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Please use this identifier to cite or link to this item: http://hdl.handle.net/10228/935

Title: State-Dependent Scaling Design for Robust Backstepping via Output Feedback 12
Authors: Ito, Hiroshi
Department of Control Engineering and Science, Kyushu Institute of Technology
九州工業大学情報工学部 制御システム工学科
伊藤, 博
Keywords: robust backstepping
state-dependent scaling
global robust stability
output feedback
observer design
input-to-state stability
matrix inequality
convex optimization
Issue Date: 1-Jun-1999
Publisher: 九州工業大学
Abstract: This paper considers global robust stabilization of a class of nonlinear systems via output feedback. A new approach to output-feedback backstepping is proposed. The approach provides us with a systematic design procedure which can handle output-feedback stabilization problems of strict-feedback nonlinear systems in a uni ed way. More importantly, the approach by itself has a mechanism of achieving robust stabilization against a general class of structured uncertainties in the procedure. Compared with the state-feedback global stabilization, the the class of uncertainties which has been treated by the literature of global robust stabilization problems via output feedback is quite restricted in spite of the practical importance of considering various locations and structure of uncertainties. The approach presented in this paper can be considered as an successful extension of the author's state-dependent design for state-feedback backstepping to the output feedback case. Thereby, this paper shows the power of the general concept of state-dependent scaling design for nonlinear systems control by looking at output-feedback stabilization problems, especially in a backstepping manner. The scaling approach allows us to treats both static and dynamic uncertainty in an uni ed way and , in addition, be able to clarify the di erence between their consequences of stabilization in a simple way. The output feedback design proposed also inherits advantages of SD scaling design such as automatic computation of backstepping based on optimization. Controllers in this paper are dynamic feedback which consists of observer and feedback gain(or controller). The essential di erence between nominal stabilization and robust stabilization is described. It is shown that observer design cannot be separated globally from controller design. The observer should be designed strong enough to compensate \nonlinear size" of the uncertainty on the entire state-space. The coupling is natural and inevitable in robust stabilization as it is for linear systems. In addition, for nonlinear systems, nonlinearity of the coupling is crucial for global stabilization which cannot be compensated globally by either feedback-gain or observer-gain independently. This fact contrasts with nominal stabilization in which it is possible to stabilize the whole system globally by designing controller strong enough whenever the observer dynamics by itself design to be only stable(or, vice versa). Strong observers required for robust stabilization may not exist unless the output have the full information of the state. If the nonlinear size of uncertainties are small enough, the global robust stabilization can be certainly achieved. This paper shows the condition of allowable size and nonlinearity of uncertainties for which robust stabilization can be done via backstepping. The condition is considered as the index which describes the largest allowable size of uncertainty in robust stabilization via linear H1 control. Indeed, for linear systems, the condition of has coupling between feedback gain and observer design(or Riccati inequalities). In addition to the coupling, the condition of the uncertainty size in this paper exhibits a recursive form because of backstepping. Another feature of the output backstepping procedures in this paper is that it does not require Young's inequality. Instead, the paper uses the Schur complements formula which gives a necessary and su cient condition for negativity of a quadratic form. This paper also proposes a novel recursive procedure of robust observer design, which resembles backstepping or forwarding for controller design.
URI: http://hdl.handle.net/10228/935
Appears in Collections: テクニカルレポート

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