ИСТИНА

Optimal control theory is a modern extension of the classical calculus of variations. Converting a calculus of variation problems into an optimal control problem requires one more conceptual extension—the addition of control variables to state equations. While the main result of the calculus of variations was the Euler equation, the Pontryagin maximum principle is main result of optimal control theory. The maximum principle was developed by a group of Russian mathematicians in the 1950s. This principle gives the necessary conditions for optimality in a wide range of dynamic optimization problems. The maximum principle includes all the necessary conditions from classical theory of calculus of variations but can be applied to a significantly wider range of problems. At present, for deterministic control models described by ordinary differential equations, the Pontryagin maximum principle is used as often as Bellman’s dynamic programming method. The optimal control problem includes the calculation of the optimal control and the synthesis of the optimal control system. Optimal control, as a rule, is calculated by numerical methods for finding the extremum of an objective function or by solving a two-point boundary value problem for a system of differential equations. The synthesis of optimal control from a mathematical point of view is a nonlinear programming problem in function spaces. This Special Issue will gather research regarding research focused on the development of novel analytical and numerical methods for solutions of optimal control or of dynamic optimization problems, including changing and incomplete information about the investigated objects, application to medicine, infectious diseases, and economic or physical phenomena. Investigations of new classes of optimization problems, optimal control of nonlinear systems, as well as the task of reconstructing input signals are invited. For example, we are interested in papers that develop new algorithms to implement some of the principles of regularization using constructive iterative procedures or in papers that create an optimal control model that can accumulate experience and improve its work on this basis or the so-called learning optimal control system. The applied papers focused on control models of economic, physical, medical (i.e., infectious diseases) or environmental processes or resource allocation on the specified time interval or on the infinite planning horizon would be of special interest. We will be happy to consider original research papers on new advances of optimal control and differential games; deterministic and stochastic control processes; combined methods of synthesis of both deterministic and stochastic systems with full information about parameters, state and perturbations; i.e., all papers that allow the use of analytical methods to study the various tasks of optimal control and its evaluation, as well as applications of optimal controls and differential games to describe complex nonlinear phenomena.