© 2003 by Institute of Mathematics and its Applications
Identification of a class of hybrid systems
1 Instituto de Investigación y Desarrollo de Procesos, Departamento de Electricidad y Electrnica, Facultad de Ciencias,, Universidad del País Vasco, Leioa (Bizkaia), Aptdo. 644 de Bilbao, Spain
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 unmodelled dynamics. The hybrid plant dealt with is composed of two subsystems one being of continuous-time type while the other is digital. 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 unmodelled dynamics provided that the plant is controllable and exponentially stable and that the input satisfies a standard condition of persistence of excitation.
Keywords: estimation schemes; hybrid systems; identification; unmodelled dynamics.