# reachSetHorizon

reachable set computation for the closed-loop system for the whole prediction horizon

## Contents

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

## Syntax

[param,res] = reachSetHorizon(sys,R0,param,Opts)

## Description

This function computes the reachable set for the closed loop system for the whole prediction horizon

## Input Arguments

sys | object containing the dynamics of the closed-loop system (class: nonlinParamSys)
R0 | initial set for reachablity analysis (class: zonotope)
param | a structure containing following options
.xc | reference trajectory (dimension: [nx,N+1])
.uc | reference trajectory control inputs (dimension: [nu,N])
.K | cell-array containing the computed feedback matrices for the tracking controller
.R | cell-array containing the time point reachable sets
.Rcont | cell-array containing the time interval reachable sets
.J | summed distance of the reference trajectory points from the terminal region
.L | value of the objective function (=cost) of the reference trajectory
.Jset | summed distance of the reachable sets from the terminal region
Opts | a structure containing following options
.nx | number of system states
.dT | time step. Prediction horizon: Opts.N * Opts.dT
.termReg | terminal region around the steady state xf (class: mptPolytope)
.fbContr | struct with name and parameter of the applied tracking controller
.ReachOptsTrack | reachability options for the CORA toolbox

## Output Arguments

param | updated struct of control law parameters
res | flag that specifies if final reachable set is fully contained in the terminal region (0 or 1)

## See Also

`reachsetMPC`

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