Approximation Metrics for Discrete and Continuous Systems

By Antoine Girard, George Pappas. IEEE Transactions on Automatic Control, 2006

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Formal verification of hybrid systems (2011, background): “In the context of hybrid systems, since states contain real-valued vectors, there is a natural metric over states, and this can be used to also define a coarser notion of simulation called approximating simulations: an approximating simulation relation with parameter ε requires observations of two r”
Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems (2008, methodology): “Approximate bisimulation has been introduced in [4], as an approximate version of the usual bisimulation relation [5], [6], and in [7] by using set-valued observations.”
Approximately bisimilar symbolic models for nonlinear control systems (2007, methodology): “In this paper we follow the line of research based on simulation/bisimulation by making use of the recently introduced notion of approximate bisimulation [GP07], that captures equivalence of systems in an approximate setting.”
Cyber–Physical Systems: A Perspective at the Centennial (2012, background): “associated with a set of labels and a set of observations where ðQ; dQÞ and ð ; d Þ are metric spaces, then, for T 1; T 2 2 T Mð ; Þ, an approximate bisimulation relation is defined as follows [106].”
Temporal logic motion planning for dynamic robots (2009, methodology): “The construction of approximate simulation relations can be done effectively using a class of functions called simulation functions [17].”