Abstract
This article contains information about causality – one of the fundamental properties of input-output of dynamic systems, in particular, objects and automatic control systems. This property belongs to the same group as the fundamental properties of control systems, that and controllability, reachability, observability, recoverability. This article includes a classification of dynamic systems by types of causality, a mathematically rigorous definition of "the index of causality", which was proposed by the author before, as well as a description of the method of calculation of indexes of causality for input-output nonlinear multidimensional input and/or output dynamic systems and the algorithm of its realization. This method is based on the using of matrices of the adjacency and the reachability of systems. The author has put into this article the concept of conditional index causality ". Such indexes should be applied in cases where a mathematical model of non-linear dynamic systems in the form of "input-state-output" include the multiplicative components on the elements of the vector of state and/or the output of systems. Indexes of the causality of dynamic systems enable you to define the structure of input-output (internal) connection in these systems. They can be used effectively in meeting the challenges of identification of objects with multidimensional inputs and outputs, as well as in the task autonomization control outputs in those objects. Indexes of causality determine also functional reproducibility of systems, i.e. the class of functions that can be implemented on their output under specified sets of initial conditions and the possible control.
Keywords: multidimensional on input and output system, nonlinear dynamic system, automatic control system, fundamental properties of input-output systems, causality, causality types, indexes of causality, conditional and unconditional indexes of causality, definition and calculating causality indexes , algorithm, scalar and multiplicative vector-functions, digraph of system, matrixes of adjacency and reachability
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