Adaptive control of stochastic bilinear systems

The minimum variance control law for bilinear systems with known parameters is shown to yield in most cases controls with infinite variance; this calls into question the use of the so-called bilinear self-tuning regulators. An adaptive weighted minimum variance controller based upon the cost with weighted control efforts is suggested for first order bilinear systems and is shown to yield boundedness of the closed loop system variables under a certain condition on the parameter estimate.