# solveOptProblem

models and solves the convex programming approximation of the terminal region computation problem.

## Contents

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

## Syntax

[obj,termReg_opt,auxData_iter] = solveOptProblem(obj,dynamics,termReg,flagInitGuessFeasible)
[obj,termReg_opt,auxData_iter] = solveOptProblem(obj,dynamics,termReg,flagInitGuessFeasible,bloatAbsErr)

## Description

This function models and solves the convex programming approximation in [1, Eq. 17] of the optimization problem described at the beginning of [1, Sec. III], which returns a robust control invariant set of nonlinear dynamical systems with maximum volume.

## Input Arguments

obj | instance of class computeTermRegNonlinSysLinApproach
dynamics | instance of class termRegNonlinSysDynamics
termReg | current candidate for the terminal region (class: termRegNonlinSysLinApproach)
flagInitGuessFeasible | indicates whether termReg admits a feasible initial guess (or not)- for consistency with polynomialization algorithm (boolean)
bloatAbsErr | (optional) scaling factor for enlarging the set of abstraction errors (see the; verification procedure described in; [2, Sec. III 2]) (bloatAbsErr >= 1)

## Output Arguments

obj | updated instance of class computeTermRegNonlinSysLinApproach
termReg_opt | updated candidate for the terminal region (class: termRegNonlinSysLinApproach)
auxData_iter | additional solution data (e.g. flag indicating; feasibility of the solution) (class: termRegNonlinSysSolutionAuxData)

## See Also

-

## 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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