# computeQuadraticController

implementation of the quadratic control law

## Contents

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

## Syntax

[zonoBig,reachSet,controlLawParam] =
computeQuadraticController(dynamic,zono,zonoR,uCorner,Opts)

## Description

This function implements the quadratic control law. The reachable set is computed for one time step of the center trajectory, which consists of multiple steps of the corner trajectories.

## Input Arguments

dynamic | object containing the system dynamics (class:; nonlinParamSys)
zono | initial zonotope (class zonotope or polyZonotope)
zonoR | parallelotope which is an overapproximation of the initial zonotope zono
uCorner | optimal control inputs for the corner trajectories (dimension: [nu,nx^2,Opts.Ninter])
Opts | structure containing user defined options for the algorithm

## Output Arguments

zonoBig | extended zonotope that results from the reachability analysis. This zonotope still includes the auxiliary states
reachSet | cell array containing the reachable sets of all intermediate time steps
controlLawParam | parameters of the computed control law

## 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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