Method of Synthesis of Multi-mode Control under the Expected Uncertainty Using the Analysis of the Phase-Space Decomposition on the Basis of the Generalized Power Maximum Condition

摘要

The problem of control synthesis under uncertainty associated with observation noise is considered. In accordance with the separation method, it is assumed that the problems of state assessment and control synthesis are solved sequentially. An uncertain mathematical model of a controlled dynamic system is given up to an accuracy of the production rules, which, unlike the known solutions, are proposed to be found using the maximum condition of the generalized power function. This allows us to find the commuting hypersurface up to an accuracy of a function called the synthesizing function. For its construction the analysis of dynamic measures on the commuting hypersurface and approximation of the obtained solution taking into account the phase space decomposition are carried out. The uncertainty of the boundaries of the phase space decomposition into areas where there is a change of modes of the dynamic system operation is considered on the basis of fuzzy inference. The constructivity of the developed method is confirmed by mathematical modeling of the solution of the problem for control synthesis of nonlinear dynamic system.