Get the overapproximation of the stochastic reach set
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This function will compute the overapproximation of the stochastic reach
set via Algorithm 2 in
J. D. Gleason, A. P. Vinod, and M. M. K. Oishi. 2018. Lagrangian
Approximations for Stochastic Reachability of a Target Tube.
online. (2018). https://arxiv.org/abs/1810.07118
Usage: See examples/lagrangianApproximations.m
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[overapprox_set, overapprox_tube] = getSReachLagUnderapprox(sys,...
target_tube, disturbance_set)
Inputs:
-------
sys - LtiSystem object
target_tube - Tube object
disturbance_set - Polyhedron or SReachEllipsoid object (bounded disturbance
set)
options - Struct of reach set options, see SReachSetOptions
Outputs:
--------
overapprox_set - Polyhedron object for the overapproximation of the
stochastic reach set
overapprox_tube- [Available for 'VHmethod' only] Tube comprising of an
overapproximation of the stochastic reach sets across the
time horizon
Notes:
* From polyhedral computation theory (implemented here when
options.compute_style is VHmethod), intersections and Minkowski differences
are best performed in facet representation and Minkowski sums are best
performed in vertex representation. However, since in this computation, all
three operations are required, scalability of the algorithm is severly
hampered, despite theoretical elegance.
* Using support functions, an arbitrarily tight polytopic overapproximation of
the set may be computed via convex optimization (linear or second order-cone
programs).
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This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/