On impulsive control of nonlinear dynamical systems based on the Volterra series

This paper presents the theoretical studies of behavioral modeling and control of nonlinear dynamical processes. The impulsive control problem is formulated in terms of generalized solutions of one class of polynomial integral equations of the first kind. Such equations naturally appear in the nonlinear systems theory to control the behaviour of nonlinear dynamical processes based on the Volterra models. The existence theorem is formulated for this class of equations and the method of construction of generalized solutions as sum of the Dirac delta functions and regular continuos functions is proposed. It is demonstrated that the number of solutions is equal to the number of roots of the certain polynomial. Some remarks on construction of classic continuos solutions to control problem are presented.