Maria Prandini - Politecnico di Milano

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Adaptive linear quadratic Gaussian control: optimality analysis and robust controller design
Maria Prandini – February, 1998

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 equivalence adaptive control schemes is a difficult task even in the ideal case when the true system belongs to the model class. This is due to the intricate interaction between control and identification in closed-loop, which can cause identifiability problems.


The objective of this thesis is twofold:


  • we aim at introducing new adaptive control schemes based on the certainty equivalence principle able to overcome the difficulties arising in standard certainty equivalence control systems. In particular, we are interested in designing adaptive controllers which ensure the overall control system stability irrespectively of the excitation characteristics of the involved signals. A further target is then to precisely characterize the corresponding performance and to study a suitable modification to the adaptive control scheme so as to obtain both stability and optimality results
  • we want to devise a new strategy for the tuning of adaptive control laws so as to incorporate robustness features with respect to parameter uncertainty. The idea is that the adaptive controller should select at each time instant a cautious control law with the objective of obtaining an acceptable performance for most models, instead of completely relying on the currently most probable model as in the certainty equivalence approach. Then, a conservative control law is applied when uncertainty is large, but, as uncertainty is reduced by means of the data collected on-line from the system, the robust adaptive controller becomes better tailored to the true system. 


Such objectives are pursued for linear, time-invariant stochastic SISO systems affected by white noise based on the infinite-horizon LQG control design method.

Last updated in February 2007