Global Normal Forms for MIMO Nonlinear Systems, with Applications to Stabilization and Disturbance Attenuation

1999 ◽  
Vol 12 (2) ◽  
pp. 121-142 ◽  
Author(s):  
B. Schwartz ◽  
A. Isidori ◽  
T. J. Tarn
Keyword(s):  
Nonlinear Systems ◽  
Normal Forms ◽  
Disturbance Attenuation ◽  
Mimo Nonlinear Systems

scholarly journals Finite-Time Stability of MIMO Nonlinear Systems Based on Robust Adaptive Sliding Control: Methodology and Application to Stabilize Chaotic Motions

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 21759-21768
Author(s):  
Ha Le Nhu Ngoc Thanh ◽  
Mai The Vu ◽  
Ngoc Phi Nguyen ◽  
Nguyen Xuan Mung ◽  
Sung Kyung Hong
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Time Stability ◽  
Chaotic Motions ◽  
Sliding Control ◽  
Finite Time Stability ◽  
Mimo Nonlinear Systems ◽  
Robust Adaptive ◽  
Control Methodology

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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