On non-asymptotic observation of nonlinear systems

In this contribution, we use the so-called algebraic derivative method for a non-asymptotic state observation of nonlinear SISO systems. We derive a general formula of a time-varying filter that allows a non-model-based, quasi-instantaneous estimation of time derivatives of arbitrary analog time signals. The estimates are based on integrals of measured signals alone. For preserving accuracy, the estimation process has to be re-initialized after some period of time. Besides resetting the estimation time-interval equidistantly, estimated absolute error bounds and integral error bounds are also used for improving the efficiency of the estimation process. As an example, we use Chen's chaotic oscillator to illustrate the velocity and the robustness of our observation method with respect to uncertainty of initial values and uniformly distributed measurement noise.