# computeTermRegNonlinSysOpt

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 = computeTermRegNonlinSysOpt(X,U,W,xEq,uEq,termRegOrder)
obj = computeTermRegNonlinSysOpt(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)] as well as the methods for verifying correctness of the candidate solutions.

## 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)
verbose | if set to true, the algorithm prints information about each iteration to the command window. If set to false, no iterative output is shown.
solverSettings | (optional) struct 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)
.constraintTolerance | constraint tolerance (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)
.tr_maxRelErr | max. relative approximation error (see [1, App. II]) (0 < tr_malRelErr < 1)
.tr_shrink | scaling factor for shrinking the trust region (see; [1, App. II]) (0 < tr_shrink < 1)
.tr_grow | scaling factor for enlarging the trust region (see; [1, App. II]) (1 < tr_grow)

## Output Arguments

obj | generated instance of the class computeTermRegNonlinSysOpt

## 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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