Markov Chains with Maximum Return Time Entropy for Robotic Surveillance

摘要: Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing return time entropy a Markov chain, subject to graph topology with travel times and stationary distribution. The is weighted average, over all nodes, first chain; objective function series that does not admit in general closed form. The features theoretical computational contributions. First, we obtain discrete-time delayed linear system for probability distribution establish its convergence properties. We show continuous compact set therefore admits global maximum; unique globally-optimal solution known only complete graphs unitary times. then upper lower bounds between well-known rate chain. To compute optimal chain numerically, asymptotic equality entropy, conditional truncated propose an iteration gradient entropy. Finally, apply these results problem. Our numerical that, model rational intruder prototypical topologies test cases, maximum performs better than several existing chains.