Adaptive Set‐Point Tracking via Repetitive Learning Control for Nonlinear Cascaded Uncertain Systems With Output Constraint

ABSTRACT This paper investigates the adaptive set‐point tracking control problem for a class of nonlinear cascaded uncertain systems with output constraint. Three kinds of uncertainties are considered in the system of interest, including nonidentical unknown control directions, additive periodic disturbance, and unmodeled dynamics. Different from the existing results, it does not require that the signs of control coefficients be identical, nor the structure of the periodic disturbance be known a priori. In view of the presence of an additive periodic disturbance and unknown control directions, the cancellation‐based feedback via backstepping is inapplicable in control design. Then, we develop a repetitive learning control strategy compensating for periodic disturbance regardless of unknown control directions. The changing supply rates technique for input‐to‐state stable (ISS) systems and a tan‐type barrier Lyapunov function are synthesized to address unmodeled dynamics with output constraint. It is shown that the tracking error converges to zero within the specified constraint, and all signals in the closed‐loop system are bounded in a semi‐global sense. Finally, two examples, including a two‐stage chemical reactor subject to periodic disturbance, validate our theoretical results.