Pontryagin Equations for Non-Linear Dynamic Systems with Random Structure

Using the theory of dynamic systems with random structure the representation of nonstationary continuous time, generally non-Gaussian, processes with distinguishable states is considered. Switching of the partial subsystems is intended to be a Poisson point process and so the model has the Markov property and the generating system itself is described by a set of stochastic nonlinear differential equations. The Pontryagin equations, for this case, are developed. It is demonstrated that influence of the process of the changing structure, for Pontryagin equations, has the same character as for generalized Fokker-Plank-Kolmogorov equations