computeTermReglinSys

compute terminal region with linear system approach, using only containment

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

T = computeTermReglinSys(benchmark, Param, Opts)

Description

This function computes a terminal region with the approach in [1] and [2].

Input Arguments

benchmark

name of the considered benchmark model (see; "aroc/benchmarks/dynamics/...")

Param

a structure containing the benchmark parameters

.U

set of admissible control inputs

.W

set of uncertain disturbances

.V

set of measurement noise

.X

set of state constraints

.Y

set of output constraints

.Yexact

set of error-free output constraints

.F
-.gamma

defines the output equation y = x + Fv + gamma

U, X, and Y need to be polytopes, or will be transformed to polytopes within the algorithm (i.e., intervals or zonotopes; can also be used here, but will be transformed to polytopes). W, V, and Ustart on the other hand need to be intervals or zonotopes.

Opts

a structure containing the algorithm settings

.N

number of time steps [{10} / positive integer]

.timeStep

sampling time [{0.1} / positive scalar]

.terminalRegionType

method used for computing the terminal region [{'implicit'} or 'fixed']

.terminalRegionSet

set type of the terminal region [{'zonotope'} or 'ellipsoid']

.taylorOrder

Taylor order for certain approximations needed during the reachability analysis [{5} / positive integer]

.genMethod

method for computing the fixed directions [{'spherical'} or 'provided']

.nGenerators

if .genMethod='spherical', .nGenerators should be the number of generators for the fixed generator matrix [{dim(X)}/ positive integer]

.G

if .genMethod='provided', .matrix should be the desired matrix for the fixed generators

.K

feedback matrix for the terminal controller

.Q

state weighting matrix for the LQR approach applied to determine the terminal controller [{eye(nx)} / positive definite; square matrix]

.R

input weighting matrix for the LQR approach applied to determine the terminal controller [{eye(nu)} / positive definite; square matrix]

Output Arguments

T

object of class termRegContainmentLinSys

References

*[1] "Approximability of the Containment Problem for Zonotopes and Ellipsotopes", A. Kulmburg et al., submited to TAC in 2024
[2] Gruber et al. (2021), Computing safe sets of linear sampled-data systems, IEEE Control Syst. Lett., vol. 5, no. 2, pp. 385-390