On certain approaches to optimization of control processes. I

We consider a general approach to approximate studies of optimal control problems on the abstract level with various representations and transformations of the object model, extension principles, localizations, sufficient optimality conditions, and on the qualitative level, the search for an approximate globally optimal control. Here we use and develop transformation methods for degenerate problems that are characteristic for applications in various domains. The resulting solution can serve as an initial approximation in subsequent iterative optimization procedures whose construction methods and properties are considered in the second part of the paper.