Quantale-Enriched Co-Design: Toward a Framework for Quantitative Heterogeneous System Design
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| Format: | Preprint |
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2026
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| _version_ | 1866912992599212032 |
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| author | Riess, Hans Huang, Yujun Klawonn, Matthew Zardini, Gioele Hale, Matthew |
| author_facet | Riess, Hans Huang, Yujun Klawonn, Matthew Zardini, Gioele Hale, Matthew |
| contents | Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent quantitative criteria such as cost, confidence, or implementation choice. In practice, these quantities are often introduced through ad hoc scalarization or by augmenting the resource space, which obscures system structure and increases computational burden. We address this limitation by developing a quantale-enriched theory of co-design. We model resources and functionalities as quantale-enriched categories and design problems as quantale-enriched profunctors, thereby lifting co-design from boolean feasibility to general quantitative evaluation. We show that the fundamental operations of series, parallel, and feedback composition remain valid over arbitrary commutative quantales. We further introduce heterogeneous composition through change-of-base maps between quantales, enabling different subsystems to be evaluated in different local semantics and then composed in a common framework. The resulting theory unifies feasibility-, cost-, confidence-, and implementation-aware co-design within one compositional formalism. Numerical examples on a target-tracking system and a UAV delivery problem demonstrate the framework and highlight how native quantitative enrichment can avoid the architectural and computational drawbacks of boolean-only formulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_29921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantale-Enriched Co-Design: Toward a Framework for Quantitative Heterogeneous System Design Riess, Hans Huang, Yujun Klawonn, Matthew Zardini, Gioele Hale, Matthew Systems and Control Logic in Computer Science Category Theory Optimization and Control 93B51, 18D20, 06F07, 93B25, 93B52, 18M30, 18M05 Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent quantitative criteria such as cost, confidence, or implementation choice. In practice, these quantities are often introduced through ad hoc scalarization or by augmenting the resource space, which obscures system structure and increases computational burden. We address this limitation by developing a quantale-enriched theory of co-design. We model resources and functionalities as quantale-enriched categories and design problems as quantale-enriched profunctors, thereby lifting co-design from boolean feasibility to general quantitative evaluation. We show that the fundamental operations of series, parallel, and feedback composition remain valid over arbitrary commutative quantales. We further introduce heterogeneous composition through change-of-base maps between quantales, enabling different subsystems to be evaluated in different local semantics and then composed in a common framework. The resulting theory unifies feasibility-, cost-, confidence-, and implementation-aware co-design within one compositional formalism. Numerical examples on a target-tracking system and a UAV delivery problem demonstrate the framework and highlight how native quantitative enrichment can avoid the architectural and computational drawbacks of boolean-only formulations. |
| title | Quantale-Enriched Co-Design: Toward a Framework for Quantitative Heterogeneous System Design |
| topic | Systems and Control Logic in Computer Science Category Theory Optimization and Control 93B51, 18D20, 06F07, 93B25, 93B52, 18M30, 18M05 |
| url | https://arxiv.org/abs/2603.29921 |