Improved Least Squares Identification for Adaptive Controllers

An improved recursive least squares algorithm for parameter estimation is presented which includes: on/off criteria to prevent parameter drift during periods of low excitation; a variable forgetting factor which maintains the trace of the covariance matrix at a user specified value; data preprocessing and normalization to improve numerical accuracy; scaling of the regressor vector to minimize the condition number of the covariance matrix; plus independent estimation of the mean values of the I/O data which can be used to eliminate errors due to d.c. bias or slowly drifting elements in the regressor vector. The algorithm can also include parameter projection to constrain the estimates to a priori specified regions and retains the formal properties such as convergence, of a true weighted least squares algorithm. The proposed algorithm is compared with other modifications suggested in the literature, and its advantages are demonstrated by a simulated example.