Adaptive output-feedback trajectory tracking for a class of uncertain second-order linear systems

In this work, we present a novel design of an explicit control strategy to solve the trajectory tracking problem for an uncertain second-order linear system with only partial availability of the state. The system parameters are unknown, and an additive constant disturbance is considered. Despite the apparent simplicity of this system, the solution requires an intricate combination of available methodologies. The proposed approach corresponds to a Lyapunov-based adaptive control strategy consisting of a reduced-order observer, a dynamic slave system and an adaptive controller with dynamic extension. Simulation results are provided to highlight the effectiveness of the proposed adaptive control strategy in accomplishing the regulation and trajectory tracking problems.