Patching continuous-time signals using high-gain observers and 3rd order splines

In real-time applications, due to disturbances or problems inherent to the measurement systems, portions of the measured signal are lost or distorted. Thus, in those cases when the control goal is to track measured signals in real-time, the continuity and smoothness of the closed-loop system may be compromised. To minimize this problem, in this work, a method to patch the continuous-time signal is proposed. The approach, based on high-gain observers and third-order splines, allows taking into account not only the initial and the ending points of the missing part of the signal but the corresponding derivatives as well. As a result, a smooth signal is obtained. To illustrate the validity of the approach, a sufficiently complex signal, named the first state of the Lorenz attractor is reconstructed in the numerical experiments.