parameter distribution matrix and nonlinear terms depending on the full state and the input.…”

“…This extension tries to increase the class of nonlinear systems for which the adaptive observer can be applied allowing to have a parameter distribution matrix and nonlinear terms depending on the full state and the input. In [16], such functions were considered just depending on the measurable output and input. The proposed parameter identification algorithm provides an ultimate bound for the state and parameter estimation error and attenuating the effects of the external disturbances.…”