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Optimization by the generalized work functional using the Bellman quasilinearization method is shown to yield the well-known result due to A.A. Krasovskii.For the nonlinear dynamic system described by the vector equatioṅthe control that is optimal by the Krasovskii generalized work functionalwhere the function V (x, t) is the solution of the linear partial differential equationIn [2], the control that is optimal by the Krasovskii functional (2) and the control that is optimal by the Bolza functional (3) obtained in an example are compared and the former is found to be an approximation of the latter.Since the first iteration of the Bellman quasilinearization method under the Bolza criterion (3) coincides with the solution of optimization by the generalized work functional (2), the authors of [3] assert that there is a direct relationship between these two methods.According to [4], the solutions of minimization by criteria (2) and (3) are exact. As is known [1], minimization by the generalized work functional (2) is equivalent to minimization by the Bolza functional (3) under an additional isoperimetric condition

Control of trajectory for flying round an obstacle is determined through optimization by the generalized work and a hierarchy of criteria. The methods of analytical mechanics are applied to form real-time controls under given constraints.

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A large-sized transformable space-based reflector has been reviewed. Features of this design are compactness in transportation, a large ratio of volumes in the opened and folded states, low mass with substantial dimensions. Given these properties, there are some problems with reliable deployment of this system, with maintaining and regulating the required form of the radio-reflective net fabric. In this paper we demonstrate the application of the mechanics of flexible thread to find the shape and force of the pull in the space-based cable-stayed reflectors. Equations showing the dependence of the form of the net fabric on the tension force in a single have been obtained. A particular problem is considered for finding the tension force at a given position of the net fabric. There have been obtained appropriate solutions for three points, two rigidly fixed and adjustable, located between them. This approach is applicable for determining the tension force in the case of using different materials and different initial conditions.