Nonlinearities enhance parameter convergence in strict feedback systems

@article{Lin1999NonlinearitiesEP,
  title={Nonlinearities enhance parameter convergence in strict feedback systems},
  author={Jung-Shan Lin and Ioannis Kanellakopoulos},
  journal={IEEE Trans. Autom. Control.},
  year={1999},
  volume={44},
  pages={89-94}
}
Following the development of a parameter convergence analysis procedure for output-feedback nonlinear systems (1995, 1998), the authors shift their attention to strict feedback nonlinear systems in this paper. They develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real… 

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References

SHOWING 1-10 OF 16 REFERENCES

Nonlinearities enhance parameter convergence: the strict-feedback case

An analytic procedure is developed which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real matrix.

Nonlinearities enhance parameter convergence in output-feedback systems

It is shown that the presence of nonlinearities usually reduces the sufficient richness requirements on the reference signals and hence enhances parameter convergence, the first result on the relationship between PE and SR for adaptive nonlinear control systems.

Systematic Design of Adaptive Controllers for Feedback Linearizable Systems

A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions,

Adaptive Control: Stability, Convergence and Robustness

The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental

Adaptive output-feedback nonlinear control with parameter convergence

Analyses the parameter convergence properties of an adaptive control scheme for output-feedback nonlinear systems. The authors show that parameter convergence is guaranteed if an appropriately

Parameter convergence of a class of adaptive controllers

This paper shows that a class of adaptive control schemes can guarantee exponential convergence of the tracking and parameter error to zero provided the reference signal is sufficiently rich.

Parameter convergence of a new class of adaptive controllers

It is shown that the new class of adaptive controllers developed using nonlinear design techniques has stronger parameter convergence properties in the presence of overparameterization.