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A Graphical Understanding of Lyapunov-based Nonlinear Control

By J. Willard Curtis and Randal W. Beard

Abstract

The class of continuous nonlinear controllers that are based on control Lyapunov functions (clfs) can be understood graphically as continuous selections from a set-valued map that takes states and maps them to control-value sets. The notion of inverse-optimality and robustness to input disturbances can also be graphically understood by this set-valued map. The graphical approach introduced in this paper makes clear the relationship between Sontag's formula, Freeman and Kokotovic' min-norm formula, and other `universal formulas', as well as shedding light on the meaning of Lyapunov redesign. Most importantly, this paper examines a null-space associated with these set-valued maps which offers the potential for significant improvement in the large-signal performance of Lyapunov-based controllers

Year: 2002
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.5936
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