Projection-operator optimization of controls of dynamic objects

The principles of application of projection-operator methods of mathematical programming for calculating optimal controls based on "immersion of control problems" in problems of finite-dimensional mathematical programming are formulated. The results obtained illustrate the technique of qualitative study of the stability of systems with optimizing feedback based on the contraction mapping principle of functional analysis. The considered technique allows one to synthesize locally optimal systems with nonlinear control objects. In this case, nonlinear models of objects are taken into account in the right-hand sides of linear manifolds, and the projection operator forms nonlinear optimal controls with feedback taking into account the operators of nonlinearities of the object.