# computeSafeInitialSet

compute a safe initial set

## Contents

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

## Syntax

[safeSet,safeInputs] = computeSafeInitialSet(termSet,Param,Opts)

## Description

This function computes a safe initial set with corresponding input sets correction sets via optimization, where the objective is to make the initial set as large as possible while steering all states into the previously determined terminal set.

## Input Arguments

termSet | previously computed safe terminal set (class: zonotope)
Param | a structure containing the benchmark parameters
.U | set of admissible control inputs (class: interval or zonotope)
.W | set of uncertain disturbances (class: interval or zonotope)
.V | set of measurement errors (class: interval or zonotope)
.X | set of state constraints (class: mptPolytope)
Opts | a structure containing following options
.Tdomain | search domain for the terminal region (class:; interval)
.N | number of time steps
.genMethod | method for computing the fixed generator matrix for the terminal set
.G | generator matrix for the terminal set (for; Opts.genMethod = `'provided'` only)
.costFun | cost function used for the optimization problem

## Output Arguments

safeSet | resulting safe initial set
safeInputs | cell-array storing the input zonotopes

## See Also

`computeTermRegZonoLinSys`

## References

- [1] Gruber et al. (2021), Computing safe sets of linear sampled-data systems, IEEE Control Syst. Lett., vol. 5, no. 2, pp. 385-390

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