The practical applicability of optimal solutions of control problems substantially depends upon the availability of feedback control schemes to compensate for unavoidable disturbances. Three numerical methods of treating these schemes are presented and discussed in this paper. They can be applied to a rather general class of optimal control problems (for example, problems with inequality constr...

In the present paper we complement the work in [2] with presenting the analytical framework for general optimal boundary control problems of the Boussinesq approximation. We prove existence of optimal controls, use results of [6] to prove existence and uniqueness of solutions to state and the adjoint system, and derive first order necessary as well as second order sufficient optimality conditions.

This paper considers the optimal control and optimal estimation problems for a class of linear parabolic diffusion-reaction partial differential equations (PDEs) with actuators and sensors at the boundaries. Diffusion-reaction PDEs with boundary actuation and sensing arise in a multitude of relevant physical systems (e.g. magneto-hydrodynamic flows, chemical reactors, and electrochemical conver...

This paper deals with boundary optimal control problem for coupled parabolic PDEODE systems. The problem is studied using infinite-dimensional state space representation of the coupled PDE-ODE system. Linearization of the non-linear system is established around a steady state profile. Using some state transformations, the linearized system is formulated as a well-posed infinite-dimensional syst...

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R. Piecewise linear finite elements are used to approximate the control as well as the state...

This paper studies the finite-horizon H∞-optimal control problem for linear hyperbolic systems when only time-sampled values of the state are available, with control acting on the boundary. The problem is formulated in a differential game framework by associating a zero-sum differential game with the original disturbance attenuation problem. The minimizing player’s minimax strategy in this game...

We study problems of boundary controllability with minimal L p-norm (p ∈ [2, ∞]) for the one-dimensional wave equation, where the state is controlled at both boundaries through Dirichlet or Neumann conditions. The problem is to reach a given terminal state and velocity in a given finite time, while minimizing the L p-norm of the controls. We give necessary and sufficient conditions for the solv...

We consider a free boundary problem modeling growth and dissolution of a crystal in radial geometry with time-dependent data at the outer boundary. Well-posedness is shown rst for in H 1 but then, motivated by an opimal control problem, for in L 2 .

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control fo...

The optimal control of infinitesimal flow disturbances experiencing the largest transient gain over a fixed time span, commonly termed “optimal perturbations,” is undertaken using a variational technique in twoand three-dimensional boundary layer flows. The cost function employed includes various energy metrics which can be weighted according to their perceived importance, simplifying the task ...