Robust adaptive tracking of continuous-time systems under the presence of unmodelled dynamics

This paper presents an indirect adaptive control scheme with pole-placement which is applicable to continuous linear time-invariant systems of unknown parameters even if the plant is not inversely stable and/or not controllable. The only assumption about the system is the property of stabilizability of the plant. The scheme is a pole-placement type while leading to performances very, close to those of model-following schemes without requiring the plant inverse stability assumption. The control objective is that the plant output should asymptotically track a reference signal, given by an arbitrary, stable filter, under a small stationary, tracking-error in some prefixed frequency interval, while ensuring robust closed-loop stability. The adaptive stabilizability and the robustness of this system under the presence of unmodelled dynamics and, possibly, bounded disturbances are proved without assuming the controllability of the modelled plant. The control is designed such that the steady-state tracking be perfect, for the chosen frequency range. in the ideal case of known plant. A normalized least-squares algorithm with a relative adaptation dead-zone and an a posteriori modification of the parameter estimates is used to update the plant parameters in the adaptive case. Two alternative algorithms for the parameter estimates modification are studied. Both of them ensure the controllability of the estimated and modified plant model for all time and at the limit. Such a property is crucial to be able to solve the stability adaptive problem of the system via the pole placement technique. On the other hand. the relative adaptation dead-zone is included for robustness purposes under unmodelled dynamics and, possibly, bounded disturbances.