Robust continuous time adaptive control by parameter projection

The authors show that a simple modification of projecting the estimates continuously to stay in a compact convex set yields an adaptive controller which is robust to bounded disturbances and small unmodeled dynamics for continuous-time plants of arbitrary relative degree. It is demonstrated that eventually all the signals enter a compact set, the size of which is independent of initial conditions. Also, the upper-bounds on the size of allowable unmodeled dynamics are independent of initial conditions. An estimate of the performance as measured by the mean-square tracking error is obtained. The results show that the projection mechanism alone is sufficient to guarantee robust boundedness and robust performance with respect to bounded disturbances and small unmodeled dynamics. Some time-varying and nonlinear uncertainties are allowed. The nominal plant is however restricted to be minimum-phase