# paramPartZonotope

wrapper for computing a partial zonotope over-approximation of the reachable set.

## Contents

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

## Syntax

partZono = computeTermRegNonlinSysPolyApproach.paramPartZonotope(pZ,idv,idp)

## Description

This function computes a partial zonotope over-approximation of a given polynomial zonotope pZ in the ids stored in idv (which include the generator scaling factors). Since we scale the generators of the initial set during optimization, we cannot use the partZonotope method of the polyZonotope class, which ignores the dependance of the center of pZ on the scaling factors.

## Input Arguments

pZ | parameterized reachable set (class: polyZonotope)
idv | vector of ids for over-approximation (interval-valued; factors like generator scaling factors)
idp | vector of ids of scalar-valued factors like the controller parameters

## Output Arguments

partZono: struct storing the components of the partial zonotope over-approximation of pZ: .c: center - does not include contributions by generators with exlusively even exponents in idv (class: polyZonotope) .G: generators (class: cell array of polyZonotopes) .E: exponent matrix of factors with id in idv (integer array of dimension [length(idv, length(partZono.G)]) .isConstGen: logical vector indicating whether partZono{i}.G is indepdendent (true) of ids in idp or not (false) (logical vector of length length(partZono.G)) .cVar: logical vector indicating whether partZono{i}.G has exclusively even exponents in idv (true - contributes to the center of the re-assembled polyZonotope) or not (false) (logical vector of length length(partZono.G)) .idv: ids of interval-valued factors like generator scaling factors)

## 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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