Abstract
The study of optimal control problems for distributed parameter systems is intimately connected to the study of partial differential equations and/or integral equations involving two or more independent variables. This chapter discusses optimal control for distributed parameter systems, and reviews algorithms for obtaining numerical solutions. Some of the simplest kinds of equations occurring in initial value problems are the parabolic equations—the heat flow or diffusion equation, the hyperbolic equations (the wave equation), and some of the equations of elasticity (the beam equation or the plate equation). The time-differential operator P may be of order one, such as in the diffusion equation, or of order two as in the wave equation or the beam equation. In cases where P is of order higher than one, the problem can be reduced to an equivalent set of first order equations with respect to time by introducing new variables. The chapter also presents the development of Green's functions from solutions of the eigenvalue-eigenfunction problem.
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