# computeInitialGuess

computes an inital guess for the polynomialization-based approach for computing terminal regions of nonlinear systems.

## Contents

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

## Syntax

initGuess = computeInitialGuess(obj,dynamics,Q,R,weights)

## Description

Computes an inital guess for the polynomialization-based approach for computing terminal regions of nonlinear systems [1]. The 7 initial guess for the terminal region itself is obtained by computing different types of (robust) invariant sets of the linearized dynamics (around the equilibrium state) and combining their generators. To obtain an initial guess for the controller, we use generator space control [2].

## Input Arguments

obj | instance of class computeTermRegNonlinSysPolyApproach
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])
weights | struct storing the weights for computing the initial guess

## Output Arguments

initGuess | initial guess for the terminal region and controller (class: termRegNonlinSysPolyApproach)

## See also

@computeTermRegNonlinSysOpt/initialGuessSet_RiccatiEq @computeTermRegNonlinSysOpt/initialGuessSet_GSB @computeTermRegNonlinSysOpt/initialGuessSet_mRPI

## 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. [2] B. Schürmann and M. Althoff, "Guaranteeing Constraints of Disturbed Nonlinear Systems Using Set-Based Optimal Control in Generator Space,", IFAC-PapersOnLine, Volume 50, Issue 1, 2017, pp. 11515-11522.

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