Get approximate stochastic reach set using Lagrangian methods
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This function will get the approximate prob_thresh level set for a stochastic
discrete time system using the Lagrangian methods in
J. D. Gleason, A. P. Vinod, M. M. K. Oishi, "Underapproximation of
Reach-Avoid Sets for Discrete-Time Stochastic Systems via Lagrangian
Methods," in Proceedings of the IEEE Conference on Decision and Control,
2017
Usage: see examples/doubleIntegratorLevelSetApprox.m
or examples/lagrangianApproximations.m
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Inputs:
-------
method_str - Lagrangian method,
'lag-over' -- Lagrangian Overapproximation
'lag-under' -- Lagrangian Underapproximation
sys - LtiSystem object
prob_thresh - Probability threshold
safety_tube - Tube object
options - Struct of reach set options, see SReachSetOptions
Outputs:
--------
approx_set - Polyhedron object for the over-/under-approximation of the
stochastic reach set
approx_tube- [Optional] Tube comprising of an over-/under-approximation of
the stochastic reach sets across the time horizon
bounded_set- [Optional] Bounded disturbance set which was used to
robustify the computation (lag-under) or
augment the input set (lag-over)
Notes:
------
* compute_style of `support` and method of `lag-over` will return only the
approx_set.
* While 'Gaussian' disturbance can have options.bound_set_method be 'polytope'
or 'ellipsoid', 'UserDefined' disturbance requires options.bound_set_method
to be 'polytope'.
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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/