Differential-geometric and group-theoretical methods in optimal control theory

DOI10.1007/BF02105209zbMath0558.93057OpenAlexW1985484962WikidataQ115392770 ScholiaQ115392770MaRDI QIDQ802515

R. V. Gamkrelidze, S. A. Vakhrameev, Andrei A. Agrachev

Publication date: 1985

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02105209

zbMATH Keywords

surveycontrollabilityaffine systemperturbed systemlinear connectionsystems on Lie groupslocal controllabilitychronological calculus

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Controllability (93B05) Nonlinear systems in control theory (93C10) Asymptotic stability in control theory (93D20) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) General properties and structure of real Lie groups (22E15) Attainable sets, reachability (93B03) Control/observation systems governed by ordinary differential equations (93C15) Connections (general theory) (53C05) Controllability of vector fields on (C^infty) and real-analytic manifolds (57R27) Model systems in control theory (93C99)

Cites Work

• Control systems subordinated to a group action: Accessibility
• The region of attainability of nonlinear systems with unbounded controls
• Control systems on semi-simple Lie groups and their homogeneous spaces
• Chronological algebras and nonstationary vector fields
• Bounds on the number of switchings for trajectories of piecewise analytic vector fields
• Minimal realizations and canonical forms for bilinear systems
• A generalization of the closed subgroup theorem to quotients of arbitrary manifolds
• Volterra series and geometric control theory
• Some properties of vector field systems that are not altered by small perturbations
• Geometric methods for nonlinear optimal control problems
• Local approximation of control systems
• Local controllability and sufficient conditions in singular problems
• Control systems on Lie groups
• Invertibility of Nonlinear Control Systems
• Single-input observability of continuous-time systems
• A Bang-Bang Theorem with Bounds on the Number of Switchings
• Realizations of nonlinear systems and abstract transitive Lie algebras
• Global controllability of nonlinear systems in two dimensions
• Existence and Uniqueness of Realizations of Nonlinear Systems
• Nonlinear Complementarity Problems in a Function Space
• On the Existence of Observable Single-Output Systems of a Simple Type
• Controlled invariance for affine control systems
• The geometry of homogeneous polynomial dynamical systems
• Generic Observability of Differentiable Systems
• Controllability and observability for affine nonlinear Hamiltonian systems
• On Local Controllability
• The unobservability ideal for nonlinear systems
• On quotients of manifolds: A generalization of the closed subgroup theorem
• An Extension of a Theorem of Nagano on Transitive Lie Algebras
• Bilinear and Nonlinear Realizations of Input-Output Maps
• On Controllability by Means of Two Vector Fields
• On the structure of irreducible state representations of a causal system
• Existence and uniqueness of minimal realizations of nonlinear systems
• Controllability of general nonlinear systems
• Carathe´odory Controllability Criterion for Nonlinear Dynamical Systems
• Nonlinear controllability and observability
• On the Observability of Polynomial Systems, I: Finite-Time Problems
• Structure Métrique des Orbites de Familles Symétriques de Champs de Vecteurs et Théorie du Temps Minimum
• Controllability of Nonlinear Systems on Compact Manifolds
• Orbits of Families of Vector Fields and Integrability of Distributions
• On The Nonlinear Control Problem with Control Appearing Linearly
• Contrôlabilité des Systèmes non Linéaires
• Title: Solution in large of control problem $\dot x=(A(1-u)+Bu)x$
• Nonlinear Controllability via Lie Theory
• System Theory on Group Manifolds and Coset Spaces
• Certain Controllability Properties of Analytic Control Systems
• The “Bang-Bang” Problem for Certain Control Systems in $GL(n,R)$
• A generic property of couples of vector fields
• A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control Problems
• The control problem $\dot x=A(u)x$
• Orbits of families of vector fields and integrability of systems with singularities
• On Local and Global Controllability
• Abstract Control Systems: Controllability and Observability
• On the Number of Directions Needed to Achieve Controllability
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item