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Hermann, Robert

Geometric structure of systems-control theory and physics. Part B. (English) Zbl 0472.49002

Interdisciplinary Mathematics. Vo. XI. Brookline, Massachussettes: Math. Sci. Press. XVIII, 484 p. (1976).
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Cited in 1 Document

MSC:

49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
49J20 Existence theories for optimal control problems involving partial differential equations
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
49J15 Existence theories for optimal control problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
49K20 Optimality conditions for problems involving partial differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc.
58E25 Applications of variational problems to control theory
37C80 Symmetries, equivariant dynamical systems (MSC2010)

Keywords:

Caratheodory approach to optimal control variational problems; Pontrjagin minimal principle; Hamilton-Jacobi theory; characteristic curves; first and second variation formulas for optimal control problems; Weierstrass condition; optimal-control distributed-parameter and field-theoretic variational problem; circuit theory; equations of motion; Abelian groups of Lagrangian symmetries; cyclic coordinates; analytical and quantum mechanics; quantization conditions; canonical transformations; invariant integrals; continuum mechanics; optimization and programming of functions on manifolds; Pareto optimals and extremals

Citations:

Zbl 0322.93001
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