Output Feedback Regulation of a Class of Lower Triangular Nonlinear Systems with Arbitrary Unknown Measurement Sensitivi
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Output Feedback Regulation of a Class of Lower Triangular Nonlinear Systems with Arbitrary Unknown Measurement Sensitivity Min-Sung Koo and Ho-Lim Choi* Abstract: In this paper, a regulation problem for a class of lower triangular nonlinear systems under unknown measurement sensitivity by output feedback is considered. The distinguished feature is that the unknown measurement sensitivity is only required to be positive and bounded. The analysis is carried out to show the relation between the gain selection of an output feedback controller and the bound of the measurement sensitivity. Then, the adaptive gain-scalings of the controller are utilized to dominate the unknown growth rate of the nonlinearity. Keywords: Lower triangular nonlinear system, measurement sensitivity, output feedback controller.
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INTRODUCTION
The global regulation problems by output feedback for nonlinear systems coped with uncertain nonlinearities have been studied for the past decades. For a class of nonlinear systems with lower triangular nonlinearities, various control schemes with observers that have on-line adaptive gains are constructed in [1–4] under some conditions such as unknown linear growth rate, bounding functions depending on output feedback rate, and unknown control direction. In [5], both high-gain and low-gain output feedback controllers are developed and engaged to systems depending on the nonlinearity types. Then, in [6], a switching control scheme is developed for systems whose nonlinearity types are not known a priori. All aforementioned results share a common fact that their control schemes are developed based on the assumption of ‘clean’ feedback circumstances. That is, the measured feedback through sensors is assumed to be so accurate. Recently, the stabilization or regulation problems of a class of nonlinear system under the measurement noise or sensitivity have attracted much attention [7–16], because some discrepancy between the real system state values and measured feedback values via sensors can occur in practice [13, 17, 18]. The study in [10] considers a case of the measurement noise where the error due to the measurement noise causes the increasing gain which can deteriorate the state estimation error. In [9], the observer with adaptive law is designed to deal with the output measurement noise in the form of y = x1 + s(t) where s(t) is the
noise. The so-called measurement sensitivity considers a different feedback distortion case such as θi (t)xi where xi denote system state in convention and θi (t) denote some bounded positive functions. Then, in [8], an output feedback controller with dual-domination technique is proposed to obtain the system stabilization under y = θ (t)x1 in which θ (t) is not necessarily a differentiable function. However, as addressed in [8], the allowed bound of θ (t) is limited to some small ranges such as θ (t) ∈ [1 − θ ∗ , 1 + θ ∗ ] where θ ∗ is somewhat small. Moreover, in [8], the size of θ ∗ tends to be reduced signi
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