16,756 research outputs found

    Probabilistic Reachability Analysis for Large Scale Stochastic Hybrid Systems

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    This paper studies probabilistic reachability analysis for large scale stochastic hybrid systems (SHS) as a problem of rare event estimation. In literature, advanced rare event estimation theory has recently been embedded within a stochastic analysis framework, and this has led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This paper presents this rare event estimation theory directly in terms of probabilistic reachability analysis of an SHS, and develops novel theory which allows to extend the novel results for application to a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the reach probability. Essentially, the approach taken is to introduce an aggregation of the discrete modes, and to develop importance sampling relative to the rare switching between the aggregation modes. The practical working of this approach is demonstrated for the safety verification of an advanced air traffic control example

    Probabilistic and Distributed Control of a Large-Scale Swarm of Autonomous Agents

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    We present a novel method for guiding a large-scale swarm of autonomous agents into a desired formation shape in a distributed and scalable manner. Our Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC) algorithm adopts an Eulerian framework, where the physical space is partitioned into bins and the swarm's density distribution over each bin is controlled. Each agent determines its bin transition probabilities using a time-inhomogeneous Markov chain. These time-varying Markov matrices are constructed by each agent in real-time using the feedback from the current swarm distribution, which is estimated in a distributed manner. The PSG-IMC algorithm minimizes the expected cost of the transitions per time instant, required to achieve and maintain the desired formation shape, even when agents are added to or removed from the swarm. The algorithm scales well with a large number of agents and complex formation shapes, and can also be adapted for area exploration applications. We demonstrate the effectiveness of this proposed swarm guidance algorithm by using results of numerical simulations and hardware experiments with multiple quadrotors.Comment: Submitted to IEEE Transactions on Robotic
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