International Journal of Control · 1987 · 324 citations · 24 references
Natural SciencesMathematicsSystems EngineeringDynamical SystemsProcess ControlSystem DynamicsAdaptive ControlControl Of Dynamical SystemsControl SystemsControl TheoryRobust ControlStability TheoryAdaptive IdentificationAdaptive SystemsAsymptotic StabilityExcitationPersistent ExcitationReduced-order ControlRobust Adaptive ControlUniform Stability
Persistent excitation is a key concept in adaptive identification and control, increasingly recognized for its role in robustness, and is expected to remain central to adaptive control analysis. The paper aims to deepen understanding of persistent excitation by (1) offering a tutorial framework that consolidates scattered results, (2) presenting new uniform asymptotic stability and robustness findings for nonlinear adaptive systems, and (3) exploring future implications, including reduced‑order model control. The authors construct a general framework for discussing persistent excitation, compile existing literature, derive new stability results linking PE to uniform asymptotic stability, and analyze how these insights inform future adaptive control problems.
The importance of the concept of persistent excitation (PE) in adaptive identification and control has been recognized for some time. Recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems. There is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control. Hence there is a real need for a deeper understanding of the concept. The paper is written with three objectives. The first, which is tutorial in nature, is to provide a general framework for the discussion of persistent excitation and to collect results in the area, which are scattered throughout the adaptive literature. The second objective is to present some new results related to the uniform asymptotic stability (u.a.s.) and robustness of adaptive systems and the relation of PE to the stability properties of a class of non-linear systems. The final objective is to discuss the implications of PE in future problems, including adaptive control using a reduced-order model.
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Some Extensions of Liapunov's Second Method
J. P. LaSalle · IRE Transactions on Circuit Theory · 1960 · 886 citations