Robust control of uncertain feedback linearizable systems based on adaptive disturbance estimation

• Published in: ISA transactions Vol. 87; pp. 1 - 9
• Main Authors: Lozada-Castillo, N., Luviano-Juárez, A., Chairez, I.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.04.2019
• Subjects: Active disturbance rejection; Adaptive estimation; Adaptive observer; Continuous least mean square; Feedback linearizable systems; Feedback linearizable systems; Adaptive estimation; Adaptive observer; Continuous least mean square; Active disturbance rejection
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2018.10.003

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance. •The controller is based on an adaptive observer in order to estimate uncertainties.•The adaptive estimator uses a classic system identification procedure (LMS).•The stability analysis was based on an innovative Lyapunov theory.•A state observer and a time varying identifier formed the adaptive approach.•The Lyapunov analysis leads to find that origin is the practical stable equilibrium point.