Adaptive Tracking of Unknown Multi-Sinusoidal Signal in Linear Systems with Arbitrary Input Delays and Unknown Sign of High Frequency Gain

摘要

The output adaptive tracking problem for a class of linear time-invariant plants with known parameters, unmeasurable state and arbitrary input delay is considered. The plant high frequency gain and its sign are uncertain. The reference signal is represented by multi-sinusoidal function of time generated by autonomous linear dynamical system of known order but with unknown parameters. The proposed adaptive control law is based on modification of augmented error approach that allows to “swap” the delay and cope with high frequency gain with unknown sign. The designed adaptive control law ensures boundness of all signals in the closed-loop system and asymptotical convergence of tracking error to zero.