Improved Tracking Performance for Systems with Uncertain Dynamics via Integration of Prescribed-Performance and Boundary-Layer Control

We study the trajectory-tracking problem for systems with uncertain nonlinear dynamics. We focus on the prescribed performance control problem, which aims to establish predefined transient- and steady-state system specifications by forcing the evolution of the tracking error inside predefined functions of time, called performance functions. A typical problem in related works is the difficulty of achieving asymptotic tracking; arbitrarily small steady-state errors can typically be achieved via discontinuous controllers or performance functions that converge to arbitrarily small values, both of which induce control chattering. We develop a novel control algorithm that solves the trajectory-tracking problem under prescribed performance specifications for control-affine systems with unknown nonlinear terms. The algorithm relies on an innovative integration of prescribed performance and boundary layer control and guarantees the finite-time convergence of the tracking error to a predefined and arbitrarily small set, independent of the performance functions, the system dynamics, or the control gains’ selection. Comparative simulation studies demonstrate that the proposed algorithm outperforms standard prescribed performance algorithms in the sense that it achieves lower steady-state errors without chattering.