On the control by H-processes

The paper considers the control problem of discrete-continuous processes with a “tubular” structure in the space of input-output variables. The similar processes occur in spaces of the fractional dimension. The modeling and control by this class of processes differ very much from the conventional parametric models that are surfaces in the same space. It is necessary to apply the appropriate non-parametric indicators for the development of the learning parametric models of the “tubular” processes. The multidimensional H-process includes both controlled and uncontrolled vector variables; the uncontrollable input variables are supervised while the operation of the multidimensional system. The defining impact is also a vector. It is necessary to coordinate the vector components of the defined controls but not to define them randomly as it is applied in practice of the automated control theory. As a result the necessity for synthesis a -controller but not a -controller arises. Firstly, it is necessary to allocate a certain intersection area of all H-processes for each component of the output variable the corresponding indicator which is applied for. As a result, we get some subarea of coordination in the space of input-output variables. Only from this subarea one can determine the defining impact for each component of the output of the multidimensional system. The following stage is the calculation of the defining impacts with a fixed vector value of the input uncontrolled variables. We analyze the case when the defining impacts for the component of the output variables are not possible in a particular situation to agree absolutely or partially. Algorithms of component definitions of a vector of the setting influences are given. Also nonparametric control algorithms for the multidimensional H-processes are given. As a result such a control unit can be referred to a matrix control systems. Thus, the latter is implemented as the algorithm for determining the defining impacts and a control algorithm by the object. It is a -controller (a control system) for the multivariate H-process. Of course there might be cases when H-processes according to all components of the output are disjoint. In such a situation it is necessary to search for the acceptable compromise to bring the state of the controlled process to the desired one.