Adaptive Regulation Problem for Linear Systems with State, Input and Output Delays

This paper concerns the problem of simultaneous adaptive compensation of external unmatched disturbance and output reference tracking for linear time-invariant (LTI) systems with state, input, and output delays. The external disturbance and the reference signal are considered as multi-harmonic signals with unknown frequencies, amplitudes, and initial phases. The disturbance is unmeasurable and affects both the input and the output of the plant. The solution to the problem is based on technique of direct adaptive control without identification of the disturbance and reference signal parameters (biases, frequencies, phases, and amplitudes). This solution contains observers of parameterized disturbance and reference signal, a special modification of augmented error model and a direct adjustable controller providing asymptotic convergence of the tracking error to zero.