# computeTermRegNonlinSysOptApproach

abstract superclass for optimization-based approaches for computing terminal regions of nonlinear systems.

## Contents

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

## Syntax

obj = computeTermRegNonlinSysOptApproach(X,U,W,xEq,uEq,termRegOrder)
obj = computeTermRegNonlinSysOptApproach(X,U,W,xEq,uEq,termRegOrder,solverSettings)

## Description

This class and its childclasses provide all methods required for formulating and solving the convex [1] or polynomial [2] approximations of the terminal region optimization problem in [2, Eq. 6].

## Input Arguments

X | set of admissible states (class: interval / polytope / zonotope)
U | set of admissible control inputs (class: interval / polytope / zonotope)
W | set of uncertain disturbances (class: zonotope)
xEq | equilibrium state (array of dimension [X.dim,1])
uEq | equilibrium control input (array of dimension [U.dim,1])
termRegOrder | order of the zonotope representing the terminal region (positive integer)
solverSettings | (optional) structure with the following optional fields
.penaltyWeight | penalty weight for soft constraints, see [1, Remark 4] (positive scalar)
.convergenceTolerance | convergence tolerance, see [1, Eq. 18] (positive scalar)
.maxIter | max. number of iterations (positive integer)
.maxCostTerms | maximum admissible number of addends in the cost function, see [1, Remark 2] (positive interger)

## Output Arguments

obj | generated instance of the class computeTermRegNonlinSysOptApproach

## 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 [2] L. Schäfer and M. Althoff, "Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis," American Control Conference, 2024, pp. 4162-4169.

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