Parameter Identification Algorithm for a LTV System with Partially Unknown State Matrix

This work is devoted to the problem of unknown parameters identification for the case when the state of the system is not measured directly and only the input and output signals of the system are known. In this paper an adaptive state observer and parameter identification algorithm for a linear time-varying (LTV) system is developed. The state matrix of the system under consideration contains unknown time-varying parameters of a known form. Every unknown parameter can be described by a second-order dynamical system, generating sinusoidal signal with unknown frequency and initial conditions. The developed algorithm allows to observe the state vector without identification of the unknown parameters using only measured output signal and known input signal. As soon as the state vector estimate is obtained, the parameter identification algorithm is applied to find unknown parameters of the system. The identification algorithm that was proposed in previous papers of the authors is used for this purpose. The system that is considered in the paper is written as general linear time-varying model. Since many nonlinear systems after linearization can be transformed into linear time-varying systems, the proposed algorithm can be applied for different technical objects, such as mobile robots, manipulators, electro-mechanical systems, etc.