approxAbsErrPwLin_eval

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

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])

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.

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])