# computeTermRegNonlinSysPolyApproach

solver class for the polynomialization-based approach for computing terminal regions of nonlinear systems.

## Contents

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

## Syntax

obj = computeTermRegNonlinSysPolyApproach(Param,Opts)

## Description

This class provides all methods required for formulating and solving the polynomial approximations of the terminal region optimization problem in [1, Eq. 6] as well as the methods for verifying correctness of its solution.

## Input Arguments

Param | a struct containing the benchmark parameters .X: set of admissible states (class: interval/zonotope/polytope) .U: set of admissible control inputs (class: interval/zonotope/polytope) .W: set of disturbances (class: zonotope)
Opts | a struct containing the algorithm settings .xEq: equlibrium state to be stabilized (double vector) .uEq: equilibrium control input (double vector) .termRegOrder: (optional) order of the zonotope representing the terminal region (positive scalar, >= 1) .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 (see superclass; constructor for shared fields)
.paramReachSetOrder | order of the zonotope enclosing the parameterized reachable set for optimization (positive integer)

## Output Arguments

obj | generated instance of the class computeTermRegNonlinSysPolyApproach

## 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. [2] V. Gaßmann and M. Althoff, "Verified Polynomial Controller Synthesis for Disturbed Nonlinear Systems, IFAC-PapersOnLine, Volume 54, Issue 5, 2021, pages 85-90.

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