# computeExactController

implementation of the exact control law

## Contents

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

## Syntax

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

## Description

This function implements the control law that uses the exact solution for the convex combinations of the corner inputs. 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 (class zonotope)
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`, `computeLinearController`

## References

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

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