On external and internal approximations for reachability sets of bilinear systems

DOI10.1134/S1064562414060052zbMath1304.93026MaRDI QIDQ2254130

V. V. Sinyakov

Publication date: 4 February 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hamilton-Jacobi-Bellman equationbilinear systemsexact reachability setexternal and internal approximationsgeometric constraints on the controlshape matrices of ellipsoids

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Nonlinear systems in control theory (93C10) Geometric methods (93B27) Attainable sets, reachability (93B03) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (1)

Partial differential equation for evolution of star-shaped reachability domains of differential inclusions

Cites Work

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• Optimization and control of bilinear systems. Theory, algorithms, and applications
• Ellipsoidal calculus for estimation and control
• A differential equation for the gauge function of the star-shaped attainability set of a differential inclusion
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• On Ellipsoidal Techniques for Reachability Analysis. Part II: Internal Approximations Box-valued Constraints
• Euclidean Algorithm and Hankel Matrices
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
• Dynamic optimization for reachability problems.

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