Active disturbance rejection robust control for uncertain systems with ill-defined relative degree

Active Disturbance Rejection (ADR) is a robust control paradigm which transforms the problem of controlling nonlinear systems by means of a direct active estimation. This estimation is further used to cancel the additive disturbances. This control design can be attained for some specific class of systems. Among others, if the system to be controlled is inputoutput linearizable (IOL), the tracking trajectories problem can be solved indeed. However, there are many examples where the system is not IOL in the whole space. The approximate IOL has been proposed to handle the control design for such class of systems that are usually known as ill-defined relative degree systems. This paper proposes the ADR based control on the adaptive estimation of the disturbance for ill-defined relative degree systems. An adaptive scheme was proposed for developing a state estimator of the uncertain system despite the poor knowledge of the plant and the presence of uncertainties. The adaptive observer uses a parametric identifier to obtain the time varying parameters required by the observer. Based on the states of the uncertain system, a switching feedback controller is able to reject actively the perturbations that affect the nonlinear system by a simple compensation scheme. The switch law for the controller was forced by the input-associated function that may cross zero when the relative degree is illdefined. This switching strategy is proposed to avoid the control singularities. A numerical example was developed for showing the observer/controller performance: The synchronization of the so-called unified chaotic system was proposed as testing problem. The obtained results in the example showed how the proposed adaptive disturbance rejection scheme can be implemented in uncertain systems.