# initialGuessSet_RiccatiEq

solves the Riccati equation for the linearized dynamics and inscribes a zonotope into the resulting ellipsoid.

## Contents

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

## Syntax

PIset = initialGuessSet_RiccatiEq(obj,dynamics,Q,R)

## Description

To obtain an initial guess for the optimization-based approaches for computing terminal regions of nonlinear systems, we solve the algebraic Riccati equation (ARE) for the linearized dynamics. Afterwards, a zonotope is inscribed into the positively invariant ellipsoid whose shape matrix is the solution of the ARE.

## Input Arguments

obj | instance of class computeTermRegNonlinSysOpt
dynamics | instance of class termRegNonlinSysDynamics
Q | state weighting matrix (positive-definite matrix of dimension; [obj.nx,obj.nx])
R | control input weighting matrix (positive-definite matrix of dimension; [obj.nu,obj.nu])

## Output Arguments

PIset | approximation of the positively invariant set (class: termRegNonlinSysLinApproach)

## See also

-

## References

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