1,040 research outputs found
Reachability analysis of linear hybrid systems via block decomposition
Reachability analysis aims at identifying states reachable by a system within
a given time horizon. This task is known to be computationally expensive for
linear hybrid systems. Reachability analysis works by iteratively applying
continuous and discrete post operators to compute states reachable according to
continuous and discrete dynamics, respectively. In this paper, we enhance both
of these operators and make sure that most of the involved computations are
performed in low-dimensional state space. In particular, we improve the
continuous-post operator by performing computations in high-dimensional state
space only for time intervals relevant for the subsequent application of the
discrete-post operator. Furthermore, the new discrete-post operator performs
low-dimensional computations by leveraging the structure of the guard and
assignment of a considered transition. We illustrate the potential of our
approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202
Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants
In this paper, we propose a new method for ensuring formally that a
controlled trajectory stay inside a given safety set S for a given duration T.
Using a finite gridding X of S, we first synthesize, for a subset of initial
nodes x of X , an admissible control for which the Euler-based approximate
trajectories lie in S at t [0,T]. We then give sufficient conditions
which ensure that the exact trajectories, under the same control, also lie in S
for t [0,T], when starting at initial points 'close' to nodes x. The
statement of such conditions relies on results giving estimates of the
deviation of Euler-based approximate trajectories, using one-sided Lipschitz
constants. We illustrate the interest of the method on several examples,
including a stochastic one
Progressive Analytics: A Computation Paradigm for Exploratory Data Analysis
Exploring data requires a fast feedback loop from the analyst to the system,
with a latency below about 10 seconds because of human cognitive limitations.
When data becomes large or analysis becomes complex, sequential computations
can no longer be completed in a few seconds and data exploration is severely
hampered. This article describes a novel computation paradigm called
Progressive Computation for Data Analysis or more concisely Progressive
Analytics, that brings at the programming language level a low-latency
guarantee by performing computations in a progressive fashion. Moving this
progressive computation at the language level relieves the programmer of
exploratory data analysis systems from implementing the whole analytics
pipeline in a progressive way from scratch, streamlining the implementation of
scalable exploratory data analysis systems. This article describes the new
paradigm through a prototype implementation called ProgressiVis, and explains
the requirements it implies through examples.Comment: 10 page
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