Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems

Abstract

Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.

On fault tolerant control structures incorporating fault estimation

“…It is assumed that the system (22), (23) is controllable to be controlled by the state feedback control law…”

“…Integrated single-step methods of fault estimation and FTC, for linear systems subject to bounded actuator or sensor faults, are proposed in [17], [27]. Specified via LMI formulations and solved using H ∞ or mixed H 2 /H ∞ optimization, the observer structures are augmented fault state observers in the standard Luenberger form [22] or unknown input augmented fault observers [25]. To guarantee desired time response, an LMI regional pole placement design strategy is proposed in [26], [27].…”

Structural-parametrical Design Method of Adaptive Observers for Nonlinear Systems

“…This direction is widely applied at design AO for nonlinear dynamic systems [14][15][16][17]. Paper [14] represents design method AO in the Luyenberger canonical form for fault estimate in nonlinear systems. The nonlinearity is known and satisfies the Lipschitz condition.…”

Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length

“…Over the past decades, observer-based fault estimation [12,13] has received considerable attention both in academic research and in industrial application domains. It has made significant progress and covered a wide scope of research issues such as linear systems [14], nonlinear systems [15], time-delay systems [16], uncertain systems [17], multiagent systems [18] and fuzzy systems [19].…”