# initialGuessSet_mRPI

computes an (invariant) outer approximation of the minimal robust positively invariant set of the linearized dynamics.

## Contents

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

## Syntax

minRPIset = initialGuessSet_mRPI(obj,dynamics,Q,R)
minRPIset = initialGuessSet_mRPI(obj,dynamics,Q,R,flag_invariant)

## Description

To obtain an initial guess for the optimization-based approaches for computing terminal regions of nonlinear systems, we compute an outer approximation of the minimal robust positvely invariant (mRPI) set of the linearized dynamics (based on [1, Alg. 2]). By default, the loop in [1, Alg. 2, line 10-16] is omitted and the output order of initGuess is set to a user-defined value (see description of input arguments). If the additional input argument flag_invariant is set to true, this loop is executed.

## Input Arguments

obj | instance of class computeTermRegNonlinSysOptApproach
dynamics | instance of class termRegNonlinSysDynamics
Q | state weighting matrix (positive-definite matrix of dimension; [obj.nx,obj.nx])
R | control input weighting matrix (positive-definite matrix of dimension; [obj.nu,obj.nu])
flag_invariant | (optional), see description - if omitted or false, the user-defined order is chosen as opts.termRegOrder (logical)

## Output Arguments

minRPIset | outer approximation of the mRPI set (class: termRegNonlinSysLinApproach)

## See also

-

## References

[1] Gruber et al., "Computing safe sets of linear sampled-data systems", 2021, IEEE Control Systems Letter, vol. 5, no. 2, pp. 385-390.

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