Parametrical modeling and identification of a class of hybrid systems under persistent excitation of the input

Abstract

This paper deals with the problem of on-line identification of a class of single-input single-output time-invariant hybrid plant which can operate under bounded disturbances and/or unmodeled dynamics. An input-output model is first designed involving filtered signals for the hybrid plant from an initial state-space description. Such a model is simultaneously driven by the standard continuous-time input plus an extra signal. The extra input is composed for all time of a signal which involves the contribution of the input and output over a finite number of previous sampling instants plus a signal which involves the contribution of the weighted integral of the continuous-time input on a set of preceding sampling intervals. The above last driving signal is due to the existing couplings between the continuous-time and digital substates of the hybrid plant. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization under uncertainties and bounded noise. The parametrical identification is asymptotically achieved in the absence of noise and unmodeled dynamics provided that the plant is controllable and exponentially stable and that the input satisfies a standard condition of persistence of excitation.