Tunnel Prescribed Control of Nonlinear Systems With Unknown Control Directions

This article solves the entry capture problem (ECP) such that for any initial tracking error, it can be regulated into the prescribed performance constraints within a user-given time. The challenge lies in how to remove the initial condition limitation and to handle the ECP for nonlinear systems under unknown control directions and asymmetric performance constraints. For better tracking performance, we propose a unified tunnel prescribed performance (TPP) providing strict and tight allowable set. With the aid of a scaling function, error self-tuning functions (ESFs) are then developed to make the control scheme suitable to any initial condition (including the initial constraint violation), where the initial values of ESFs always satisfy performance constraints. In lieu of the Nussbaum technique, an orientation function is introduced to deal with unknown control directions while such way is capable of reducing the control peaking problem. Using ESFs, together with TPP and an orientation function, the resulted tunnel prescribed control (TPC) leads to a solution for the underlying ECP, which also exhibits a low complexity level since no command filters or dynamic surface control is required. Finally, simulation results are provided to further demonstrate these theoretical findings.