Transient bounds for adaptive control systems

Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. In this note, we consider how these theories may be applied to adaptive control to quan...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1994-01, Vol.39 (1), p.171-175
Main Authors: Zhuquan Zang, Bitmead, R.R.
Format: Article
Language:English
Subjects:
Adaptative systems
Adaptive control
Adaptive systems
Applied sciences
Computer science
control theory
systems
Control systems
Control theory. Systems
Controllability
Error correction
Exact sciences and technology
Nonlinear control systems
Robustness
Signal analysis
Stability
Transient response
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Summary:Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. In this note, we consider how these theories may be applied to adaptive control to quantify transient response. This involves the explicit description of the constants appearing in the passivity theorem and/or the small gain theorem which characterize both system gains and initial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which connects initial state conditions with the input-output analysis. Applying these general theorems to adaptive control, we are able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response. The implication of these sufficient results is that without both bounds upon initial conditions and guarantees of excitation, potentially extreme transient excursions of system variables are possible even though global convergence and asymptotic performance are guaranteed.< >
ISSN:0018-9286
1558-2523
DOI:10.1109/9.273360