Testing the covariant-tensor multivalent structure of a continuous control system using the SVD-expansion technology (Q2783619)

Consider a class of multidimensional dynamic systems described by the vector-tensor differential equation \(\dot x={\text{col}}(f_1(x(t), u(t)), \dots, f_n(x(t), u(t)))\), \(t_0 \leq t \leq t_1\). The problem consists in testing the covariant-tensor structure of the state equations of a continuous control system. It can be obtained by conducting a numerical diagnostic procedure to verify algorithmically the following two propositions: (a) there exists a certain differential equation such that its solution is of Carathéodory-type (C-solution), (b) the differential system realizing (a) is a unique one. A theorem that provides conditions for a solution to be a C-solution is proved, and the testing algorithm based on the theorem is presented using an SVD-expansion.