# reachLinearController

reachabilty analysis for the linear approximation of the exact control law

## Contents

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

## Syntax

[Rfin,reachSet] = reachLinearController(dynamic,R0,cu,Gu,inputAssign,Opts)

## Description

Computes the reachable set at the end of one timestep of the center trajectory as well as all reachable sets during this timestep.

## Input Arguments

dynamic | object containing the system dynamics (class:; nonlinearSys)
R0 | extended initial zonozope, which contains the state as well as the auxiliary states (dimension: 2*nx)
cu | cell array containing the center vectors of the input zonotopes for each intermediate timestep (dimension cell array: Opts.Ninter,; diemnsion entries: [nu,1])
Gu | cell array containing the generator matrices of the input zonotopes for each intermediate timestep (dimension cell array: Opts.Ninter,; diemnsion entries: [nu,nx])
inputAssign | Matrix that encode the information which generator of the first input zonotope belongs to which generator of the initial state zonotope R0 (dimension: [nx,zonotope order of R0])
Opts | structure containing user defined options for the algorithm

## Output Arguments

Rfinal | final zonotope at the end of reachability analysis
reachSet | cell array containing the reachable sets of all intermediate time steps

## See Also

`convexInterpolationControl`, `computeLinearController`

## References

- [1] Schuermann et al. (2017), Convex interpolation control with formal guarantees for disturbed and constrained nonlinear systems

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