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R. St-Aubin, J. Friedman, and Alan K. Mackworth.
A Formal Mathematical Framework for Modeling Probabilistic Hybrid Systems. *Annals of Mathematics and Artificial Intelligence*,
37(3-4):397–425, 2006.

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 realtime 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.

@Article{AMAI06, author = {R. St-Aubin and J. Friedman and Alan K. Mackworth}, title = {A Formal Mathematical Framework for Modeling Probabilistic Hybrid Systems}, year = {2006}, journal = {Annals of Mathematics and Artificial Intelligence}, volume = {37}, number = {3-4}, pages = {397--425}, 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 realtime 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. }, bib2html_pubtype ={Refereed Journal}, bib2html_rescat ={}, }

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