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A formal mathematical framework for modeling probabilistic hybrid systems

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Abstract

The development of autonomous agents, such as mobile robots and software agents, has generated considerable research in recent years. Robotic systems, which are usually built from a mixture of continuous (analog) and discrete (digital) components, are often referred to as hybrid dynamical systems. Traditional approaches to real-time hybrid systems usually define behaviors purely in terms of determinism or sometimes non-determinism. However, this is insufficient as real-time dynamical systems very often exhibit uncertain behavior. To address this issue, we develop a semantic model, Probabilistic Constraint Nets (PCN), for probabilistic hybrid systems. PCN captures the most general structure of dynamic systems, allowing systems with discrete and continuous time/variables, synchronous as well as asynchronous event structures and uncertain dynamics to be modeled in a unitary framework. Based on a formal mathematical paradigm exploiting abstract algebra, topology and measure theory, PCN provides a rigorous formal programming semantics for the design of hybrid real-time embedded systems exhibiting uncertainty.

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, 201-2366 Main Mall, Vancouver, BC, Canada

    Robert St-Aubin, Joel Friedman & Alan K. Mackworth

Authors
  1. Robert St-Aubin
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  2. Joel Friedman
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  3. Alan K. Mackworth
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Correspondence to Robert St-Aubin.

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St-Aubin, R., Friedman, J. & Mackworth, A.K. A formal mathematical framework for modeling probabilistic hybrid systems. Ann Math Artif Intell 47, 397–425 (2006). https://doi.org/10.1007/s10472-006-9035-0

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  • DOI: https://doi.org/10.1007/s10472-006-9035-0

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