Simple Indirect Adaptive Control Without a Diophantine Equation and Without The Sign of The High Frequency Gain

The adaptive control of general delay, linear time-varying systems is addressed. We devise a new model reference adaptive control law which does not require the solution of a Diophantine equation, and does not require a priori knowledge of the sign of the high frequency gain. This control law coupled with the parameter estimation equations allows a simple representation of the closed loop system which greatly eases the stability and performance analysis of the closed loop system, and has potential for generalization to adaptive pole placement, and other control laws suitable for non-minimum phase systems. For the Kalman filter estimator coupled with our control law we obtain stability without persistence of excitation, and without knowledge of the sign of the high frequency gain.