Construction of Lyapunov Functions for Hybrid Piecewise-Deterministic Markov Processes

نویسندگان

  • Alexandre R. Mesquita
  • João P. Hespanha
چکیده

We present a method for the construction of Foster-Lyapunov functions to prove ergodicity of hybrid piecewise-deterministic Markov processes. Our method searches for the Lyapunov function that maximizes a measure of the rate of convergence that appears in the theory of large deviations. We provide conditions under which such a Lyapunov function is the limit of an iterative procedure. Analytical solutions are often possible as exemplified with a problem for which a Lyapunov function was not known before: the problem of controlling the probability density of a swarm of robotic agents.

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تاریخ انتشار 2009