Adaptive state observer synthesis for a class of nonstationary bilinear systems under conditions of partial parametric uncertainty

Abstract

An adaptive observer for a bilinear nonstationary dynamic system under partial parametric uncertainty is proposed. The problem is solved under the assumption that the unknown parameters are contained in the matrix/ vector at the control signal. The key idea of the proposed algorithm is a new parameterization of the object based on two functions, one of which can be found analytically using the known and measured signals of the system. The use of linear filters allows us to reduce the system to the form of a linear static regression model containing unknown constant parameters; at the next stage, the unknown parameters are estimated using a gradient algorithm. Since the unknown constant parameters are mathematically related to the unknown initial conditions of the state vector and the unknown variable parameters in the matrix/vector of control, the estimates of the unknown components of the state vector and the estimate of the unknown parameter are derived based on the estimates obtained. It is shown that the proposed method advantage consists in the possibility of application to a sufficiently wide class of bilinear systems, to which, in particular, Euler-Lagrange systems describing many real technical objects and robotic systems can be reduced.