approxAbsErrQuad_eval

evaluates the quadratic approximation of the abstraction error.

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

approxAbsErr = approxAbsErrQuad_eval(var_dzquad,var_exploitTR,quadCoeff,bilinCoeff,trCoeff)

Description

This function evaluates one of the quadratic approximation of the abstraction error proposed in [1, Proposition 1].

Input Arguments

var_dzquad

squared semi-edge lengths of interval enclosing the Cartesian product of the terminal region, the set of admissible control inputs and the set of disturbances (array of dimension [nx+nu+nw,1])

var_exploitTR

scalar measuring the exploitation of the trust region, see [1, Eq. 28a]

quadCoeff

coefficients of the quadratic terms [1, Eq. 27a] (array of dimension [nx,1])

bilinCoeff

coefficients of the bilinear terms in [1, Eq. 27a] (array of dimension [nx,1])

trCoeff

coefficients of the linear term, see [1, Eq. 27b] (array of dimension [nx,1])

Output Arguments

approxAbsErr

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

References

[1] L. Schäfer et al. "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", in IEEE Transactions on Automatic Control, vol. 69, no. 2, pp. 755-770, 2024

var_dzquad	squared semi-edge lengths of interval enclosing the Cartesian product of the terminal region, the set of admissible control inputs and the set of disturbances (array of dimension [nx+nu+nw,1])
var_exploitTR	scalar measuring the exploitation of the trust region, see [1, Eq. 28a]
quadCoeff	coefficients of the quadratic terms [1, Eq. 27a] (array of dimension [nx,1])
bilinCoeff	coefficients of the bilinear terms in [1, Eq. 27a] (array of dimension [nx,1])
trCoeff	coefficients of the linear term, see [1, Eq. 27b] (array of dimension [nx,1])