Control Under Lack of Information (1995)

The mathematical theory of control, essentially developed during the last decades, is used for solving many problems of practical importance. The efficiency of its applications has increased in connection with the refine- ment of computer techniques and the corresponding mathematical soft- ware. Real-time control schemes that include computer-realized blocks are, for example, attracting ever more attention. The theory of control provides abstract models of controlled systems and the processes realized in them. This theory investigates these models, proposes methods for solv- ing the corresponding problems and indicates ways to construct control algorithms and the methods of their computer realization. The usual scheme of control is the following: There is an object F whose state at every time instant t is described by a phase variable x. The object is subjected to a control action u. This action is generated by a control device U. The object is also affected by a disturbance v generated by the environment. The information on the state of the system is supplied to the generator U by the informational variable y. The mathematical character of the variables x, u, v and yare determined by the nature of the system.