Parametric uncertain second-order linear system output-adaptive stabilization: An integral and MRCA based approach

Abstract

This work proposes a solution for the adaptive stabilization of second-order linear systems with unknown parameters using only position measurements. Only the sign of the control law is known and the system is affected by constant perturbations. The crux of the proposed control scheme the use of an alternative representation of the system obtained through integrating over time the original system representation. In this way, the whole state of the alternative representation is available from measurements, and an extended state space representation is obtained through the alternative representation and the differential equation related to the integral over time of the original input. Later, an Adaptive Control methodology and an backstepping procedure are used to establish closed-loop stability. Simulation results support the findings.