A variable structure gradient adaptive algorithm for a class of dynamical systems

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A standard assumption in adaptive control is that the parameters being estimated are either constant or vary 'slowly' as a function of time. This paper investigates the adaptive control of a class of systems in which the parameters vary as a specified function of state. The dynamic structure of the systems may be either linear or nonlinear. For this class of systems, the state space is separated into distinct subsets. The parameters are then required to remain constant, or be slowly time varying, within the subsets. Given a controller for the system, an analysis of the output error dynamics and the parameter error dynamics leads to a parameter adaptation algorithm with a variable structure. The stability and convergence of both the parameter error and the output tracking error are investigated. An analysis of SISO linear systems with full state information is used to motivate and illustrate the treatment of SISO feedback linearizable systems.

Original languageEnglish (US)
Pages (from-to)171-186
Number of pages16
JournalSystems and Control Letters
Issue number3
StatePublished - Mar 16 1998
Externally publishedYes


  • Adaptive control
  • State-varying parameters
  • Switching algorithm


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