ADAPTIVE LINEAR-QUADRATIC GAUSSIAN CONTROL - THE COST-BIASED APPROACHREVISITED

In adaptive control, a standard approach is to resort to the so-called certainty equivalence principle which consists of generating some sta ndard parameter estimate and then using it in the control law as if it were the true parameter. As a consequence of this philosophy, the est imation problem is decoupled from the control problem and this substan tially simplifies the corresponding adaptive control scheme. On the ot her hand, the complete absence of dual properties makes certainty equi valent controllers run into an identifiability problem which generally leads to a strictly suboptimal performance. In this paper, we introdu ce a cost-biased parameter estimator to overcome this difficulty. This estimator is applied to a linear quadratic Gaussian controller. The c orresponding adaptive scheme is proven to be stable and optimal when t he unknown system parameter lies in an infinite, yet compact, paramete r set.