Sampled-Data Adaptive Observer For a Class of State-Affine Output-Injection Nonlinear Systems

Abstract

The problem of observer design is addressed for outputinjection nonlinear systems. A major difficulty with this class of systems is that the state equation involves an output-dependent term that is explicitly dependent on unknown parameters. As the output is only accessible to measurement at sampling times, the outputdependent term turns out to be (almost all time) subject to a double uncertainty, making previous adaptive observers inappropriate. Presently, a new hybrid adaptive observer is designed and shown to be exponentially convergent under ad-hoc conditions.

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

“…Therefore, based on Lemma 3, V is an ISS Lyapunov function for system (14), and system (14) is ISS with respect to inputs̃and w, and, hence, its trajectories satisfy the bounds given by (19) and (20).…”

“…On the other hand, in the work of Efimov and Fradkov, 19 a new impulsive adaptive observer showed that an impulsive feedback can improve the convergence rate or relax the requirement on persistency of excitation. For a class of nonlinear sampled-data systems, in the work of Folin et al, 20 a new hybrid adaptive observer was designed and shown to be exponentially convergent under some common conditions. In the same vein, in the work of Ahmed-Ali et al, 21 an adaptive observer was proposed for systems with cascade structure, including finite-dimensional dynamics followed by infinite-dimensional dynamics.…”

Adaptive State Observer for Robot Manipulators Diagnostics and Health Degree Assessment

“…The relative errors between the expected output torque and the actual output torque can be represented as |1 − θ|. Therefore, regarding θ as the unknown parameter, we apply the idea of adaptive state observer (ASO) [29] to identify the value of θ. Before giving the fault detection algorithm, some assumptions are given below.…”

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

“…In [5] an adaptive observer for a class of parabolic PDEs is proposed, the observer is designed to provide online estimates of the system state and unknown parameters based on sampled data and also sufficient conditions for the observer to be exponentially convergent are established. On the other hand, a hybrid adaptive observer is designed in [6] and it is shown that the state estimation error is exponentially convergent if the sampling period is small enough and a persistent excitation condition holds. In this vein, in [7] an adaptive observer was proposed to exponentially estimate the state and the unknown parameters under a persistent excitation condition for uniformly observable Multiple-Input-Multiple-Output (MIMO) nonlinear systems.…”