Innovative non-asymptotic and robust estimation method using auxiliary modulating dynamical systems

Abstract

In this paper, we aim to introduce an innovative non-asymptotic and robust estimation method based on the observable canonical form by means of a set of auxiliary modulating dynamical systems. The latter auxiliary systems are given by the controllable canonical form with zero initial condition. The proposed method can be applied to many kinds of linear and nonlinear systems. In this paper, it is applied to estimate the states and the output’s derivatives for linear singular systems with multiple inputs and multiple outputs in noisy environment. First, the considered singular system is transformed into a form similar to the Brunovsky’s observable canonical form with the injection of the inputs’ and outputs’ derivatives. Second, algebraic integral formulas are obtained both for the state variables and the outputs’ derivatives. After giving solutions of the required auxiliary systems, error analysis in discrete noisy case is addressed, where a provided noise error bound can be used to select design parameters. In the end, numerical simulations are given to illustrate the performance of the proposed method.