During a long period of time the important problem of the theory and practice of control systems still remains a problem of providing restrictions, imposed on movement of a dynamic system. The most known approaches of its solving are based on using L. S. Pantrjagin's principle of maximum [1] -[4] and a method of dynamic programming (a principle of optimality) of R.Bellman [5] -[8]. First of all in these approaches an optimum control is obtained which should provide optimality and set restrictions. However efficient control of system not necessarily is optimum, which allows speaking about some narrowness of the specified approaches. At the same time procedure of synthesis is complex enough and ineffective for a high dimension system. Other approaches are known - direct approaches to synthesis of control by restrictions on system motion. Methods of numerical synthesis [9] -[12], methods on the basis of use of Lyapunov's functions [13] -[16] and methods of an inverse problem of dynamics [17] -[19] can be related to them. Using of numerical approaches, despite of their practically unlimited applicability to the most various classes of dynamic systems, is connected with construction of effective approximating models, that itself is enough challenge. Besides the procedure of searching of required decisions frequently leads to non-standard extreme problems or to mixed algebraic inequalities which have no effective decision ways. Application of methods on the base of Lyapunov's functions is referred to a problem of formulating Lyapunov's functions and of solving the equations or Lyapunov's inequalities. The given problem most easily can be solved for linear systems and in more general cases with enough arbitrary restrictions its decision is referred to essential difficulties. Using of methods of inverse problem of dynamics is referred to serious difficulties too because of a problem of choice of desirable movement, which restrictions should be also carried out.
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