# verifyTerminalRegion

verifies invariance of the terminal region.

## Contents

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

## Syntax

[flagVerified,termReg_verified] = verifyTerminalRegion(obj,dynamics,termReg)

## Description

This function implements the verification procedure described in [1, Sec. III 2]. Compared to the paper, we make the following modification to deal with violations of the time-interval constraint in [1, Eq. (6b)]: we tighten the polytope, which represents the set of admissible states, in every direction in which the containment condition is violated. The tightening is chosen as the difference of the support function of the reachable set in the violating direction A(j,:) and b(j).

## Input Arguments

obj | instance of class computeTermRegNonlinSysOpt
dynamics | instance of class termRegNonlinSysDynamics
termReg | converged solution (class: termRegNonlinSysOpt)

## Output Arguments

flagVerified | true if the verification was succesful, false otherwise (logical)
termReg_verified | verified terminal region (class: termRegNonlinSysOpt)

## See Also

@computeTermRegNonlinSysOpt/checkInvariance

## 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.

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