Robust adaptive guaranteed cost tracking control for high‐order nonlinear systems with uncertainties based on high‐order fully actuated system approaches

This article investigates the robust adaptive guaranteed cost tracking (RAGCT) control problems for two class of high‐order nonlinear systems with time‐varying uncertainties. A special nonlinear function, named as the local smooth nonlinear function, is introduced, which is crucial for our controller design. Then, using the function and the recently proposed high‐order fully actuated (HOFA) system approaches, a novel RAGCT controller for HOFA system with time‐varying uncertainty is designed, which guarantees the global boundedness of the closed‐loop system within finite time. Then, based on the result about the above HOFA system, the RAGCT controller for a class of strict‐feedback systems with high‐order form and time‐varying uncertainties is obtained, which also guarantees that the closed‐loop system is globally bounded within finite time. Most importantly, two designed controllers can preset arbitrarily the upper bounds of cost functions characterizing the tracking performance independent of the system initial values and the time‐varying uncertainties, which optimizes greatly the system tracking performance, and is difficult to achieve by using existing guaranteed cost control methods. Finally, two simulation examples including one‐link manipulator are provided to show the effect and the practicability of our proposed control method.