Evolution and prospects of approximate methods of optimal control

The article gives a brief overview of approximate methods of optimal control and the ideas underlying them. Material is presented in terms of optimization and improvement control problems in the standard form for discrete and continuous control systems. The first and second orders methods and the improvement of complex processes are considered. The algorithms based on a study of reachable sets and multidimensional approximations are described. An extensive bibliography containing the main obtains theoretical and applied results, that enables developers of new methods to assess the state of arts in this area. Possible directions of further development of approximate methods of optimal control in accordance with progress in the field of high-performance computing are indicated.