Explicitly solvable non-linear optimal control problems

DOI10.1080/00207178808906344zbMath0635.93039OpenAlexW2083550960MaRDI QIDQ3775420

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Publication date: 1988

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207178808906344

zbMATH Keywords

collective HamiltoniansLie-Berezin-Kirillov symplectic structuresoptimal control problems on differentiable manifolds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear systems in control theory (93C10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Control/observation systems governed by ordinary differential equations (93C15) Manifolds and measure-geometric topics (49Q99)

Related Items (8)

Geometrical and topological methods in optimal control theory ⋮ Geometric approach to non-linear optimal control problems ⋮ Lie algebraic aspects of the finite nonperiodic Toda flows ⋮ On the geometry of Riemannian cubic polynomials. ⋮ Isoholonomic problems and some applications ⋮ The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces ⋮ Optimal control and geodesic flows ⋮ The role of systems biology, neuroscience, and thermodynamics in network control and learning

Cites Work

• Completely integrable systems, Euclidean Lie algebras, and curves
• Geometric methods for nonlinear optimal control problems
• On the optimal control of bilinear systems and its relation to Lie algebras
• Lie Theory and Control Systems Defined on Spheres
• Algebraic Riccati equation and symplectic algebra
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