Limits of performance in reference-tracking and path-following for nonlinear systems
| Authors: | Aguiar A. Pedro, University of California, Santa Barbara, United States
Hespanha Joao P., University of California, Santa Barbara, United States
Kokotovic Petar, University of California, Santa Barbara, United States |
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| Topic: | 2.3 Non-Linear Control Systems |
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| Session: | Output Regulation and Tracking |
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| Keywords: | Limits of performance, non-minimum phase nonlinear systems, path-following,reference-tracking, cheap-control |
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Abstract
We investigate limits of performance in reference-tracking and path-followingand highlight an essential difference between them. For a class of nonlinearsystems, we show that in reference-tracking, the smallest achievable L_2norm of the tracking error is equal to the least amount of control energyneeded to stabilize the zero-dynamics of the error system. We then show thatthis fundamental performance limitation does not exist when the controlobjective is to force the output to follow a geometric path without atiming law assigned to it. This is true even when an additional desired speedassignment is required to be satisfied asymptotically or in finite time.
