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.

这项工作提出了一种解决方案，仅使用位置测量值就可以自适应地稳定具有未知参数的二阶线性系统。只有控制定律的符号已知，并且系统会受到持续扰动的影响。所提出的控制方案的症结在于使用系统的替代表示，该替代表示是通过对原始系统表示随时间进行积分而获得的。这样，可从测量中获得替代表示的整个状态，并通过替代表示和与原始输入随时间的积分有关的微分方程获得扩展的状态空间表示。后来，自适应控制方法和后推程序用于建立闭环稳定性。仿真结果支持了这一发现。