Realization of exact tracking control for nonlinear systems via a nonrecursive dynamic design

Abstract

This paper investigates a novel nonrecursive tracking control law design for a class of nonlinear systems via dynamic output feedback. As the main contribution of this paper, a global nonrecursive tracking design procedure is first proposed to render a simple construction of a realizable output feedback control law, whose gain selections follow the conventional pole placement approach while the stability margin can be guaranteed via a sufficiently large scaling gain. By introducing a Lyapunov function which neglects the virtual controllers in essence, rigorous analysis is presented to ensure the global stability. In addition, finite-time and asymptotical tracking results can now be achieved within the same design framework whereas the tunable homogeneous degree plays as a key role. As another contribution, by proposing a saturated dynamic compensator, a less ambitious but practical control objective, namely semiglobal stability is achieved of the closed-loop system to relax the requirement of the restrictive growth conditions for global control design. Taking consideration of the case when system is subject to mismatched disturbances, a unified design and stability analysis framework shows that the practical tracking result can also be realized. A numerical example is provided to illustrate the effectiveness of the nonrecursive design and the simplicity of the proposed tracking control algorithm.