Full-Order Observer for a Class of Nonlinear Systems With Unmatched Uncertainties: Joint Attractive Ellipsoid and Sliding Mode Concepts

Abstract

This article addresses the problem of state estimation of controlled affine nonlinear systems in the presence of disturbances and uncertainties in the state equation. The proposed algorithm synthesizes a full-order observer, which joins the concepts of sliding mode observer and the ultimate uniform bounded stability. For this, on the state equation of the system, a transformation is used to disjoin the measured state variables of the unmeasured ones. In this way, the measured state variables are used to design an observation function, such that, in finite time, the full-order observer behaves as a reduced-type observer. Furthermore, the obtained reduced system only contains the estimation error associated with the unmeasured state variables. In order to reconstruct the unavailable state variables, the reduced system is treated by means of the application of the attractive ellipsoid method, involving the solution of a linear matrix inequality. Thus, without the use of unavailable state variables, the reduced estimation error dynamic trajectories arrive at a small-size ultimate bound. This means that the estimated state variables are an approximation of the real ones. To illustrate the theoretical contribution, the proposed algorithm is applied to underactuated robots driven by dc motors and tested using a benchmark system in real-time experimentation.