In past decades, the optimal control of distributed parameter system had been received much more attention in academic field. A wide spectrum of problems in applications can be solved by methods of optimal control, such as chemical engineering and vehicle dynamics. Modern optimal control theories and applied models are not only represented by ODE, but also by PDE, especially nonlinear parabolic...

Both of feedback stabilization and optimal control problems are analyzed for a parabolic partial differential equation with Neumann boundary control. This PDE serves as a model of heat exchangers in a conducting rod. First, we explicitly construct an output-feedback operator which exponentially stabilizes the abstract control system representing the model. Second, we derive a controller which, ...

In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of no...

We present a spatial domain decomposition (DD) method for the solution of discretized parabolic linear–quadratic optimal control problems. Our DD preconditioners are extensions of Neumann-Neumann DD methods, which have been successfully applied to the solution of single elliptic partial differential equations and of linear–quadratic optimal control problems governed by elliptic equations. We us...

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes ...

This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...

Pontryagin's principle is used to study the shape of the supersonic part of the nozzle of a carbon dioxide gas-dynamic laser whose gain is maximal. The exact shape is obtained for the uncoupled approximation of Anderson's bimodal model. In this case, if sharp corners are allowed, the ceiling of the supersonic part consists of a slant rectangular sheet followed by a horizontal one; otherwise...

We review an emerging application field to parabolic partial differential equations (PDEs), that’s economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic application of the maximum principle to the latter leads to single out a serious illpo...