implicit_oneStepReachability

Computes one step of linear reachability analysis, as used by the linSys algorithm

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

[Rtp, Rti, ctrl_variable, utotal, additional_variables, additional_constraints] = implicit_oneStepReachability(Rtp_previous, optsInternal)

Description

Computes one step of linear reachability analysis, using the implicit approach for the controller. This entire algorithm is set up such that the reachability is computed symbolically, which is why we couldn't use CORA directly here.

Input Arguments

Rtp_previous

Struct containing the symbolic variables describing the time-point solution from the previous step

optsInternal

Struct containing internal parameters

Output Arguments

Rtp

Struct containing the symbolic variables describing the time-point solution

Rti

Struct containing the symbolic variables describing the time-interval solution

ctrl_variable

Struct containing the symbolic variables necessary to describe the controller

utotal

Struct containing the symbolic variables describing the input

additional_variables
additional_constraints

These are the auxilliary variables and constraints that are needed to build the optimization problem, but don't necessarily have an interpretation.

References

*[1] "Approximability of the Containment Problem for Zonotopes and Ellipsotopes", A. Kulmburg et al., submited to TAC in 2024

Rtp_previous	Struct containing the symbolic variables describing the time-point solution from the previous step
optsInternal	Struct containing internal parameters

Rtp	Struct containing the symbolic variables describing the time-point solution
Rti	Struct containing the symbolic variables describing the time-interval solution
ctrl_variable	Struct containing the symbolic variables necessary to describe the controller
utotal	Struct containing the symbolic variables describing the input
additional_variables additional_constraints	These are the auxilliary variables and constraints that are needed to build the optimization problem, but don't necessarily have an interpretation.