# optimizeRCIpoly

solves the polynomial programming approximation of the terminal region computation problem.

## Contents

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

## Syntax

[sol,fVal] = optimizeRCIpoly(obj,termReg,approx_R,mapsParamReduce,paramAbsErr_coefficients,p0)

## Description

This function models and solves the polynomial programming approximation in [1, Eq. (19)] of the optimization problem in [1, Eq. (6)], which returns a robust control invariant set of a given nonlinear dynamical system with maximum volume.

## Input Arguments

obj | instance of class computeTermRegNonlinSysPolyApproach
termReg | initial guess for the terminal region (class: polyZonotope)
approx_R | parameterized approximation of the time-pointreachable set (see [1,; Eq. (17)]; (class: polyZonotope);
mapsParamReduce | struct storing the parameterization of the lengths of the reducing generators in the optimization variables
paramAbsErr_coefficients | struct storing the coefficients of the parameterized approximation of the abstraction error
p0 | initial guess for the controller parameters (double vector)

## Output Arguments

sol | struct storing the solution of the polynomial program .p: controller parameters .delta_c: translation of the terminal region center .s: terminal region generator scaling factors .sCost: cost set generator scaling factors .sRed: reducing generator scaling factors .sAbsErr: abstraction error interpolation factors .exploitTR: scalar indicating the trust region exploitation .slack: slack variables of softened constraints
fVal | value of the nominal cost function (size of sol.costSet)

## See Also

-

## References

[1] 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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