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Communication Dans Un Congrès Année : 2021

SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions

Résumé

This paper focuses on the computation of joint spectral radii (JSR), when the involved matrices are sparse. We provide a sparse variant of the procedure proposed by Parrilo and Jadbabaie, to compute upper bounds of the JSR by means of sum-of-squares (SOS) relaxations. Our resulting iterative algorithm, called SparseJSR, is based on the term sparsity SOS (TSSOS) framework, developed by Wang, Magron and Lasserre, yielding SOS decompositions of polynomials with arbitrary sparse support. SparseJSR exploits the sparsity of the input matrices to significantly reduce the computational burden associated with the JSR computation. Our algorithmic framework is then successfully applied to compute upper bounds for JSR, on randomly generated benchmarks as well as on problems arising from stability proofs of controllers, in relation with possible hardware and software faults.

Dates et versions

hal-02923348 , version 1 (27-08-2020)

Identifiants

Citer

Jie Wang, Martina Maggio, Victor Magron. SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions. 2021 American Control Conference (ACC), May 2021, New Orleans, United States. ⟨10.23919/ACC50511.2021.9483347⟩. ⟨hal-02923348⟩
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