Optimal Control of Distributed Parameter System with Incomplete Information About the Initial Condition

摘要

In this paper we consider an optimal control problem for a system described by a linear partial differential equation of the parabolic type with Dirichlet's boundary condition. We impose some constraints on the control. The performance functional has the integral form. The control time T is fixed. The initial condition is not given by a known function but belongs to a certain set (incomplete information about the initial state). The problem formulated in this paper describes the process of optimal heating, of which we do not have exact information about the initial temperature on the heated object. We present an example in which the set of admissible controls and one of initial conditions are given by means of the norm constraints too. The application of the well-known projective gradient method in the Hilbert space allows us to obtain the numerical solution for our optimization problem. (Atomindex citation 14:780540)