Logical Approach to Control: Mathematical Basis and Applications

This paper presents a survey of some results which have been obtained in ISDCT in the field of development of some new methods for logical control of dynamical systems. Some fundamental difficulties of deduction problem were a barrier to the wide development and application of automated deduction in the loop of control. The main point of this paper is to show that automatic theorem proving technique can and should be used in intelligent control of complex systems. There are two basic reasons for that. The 1st reason is that the modern intelligent control systems lack the required intelligence yet. The 2nd one is determined by the merits of new logical tools which allow to overcome the obstacles of extensive application of the 1st and higher order logics in specific classes of on-line problems like control. Such logical instrument is described and discussed here with applications to moving objects.