# approxAbsErrPwLin_con

returns the (linear inequality) constraints encoding the piece-wise linear approximation of the abstraction error.

## Contents

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

## Syntax

[cIneqStruct, cIneqStructAux] = approxAbsErrPwLin_con(obj,candTermReg,paramAbsErr_coefficients,idxVars)

## Description

This function returns the (linear inequality) constraints encoding the piece-wise linear approximation of the abstraction error proposed in [1, Example 1].

## Input Arguments

obj | instance of class computeTermRegNonlinSysPolyApproach
candTermReg | current candidate for the terminal region (polyZonotope/struct storing the; parameters of a polyZonotope)
paramAbsErr_coefficients | struct storing the coefficients of the piece-wise linear approximation of the abstraction error .origin: upper bound on the abstraction error at 0xUxW (array of dimension [obj.nx,1]) .termReg: upper bound on the abstraction error at box(candTermReg)xUxW (array of dimension [obj.nx,1]) .tr upper bound on the abstraction error at box(candTermReg+trust_region)xUxW (array of dimension [obj.nx,1])
idxVars | struct storing the indices of the optimization variables

## Output Arguments

cIneqStruct | struct storing the matrix and right-hand side of the linear inequality constraint ensuring [1, Eq. (20b)]
cIneqStructAux | struct storing the matrix and right-hand side of the auxiliary linear inequality constraints

## See Also

@computeTermRegNonlinSysPolyApproach/approxAbsErrPwLin_coefficients

## References

[1] L. Schäfer and M. Althoff, "Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis," American Control Conference, 2024, pp. 4162-4169.

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