Control of distributed systems with generalized input

The paper is concerned with the representation of the solutions of systems with distributed parameters under impulse control inputs. The use of generalized (impulse) inputs requires the study of generalized (discontinuous) solutions and extension of the concept of the solution. The concept of the generalized solution for a system with distributed parameters is introduced and the optimal control in the class of generalized solutions is investigated. The method of discontinuous time substitution is shown to be helpful in reducing the initial problem with unbounded controls to the classical problem and in formulating a theorem on the existence of a solution under different types of constraints.