Communications in Information & Systems

A Geometric Framework for Stabilization by Energy Shaping: Sufficient Conditions for Existence of Solutions

Bahman Gharesifard, Andrew D. Lewis, and Abdol-Reza Mansouri

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Abstract

We present a geometric formulation for the energy shaping problem. The central objective is the initiation of a more systematic exploration of energy shaping with the aim of de- termining whether a given system can be stabilized using energy shaping feedback. We investigate the partial differential equations for the kinetic energy shaping problem using the formal theory of partial differential equations. The main contribution is sufficient conditions for integrability of these partial differential equations. We couple these results with the integrability results for potential energy shaping. This gives some new avenues for answering key questions in energy shaping that have not been addressed to this point.

Article information

Source
Commun. Inf. Syst. Volume 8, Number 4 (2008), 353-398.

Dates
First available in Project Euclid: 6 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.cis/1241616525

Mathematical Reviews number (MathSciNet)
MR2495746

Zentralblatt MATH identifier
1168.93008

Citation

Gharesifard, Bahman; Lewis, Andrew D.; Mansouri, Abdol-Reza. A Geometric Framework for Stabilization by Energy Shaping: Sufficient Conditions for Existence of Solutions. Commun. Inf. Syst. 8 (2008), no. 4, 353--398.https://projecteuclid.org/euclid.cis/1241616525


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