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Closed-loop analysis of slow adaptation in the control of unknown dynamic hysteretic systems

This paper continues the analysis of an adaptive control approach for a class of systems represented by an unknown hysteresis nonlinearity preceding unknown linear dynamics. In previous work, the multi-time-scale slow adaptation technique has been shown to produce local, asymptotic parameter convergence in an identification problem. In this paper, the same multi-time-scale slow adaptation technique is applied to the closed-loop adaptive control system. Stability of the closed-loop system is examined under the given control, using averaging theory and singular perturbation techniques. It is shown that, for sufficiently small initial conditions, both the parameter error and the output error converge exponentially to zero under appropriate conditions.