# computeAlpha

compute the control law for generator space control

## Contents

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

## Syntax

alpha = computeAlpha(R0,A,B,c,xf,iter,Opts)

## Description

Computes the control law for one time step by solving an optimal control problem in a set based manner for the control algorithm that is based on optimal control in generator space (see Eq. (12) and (13) in [1]).

## Input Arguments

R0 | initial set of states (class: zonotope)
A | cell-array storing the system matrices of the linearized discrete time system
B | cell-array storing the input matrices of the linearized discrete time system
c | cell-array storing the constant offsets of the linearized discrete time system
xf | cell-array storing the goal states for all time steps
iter | current time step
Opts | a structure containing the algorithm settings
.U | set of admissible control inputs
.N | number of time steps
.Ninter | number of intermediate time steps
.nx | number of states
.nu | number of inputs
.extHorizon.active | use extended optimization horizon for optimal control problems [{false} / true]
.extHorizon.horizon | length of the extended optimization horizon in center trajectory time steps [{`'all'`} / positive integer]
.extHorizon.decay | decay function for the objective function of the optimization problem with extended optimization horizon [{`'fall+End'`} / `'uniform'` / `'fall'` /; `'fallLinear'` / `'fallLinear+End'` /; `'fallEqDiff'` / `'FallEqDiff+End'` /; `'rise'` / `'quad'` / `'riseLinear'` /; `'riseEqDiff'` / `'end'`]

## Output Arguments

alpha | computed control law parameters alpha

## See Also

`generatorSpaceControl`

## References

- [1] Schuermann et al. (2017), Guaranteeing constraints of disturbed nonlinear systems using set-based optimal control in generator space

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