The Application of Total Energy as a Lyapunov Function for

Examination of total energy shows that the global limit behavior of a dissipative mechanical system is essentially equivalent to that of its constituent gradient vector field. The class of “navigation functions” is introduced and shown to result in “almost global” asymptotic stability for closed loop mechanical control systems upon which a navigation function has been imposed as an artifical potential energy. Two examples from the engineering literature – satellite attitude tracking and robot obstacle avoidance – are provided to demonstrate the utility of these observations.

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