A geometric framework for stabilization by energy shaping: Sufficient conditions for existence of solutions∗
نویسندگان
چکیده
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 determining 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 of Lewis [2006]. This gives some new avenues for answering key questions in energy shaping that have not been addressed to this point.
منابع مشابه
A geometric approach to energy shaping
In this thesis is initiated a more systematic geometric exploration of energy shaping. Most of the previous results have been dealt with particular cases and neither the existence nor the space of solutions has been discussed with any degree of generality. The geometric theory of partial differential equations originated by Goldschmidt and Spencer in late 1960’s is utilized to analyze the parti...
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