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This work was supported in part by Poul Due Jensen Foundation under Grant 883901; in part by the Villum Investigator under Grant S4OS; in part by the project SER-ICS under Grant PE00000014; in part by the FSC Regional Tuscan Project AUTOXAI2J53D21003810008; and in part by the Project Tuscany Health Ecosystem (THE), CUP: B83C22003920001, under the MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU. Recommended by Associate Editor Eric C.Kerrigan.

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Proper Lumping for Positive Bilinear Control Systems

Publicat a:Ieee Transactions On Automatic Control. 69 (11): 8120-8127 - 2024-11-01 69(11), DOI: 10.1109/TAC.2024.3410153

Autors: Jimenez-Pastor, Antonio; Toller, Daniele; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea

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Positive systems naturally arise in situations where the model tracks physical quantities. Although the linear case is well understood, analysis and controller design for nonlinear positive systems remain challenging. Model reduction methods can help tame this problem. Here, we propose a notion of model reduction for a class of positive bilinear systems with (bounded) matrix and exogenous controls. Our reduction, called proper positive lumping, aggregates the original system such that states of the corresponding reduced model represent nonnegative linear combinations of original state variables. In this article, we prove a characterization result showing that the reductions by proper positive lumping are exactly those preserving the optimality of a suitable class of value functions. Moreover, we provide an efficient polynomial-time algorithm for the computation of the minimal lumping. We numerically evaluate our approach by applying it to a number of benchmark case studies.

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