Global Practical Tracking with Prescribed Transient Performance for High-Order Uncertain Nonlinear Systems

This paper considers the global practical tracking with prescribed transient performance for a class of high-order uncertain nonlinear systems. Our tracking problem has two remarkable features. One is to guarantee the tracking error to evolve within a prescribed funnel. The other is to allow heavy nonlinearities and serious unknowns in the systems, especially the unknown control directions. For these, delicate time-varying gains are introduced to ensure the prescribed transient performance. Simultaneously, such time-varying gains can effectively compensate the serious unknowns in the systems and the reference signal, and particularly, compensate the unknown control directions by combining generalized Nussbaum functions. Then, a time-varying state-feedback controller is constructed, such that the solutions of the resulted closed-loop systems are globally bounded, and the tracking error evolves within the prescribed funnel.