# localCornerControl

Solve optimal control problem for the corner states of the parallelotope

## Contents

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

## Syntax

[uTotal, xt]= localCornerControl(system,xf,vert,h,Q,R,steps,lenHorizon,Opts)

## Description

This function solves an optimal control problem for all vertices of the initial parallelotope (see Lines 6-8 of Alg. 1 in [1]).

## Input Arguments

system | object containing the system dynamics (class:; nonlinearSys)
xf | desired final state at the end of the control process (dimension: [nx, 1])
vert | vertices of the initial parallelotope. (dimension: [nu,2^nx])
h | length of one timestep of the multiple shooting algorithm
Q | weighting matrix for the final state of the optimal control problem (dimension: [nx,nx])
R | weighting matrix for the input term of the optimal control problem (dimension: [nu,nu])
steps | number of intermediate timesteps of the corner trajectories during one timestep of the center trajectory
lenHorizon | length of the optimization horizon in center trajectory time steps
Opts | a structure containing following options
.parallel | boolean value that determines if parallel computing should be used or not (0 or 1)
.useAcado | use ACADO toolbox for solving the optimal control problem. Fmincon is used otherwise (0 or 1)
.extHorizon.decay | decay function for the objective function of the optimization problem with extended optimization horizon [`'uniform'` / `'fall'` / `'fall+end'` /; `'fallLinear'` / `'fallLinear+End'` /; `'fallEqDiff'` / `'FallEqDiff+End'` /; `'rise'` / `'quad'` / `'riseLinear'` /; `'riseEqDiff'` / `'end'`]

## Output Arguments

uTotal | optimal control inputs for the corner trajectories (dimension: [nu,2^nx,steps*lenHorizon])
xt | resulting corner trajectories (dimension: [nx,2^nx,steps*lenHorizon])

## See Also

`convexInterpolationControl`, `optimalControl`, `optimalControlFmincon`

## References

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

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