Parameter Estimation in Input Matrix Under Gain Constraints in Specified Frequency Ranges

Abstract

This paper addresses parameter estimation problem of Continuous-/Discrete-Time (CT/DT) Linear Time-Invariant (LTI) systems, whose gain properties should satisfy given constraints in a priori specified frequencies, using measured data. The following are supposed in our problem: i) only input matrix has parameters to be estimated; ii) the state and the input are both measured, and the derivative of the state is also measured in CT case, and iii) the gain constraints in specified frequency ranges are given beforehand. Under these suppositions, a formulation to minimize the difference between the measured state derivative and the expected state derivative (in CT case) or the difference between the measured one-step-ahead state and the expected one-step-ahead state (in DT case) in Euclidean norm with the supposed gain constraints satisfied is given in terms of Linear Matrix Inequality (LMI). The effectiveness of the proposed method is demonstrated by an academic example in DT case as well as flight data obtained by JAXA’s airplane in CT case.