Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization

DOI10.1137/15M1053347zbMath1356.34058arXiv1512.05599MaRDI QIDQ5506818

Deqing Huang, David Goluskin, Sergei Chernyshenko, Giovanni Fantuzzi

Publication date: 16 December 2016

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.05599

zbMATH Keywords

boundstime averagessum-of-squares optimizationstochastic expectations

Mathematics Subject Classification ID

Semidefinite programming (90C22) Ordinary differential equations and systems with randomness (34F05) Qualitative theory for ordinary differential equations (34C99) Asymptotic properties of solutions to ordinary differential equations (34D05)

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Uses Software

• Matlab
• Sostools
• SDPA
• SeDuMi
• SDPT3
• YALMIP
• Mosek

Cites Work

• Unnamed Item
• Unnamed Item
• Solving semidefinite-quadratic-linear programs using SDPT3
• Dissipation inequalities for the analysis of a class of PDEs
• Global stability analysis of fluid flows using sum-of-squares
• Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
• What are SRB measures, and which dynamical systems have them?
• Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results
• Semidefinite programming relaxations for semialgebraic problems
• Interval analysis: Theory and applications
• Computing sum of squares decompositions with rational coefficients
• A practical difference scheme for Fokker-Planck equations
• Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
• Polynomial sum of squares in fluid dynamics: a review with a look ahead
• Stability Analysis for a Class of Partial Differential Equations via Semidefinite Programming
• Convex Computation of the Region of Attraction of Polynomial Control Systems
• Bounds on Real Eigenvalues and Singular Values of Interval Matrices
• On statistical attractors and the convergence of time averages
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Bounding Stationary Expectations of Markov Processes
• SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition
• Semidefinite Optimization and Convex Algebraic Geometry
• Pre- and Post-Processing Sum-of-Squares Programs in Practice
• Sum-of-squares approach to feedback control of laminar wake flows
• Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application
• SRB measures as zero-noise limits

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