Identification and adaptive control for systems with unknown orders, delay, and coefficients

An analysis that gives recursive estimates for time-delay, system orders, and coefficients of single-input, single-output linear discrete-time deterministic and stochastic systems with uncorrelated noise is presented. It is assumed that a lower bound for the time delay and upper bounds for system order are known. The optimal adaptive control is designed for both tracking and linear quadratic regulation when the system parameters, including time-delay, orders, and coefficients, are unknown. The rates of convergence are derived the coefficient estimates to their true values and the loss functions to their minima