Fault Diagnosis for a Class of Robotic Systems with Application to 2-DOF Helicopter

This paper considers a general approach to fault diagnosis using a generalized Hamiltonian system representation. It can be considered that, in general, nonlinear systems still represent a problem in fault diagnosis because there are results only for a specific class of them. Therefore, fault diagnosis remains a challenging research area despite the maturity of some of the available results. In this work, a type of nonlinear system that admits a generalized Hamiltonian representation is considered; in practice, there are many systems that have this kind of representation. Thereupon, an approach for fault detection and isolation based on the Hamiltonian representation is proposed. First, following the classic approach, the original system is decoupled in different subsystems so that each subsystem is sensitive to one particular fault. Then, taking advantage of the structure, a simple way to design the residuals is presented. Finally, the proposed scheme is validated at the two-degree of freedom (DOF) helicopter of Quanser®, where the presence of faults in sensors and actuators were considered. The results show the efficacy of the proposed scheme.

Adaptive Synchronization of Filippov Systems with Unknown Parameters via Sliding Mode Control

In this paper, adaptive synchronization of Filippov systems with unknown parameters is investigated via sliding mode control. In order to obtain smooth error systems, Filippov systems are redesigned by the Generalized Hamiltonian system. The sliding mode control is applied to the error systems and stabilizes their zero solutions. Adaptive synchronization of chaotic systems via sliding mode control is investigated with the applications to Chua's system and the Duffing Oscillator with dry friction. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.

A new hierarchy of integrable system of1+2dimensions: from Newton's law to generalized Hamiltonian system. Part II

The Hamiltonian equation provides us an alternate description of the basic physical laws of motion, which is used to be described by Newton's law. The research on Hamiltonian integrable systems is one of the most important topics in the theory of solitons. This article proposes a new hierarchy of integrable systems of1+2dimensions with its Hamiltonian form by following the residue approach of Fokas and Tu. The new hierarchy of integrable system is of fundamental interest in studying the Hamiltonian systems.