# reachSetGenSpaceContr

computes the reachable set for one time step

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See Also

## Syntax

[reachSet,R] = reachSetGenSpaceContr(sys,R,P,alpha,Opts)

## Description

This function computes the reachable set of the controlled system for one time step of the controller that is based on optimal control in generator space.

## Input Arguments

sys | object with the closed-loop dynamics (class: nonlinearSys)
R | initial set (class: zonotope)
P | parallelotope enclosure of the initial set (class: zonotope)
alpha | cell-array storing the control law for the time step
Opts | a struct containing the following fields
.Ninter | number of intermediate time steps
.reachSteps | number of reachability steps in each time step
.U | set of admissible control inputs
.ReachOpts | settings for reachability analysis with CORA
.nx | number of states
.nu | number of inputs

## Output Arguments

reachSet | object of class reachSet storing the reachable set
R | final reachable set

## See Also

`generatorSpaceControl`

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