Performance limitations in reference tracking and path following for nonlinear systems

We investigate limits of performance in reference-tracking and path-following and highlight an essential difference between them. For a class of nonlinear systems, we show that in reference-tracking, the smallest achievable L2 norm of the tracking error is equal to the least amount of control energy needed to stabilize the zero-dynamics of the error system. We then show that this fundamental performance limitation does not exist when the control objective is to force the output to follow a geometric path without a timing law assigned to it. This is true even when an additional desired speed assignment is required to be satisfied asymptotically or in finite time. Key words: Limits of performance, non-minimum phase nonlinear systems, path-following, reference-tracking, cheap-control.

• Type: Journal
• Year: 2008
• Where: AUTOMATICA
• Authors: A. Pedro Aguiar, João Pedro Hespanha, Petar V. Kokotovic
• Keywords: Achievable L2 Norm, AUTOMATICA 2008, Fundamental Performance Limitation, Nonlinear Systems