Adaptive self-tuning control describes a body of approaches where a controller design method based on a system model is combined with an on-line estimator of the model parameter. The appealing feature of adaptive controllers consists in their ability to automatically adjust themselves so as to adapt to the true system. The more commonly adopted strategy for the design of adaptive control laws is the certainty equivalence approach. Its success is mainly due to its conceptual simplicity, since it consists in estimating the unknown parameter via some identification method and then using the estimate to design the control law as if it were the true value of the unknown parameter. On the other hand, working out stability and optimality results for certainty quivalence adaptive control schemes is a difficult task even in the ideal case when the true system belongs to the model class.

This is mainly due to the intricate interaction between control and identification in closed-loop, which can cause identifiability problems. In particular, standard parameter estimation techniques do not guarantee the estimated plant to be stabilizable, thus leading to a paralysis in the certainty equivalence control law selection.

In this presentation, new identification methods ensuring both uniform stabilizability of the estimated model and suitable closed-loop identification properties are introduced. This is obtained by adding an appropriate extra term to the least squares performance index which penalizes those parameterizations corresponding to non stabilizable models while preserving the fundamental properties of the least squares estimate (PLS, penalized least squares). A general stability result is then proved for PLS-based adaptive control schemes. In particular, adaptive stability is obtained for infinite-horizon LQG control. Moreover, the performance achieved with the proposed LQG control scheme is precisely characterized and a suitable modification to the adaptive control scheme so as to obtain both stability and optimality results is set up.

Biography

Maria Prandini was born in Brescia, Italy, in 1969. She received the laurea in Electronics Engineering from Politecnico of Milano, Italy, in 1994, and the Ph.D. degree in Electronics Engineering from the University of Brescia, Italy, in 1998. From October 1997 - February 1998, she was a teaching assistant for the course of Automatic Control at the University of Brescia, Italy. In the period March 1998 - July 1998, she was a visiting scholar at the Delft University of Technology, Delft, The Netherlands. She is currently a visiting post-doctoral research engineer at University of California, Berkeley, where in the spring 1999, she taught a graduate level course on stochastic systems.

Her research interests include stochastic system, identification and adaptive control; air traffic management systems; probabilistic verification of hybrid systems; and probabilistic pursuit-evasion games.