Optimal control of a system governed by an elliptic partial differential equation

Control Problems Governed by a Pseudo - Parabolic Partial Differential Equation

Let G be a bounded domain in R" and Q = G X (0, T). We consider the solution^«) of the pseudo-parabolic initial-value problem (1 + M(x))y,(u) + L(x)y(u) = u in L2(Q), y(-,0;u) = 0 in L2(G), to be the state corresponding to the control u. Here M(x) and L{x) are symmetric uniformly strongly elliptic second-order partial differential operators. The control problem is to find a control un in a fixe...

Optimal Control of Light Propagation Governed by Eikonal Equation within Inhomogeneous Media Using Computational Adjoint Approach

A mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎The method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎The problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

Domain Decomposition Methods with Coupled Transmission Conditions for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations

Optimal Control of Dynamical Systems Governed by Partial Differential Equations: A Perspective from Real-life Applications ⋆

This survey article summarizes some ideas of the two principle procedures for solving optimal control problems governed by partial differential (algebraic) equations: the indirect method or first-optimize-then-discretize approach based on first-order necessary conditions, and the direct method or first-discretize-then-optimize approach based on non-linear programming software. The focus of this...

Optimal Control of a Delay Partial Differential Equation

Differential equations are one of the most widespread mathematical tools used to describe physical phenomena. Ordinary differential equations (ODE’s) involve a single independent variable, and partial differential equations (PDE’s) are used when more than one independent variable is required. It is not surprising that models used to describe a physical process often involve time as an independe...