Adaptive control of systems with input saturation: A scheme using output derivatives of order up to relative degree

In this paper, the main attention is focused on transient property of control input signal, we propose a novel adaptive controller for time-continuous single-input single-output linear systems with an input saturation in which i-th derivatives of the output signal (i = 1, ···, relative degree) are available. To improve the control performance, a novel estimator using an observer for the tracking error signals is proposed. Using the estimator, it is shown theoretically that the tracking error between the controlled object output and the reference model output can converge to zero when the initial value of the tracking error satisfies a condition.