Stable Set-Valued Integration of Nonlinear Dynamic Systems using Affine Set-Parameterizations

DOI10.1137/140976807zbMath1326.65088OpenAlexW1835264310MaRDI QIDQ3195246

Benoît Chachuat, Boris Houska, Mario E. Villanueva

Publication date: 22 October 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10044/1/30358

zbMATH Keywords

algorithmconvergence analysisstability analysisordinary differential equationsperiodic orbitreachability analysisset-valued integrationaffine set-parameterizationcubic oscillator system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) General methods in interval analysis (65G40) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Periodic orbits of vector fields and flows (37C27) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (6)

Towards rigorous robust optimal control via generalized high-order moment expansion ⋮ Sensitivity Analysis of Uncertain Dynamic Systems Using Set-Valued Integration ⋮ Global optimization in Hilbert space ⋮ Convergence-order analysis for differential-inequalities-based bounds and relaxations of the solutions of ODEs ⋮ A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains ⋮ Exploiting nonlinear invariants and path constraints to achieve tighter reachable set enclosures using differential inequalities

Uses Software

• SUNDIALS
• RODAS
• ACADO
• dcc

Cites Work

• SUNDIALS
• Convergence analysis of Taylor models and McCormick-Taylor models
• Improved relaxations for the parametric solutions of ODEs using differential inequalities
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• Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
• Global solution of optimization problems with parameter-embedded linear dynamic systems.
• Ellipsoidal calculus for estimation and control
• Computation and application of Taylor polynomials with interval remainder bounds
• Validated solutions of initial value problems for ordinary differential equations
• A rigorous global optimization algorithm for problems with ordinary differential equations
• Taylor forms -- use and limits.
• Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs
• Validated solutions of initial value problems for parametric ODEs
• Nonlinear convex and concave relaxations for the solutions of parametric ODEs
• ACADO toolkit-An open-source framework for automatic control and dynamic optimization
• The Art of Differentiating Computer Programs
• McCormick-Based Relaxations of Algorithms
• Introduction to Interval Analysis
• Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
• On Taylor Model Based Integration of ODEs
• Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations
• Set-theoretic methods in control
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