# approxAbsErrPwLin_coefficients

computes the coefficients of the piece-wise linear approximation of the abstraction error.

## Contents

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

## Syntax

coefficients = approxAbsErrPwLin_coefficients(obj,dynamics,candTermReg)

## Description

This function computes the semi-edge lengths of an interval enclosing the abstraction error (conservative polynomialization algorithm with tensor order 3). These serve as the coefficients of the piece-wise linear approximation of the abstraction error proposed in [1, Example 1].

## Input Arguments

obj | instance of class computeTermRegNonlinSysPolyApproach
dynamics | instance of class termRegNonlinSysDynamics
candTermReg | current candidate for the terminal region (class: polyZonotope)

## Output Arguments

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])

## See Also

@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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