# initOptProblem

initialize optimal control problem for linear MPC

## Contents

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

## Syntax

[opt,optInit] = initOptProblem(Opts)

## Description

This function constructs the optimal control problem for linear model predictive control as descibed in Sec. IV.C in [1] using the YALMIP optimizer.

## Input Arguments

Opts | a structure containing the algorithm settings
.N | number of time-steps until safe terminal set is reached starting in safe initial set
.K | feedback matrix
.xf | desired final state
.termReg | terminal region
.XKX | feedback matrix for the extended system dynamics
.taylor | struct containing the propagation matrices for the linear system
.U | input set
.X | set of state constraints
.nx | number of states
.nx | number of inputs

## Output Arguments

opt | resulting YALMIP optimizer object
optInit | resulting YALMIP optimizer object for the initial optimal control problem

## See Also

`linSysMPC`

## References

- *[1] F. Gruber and M. Althoff, “Scalable robust model predictive control for linear sampled-data systems," CDC 2019

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