Robust semiglobal stabilization of minimum-phase input-output linearizable systems via partial state and output feedback

1995 ◽  
Vol 40 (6) ◽  
pp. 1029-1041 ◽  
Author(s):  
Zongli Lin ◽  
A. Saberi
Keyword(s):  
Output Feedback ◽  
Minimum Phase ◽  
Input Output ◽  
Partial State ◽  
Semiglobal Stabilization

Approximate Input-Output Feedback Linearization of Non-Minimum Phase System using Vanishing Perturbation Theory

2015 ◽  
pp. 173-201
Author(s):  
Monia Charfeddine ◽  
Khalil Jouili ◽  
Naceur Benhadj Braiek
Keyword(s):  
Perturbation Theory ◽  
Output Feedback ◽  
Feedback Linearization ◽  
Main Idea ◽  
Input State ◽  
Phase System ◽  
Minimum Phase ◽  
Input Output ◽  
Approximate System ◽  
System Input

The inverse of a non-minimum-phase system being unstable, standard input-output feedback linearization is not effective to control such systems. In this chapter is a presentation of a new tracking control method for the nonlinear non-minimum-phase system. Indeed, the main idea here is to dismiss a part of system dynamics in order to make the approximate system input-state feedback linearizable. The neglected part is then considered as a perturbation part that vanishes at the origin. Finally, a linear controller is designed to control the approximate system. Stability is analyzed using the vanishing perturbation theory. The efficacy and usage of the proposed approach is evaluated in an illustrative inverted cart-pendulum example.

Disturbance Attenuating Adaptive Controllers for Parametric Strict Feedback Nonlinear Systems With Output Measurements

1999 ◽  
Vol 121 (1) ◽  
pp. 48-57 ◽  
Author(s):  
I. Egemen Tezcan ◽  
Tamer Bas¸ar
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Robust Adaptive Control ◽  
Disturbance Attenuation ◽  
Parameter Estimates ◽  
Minimum Phase ◽  
Feedback Form ◽  
Output Measurement ◽  
Adaptive Controllers ◽  
Strict Feedback

We present a systematic procedure for designing H∞-optimal adaptive controllers for a class of single-input single-output parametric strict-feedback nonlinear systems that are in the output-feedback form. The uncertain nonlinear system is minimum phase with a known relative degree and known sign of the high-frequency gain. We use soft projection on the parameter estimates to keep them bounded in the absence of persistent excitations. The objective is to obtain disturbance attenuating output-feedback controllers which will track a smooth bounded trajectory and keep all closed-loop signals bounded in the presence of exogenous disturbances. Two recent papers (Pan and Bas¸ar, 1996a; Marino and Tomei, 1995) addressed a similar problem with full state information, using two different approaches, and obtained asymptotically tracking and disturbance-attenuating adaptive controllers. Here, we extend these results to the output measurement case for a class of minimum phase nonlinear systems where the nonlinearities depend only on the measured output. It is shown that arbitrarily small disturbance attenuation levels can be obtained at the expense of increased control effort. The backstepping methodology, cost-to-come function based H∞ -filtering and singular perturbations analysis constitute the framework of our robust adaptive control design scheme.

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