Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

• Published in: IEEE transactions on automatic control Vol. 61; no. 3; pp. 834 - 839
• Main Authors: Kamalapurkar, Rushikesh, Fischer, Nicholas, Obuz, Serhat, Dixon, Warren E.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Compensation; Computer simulation; Delay; Delays; Dynamical systems; Feedback control; Mathematical models; Nonlinear dynamics; Nonlinear systems; Robustness; Stability analysis; Time-varying systems; Trajectory; robust control; Delay systems; uncertain systems; nonlinear control systems; Lyapunov methods
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2451472

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, sufficiently small time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying. Numerical simulations illustrate robustness of the developed method to various combinations of simultaneous input and state delays.