paramPartZonotope
wrapper for computing a partial zonotope over-approximation of the reachable set.
Contents
Syntax
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
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pZ |
parameterized reachable set (class: polyZonotope) |
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idv |
vector of ids for over-approximation (interval-valued; factors like generator scaling factors) |
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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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