Some Principal Features of
"Unified Geometric Theory of Control (UGTC)" or
"Theory of Control Structures (TCS)"
A.G.Butkovskiy
It is considered the main features of Unified Geometrical Theory of Control (UGTC) or Theory of Control Structures (TCS). It is given the exact mathematical definitions for system, control system, control (itself as a connection in fibre space conserving given structure); multidimensional differential control systems described differential m-forms, eigen-optimal control (as a some metric structure), necessary and sufficient conditions for eigen-optimal control in terms closed and exact differential m-forms and in terms of energy-momentum tensor of given control system. Also it is considered the deep similarity between controls and gauge (calibration) fields which described the forces in physics. Formulation of "multidimensional triangle inequality" as a "Multidimentional Optimality Principle" generalizing 1-Dimentional Bellman's Optimality Principle are given.
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