Book ChapterDOI
Hopf bifurcation in an adaptive system with inmodeled dynamics
B. Cyr,B. Riedle,Petar V. Kokotovic +2 more
- pp 261-262
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TLDR
Adaptive schemes can exhibit a “nonlinear” instability in which the linear system with fixed parameters is stable, but this instability is a Hopf bifurcation caused by unmodeled dynamics.Abstract:
Adaptive schemes can exhibit a “nonlinear” instability in which the linear system with fixed parameters is stable. This instability is a Hopf bifurcation caused by unmodeled dynamics.read more
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Journal ArticleDOI
Qualitative classification of the dynamics of a class of adaptive feedback systems
TL;DR: In this article, the authors consider a class of adaptive feedback systems of arbitrary order with unmodeled dynamics and constant disturbances and demonstrate that the dynamical behavior of any system in this class must conform to a limited number of options varying according to the selection of system parameters such as the leakage constant and the adaptation step-size.
Book ChapterDOI
Bifurcations and chaos in a periodically forced prototype adaptive control system
Yuri A. Kuznetsov,Carlo Piccardi +1 more
TL;DR: In this paper, the behavior of an adaptive control system with a sinusoidal component superposed over a constant disturbance or reference input is analyzed, and the local bifurcations of the low-period solutions are numerically detected by means of a continuation method, and different modes of behavior and the transitions among them are classified.
References
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Proceedings ArticleDOI
Bounded error adaptive control
B. Peterson,Kumpati S. Narendra +1 more
TL;DR: In this paper, the problem of identifying and controlling when plant output is corrupted with disturbance and when plant parameters vary with time is considered, and the error model can be described by a non-homogeneous differential equation.
Proceedings ArticleDOI
Robustness of adaptive control algorithms in the presence of unmodeled dynamics
TL;DR: In this article, an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances is presented.
Journal ArticleDOI
Stable model reference adaptive control in the presence of bounded disturbances
TL;DR: In this paper, the adaptive control of a linear time-invariant plant in the presence of bounded disturbances is considered, and the adaptive controller suggested assures the boundedness of all signals in the overall system.
Journal ArticleDOI
Exponential convergence of adaptive identification and control algorithms
TL;DR: Output and equation error adaptive identification algorithms and an adaptive control algorithm are shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions.