# reachExactController

reachabilty analysis for the exact control law implementation

## Contents

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

## Syntax

[Rfinal,reachSet] = reachExactController(dynamic,R0,param,Opts)

## Description

Computes the reachable sets 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:; nonlinParamSys)
R0 | extended initial zonotope, which contains the state as well as the auxiliary states (dimension: 2*nx,; class zonotope or polyZonotope)
param | parameter vector. Containts the optimal inputs for the vertices of the parallelotope, which are needed for the online implementation of the control law (dimension: [nu*(2^nx),1])
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`, `computeExactController`

## References

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

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