Solution of variational dynamic problems under parametric uncertainty

Abstract

The paper deals with a number of variational dynamic problems with parameters subject to unknown smooth drift in time. Solution schemes are considered using both the classical variational method and reduction of the original problem to a conditional nonholonomic adaptive optimal control problem. In the second case, a solution is found with the help of the dynamic programming method and a specially chosen adjustment algorithm for unknown parameters.

Variational Synthesis of Controlled Dynamic Mappings

“…The idea to reduce a dynamic system to an expanded Hamilton form with simultaneous attachment of the formalism of classical calculus of variation was realized before as well (see, for example, [6][7][8] and [20,21] for adaptive systems). It turned to be that such structures were able to work in the construction of controlled canonical mappings in Hamilton systems for the purpose of writing the equations of motion in a more comfortable form.…”

Variational Dynamic Problems with Parameters and Their Adaptive Interpretation

“…Hence, in particular, the multiplier λ is equal to the constraining force that must be applied at the point with mass m so that it may move according to the differential law mẍ = − ∂U/∂x. Finally, we may mention that differential relations in the form of equations of motion are widely used for studying different dynamic systems in control theory and variational calculus [7,[11][12][13].…”