Practical control optimization schemes based on the extension principle

A general approach to solve problems approximately via the extension principle and its realization schemes are described. The main attention is paid to nontraditional schemes of transformation of models via the extension principle with regard for the specifics of applied optimal control problems, viz., convexation of sets of velocities of nonlinear systems for enhancing the effectiveness of iterative control refinement procedures, reduction of the order of a system through elimination of passive relations in degenerate problems, construction of a ranked family of models, and sequential approximation procedures. The approach in general is a good base for realizing approximation schemes with accuracy estimates.