# approxAbsErrPwLin_eval

evaluation function for the piece-wise linear approximation of the abstraction error.

## Contents

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

## Syntax

approxAbsErr = approxAbsErrPwLin_eval(obj,candTermReg_sc,s,delta_c,paramAbsErr_coefficients)

## Description

This function returns the value of the piece-wise linear approximation of the abstraction error proposed in [1, Example 1].

## Input Arguments

obj | instance of class computeTermRegNonlinSysPolyApproach
candTermReg_sc | parameterized candidate terminal region (center and generator scaling factors) (polyZonotope/struct storing the; parameters of a polyZonotope)
s | generator scaling factors for the candidate terminal region (double vector)
delta_c | center translation for the canddiate terminal region (array of dimension [obj.nx,1])
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])

## Output Arguments

approxAbsErr | (lower bound of) abstraction error approximation (non-negative array of dimension [obj.nx,1])

## See Also

@computeTermRegNonlinSysPolyApproach/approxAbsErrPwLin_coefficients @computeTermRegNonlinSysPolyApproach/approxAbsErrPwLin_con

## 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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