Optimal Control of One-Dimensional Partial Differential Equations on Graphs

Abstract

In this chapter we continue the discussion of domain decomposition of optimal control problem for partial differential equations started in Chapter 4. However, here we focus on partial differential equations on graphs and, more precisely, on elliptic and hyperbolic equations. We first discuss elliptic optimal control problems on graphs. The global problem is defined and domain decomposition procedures are formulated in the cases of both distributed and boundary controls. Next we consider optimal control problems for hyperbolic systems, in which final value control is emphasized. Higher-dimensional analogs of the methods and results obtained here are discussed in Chapters 6 to 9.