# computeTrustRegionExploitation

computes a scalar measure for the exploitation of the trust region.

## Contents

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

## Syntax

trExploitation = computeTrustRegionExploitation(obj,var_s,termRegSet)

## Description

This function computes the smallest value of the auxiliary variable tau_0 in the constraint in [1, Eq. 28a], which is considered a scalar measure for the exploitation of the trust region. It holds that zonotope(termReg.c,termReg.G*diag(var_s)) \subseteq termReg + trExploitation*tr_set, i.e., 0 <= trExploitation <= 1 for any feasible var_s. We require (a feasible value of) tau_0 to evaluate the parameterized approximation of the abstraction error.

## Input Arguments

obj | instance of class computeTermRegNonlinSysLinApproach
var_s | generator scaling factors (array of dimension [size(termReg.G,2),1])
termReg | current candidate for the terminal region (class: zonotope)

## Output Arguments

trExploitation | scalar between 0 and 1

## See Also

@computeTermRegNonlinSysLinApproach/approxAbsErrQuad_eval

## 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

© 2018-2026 I6 Technische Universität München `•` Website `•` License