Let ug the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between μug1 + (1 − μ)ug2 and uμg1+(1−μ)g2 for μ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated...

The stabilization of the transverse vibration of an axially moving string is implemented using time-varying control of either the boundary transverse motion or the external boundary forces. The total mechanical energy of the translating string is a Lyapunov functional and boundary control laws are designed to dissipate the total vibration energy of the string at the left and/or right boundary. ...

Linear and nonlinear optimal control have been investigated in transitional channel and boundary layer flows. The flow phenomena that we study are governed by the incompressible Navier–Stokes equations and the main aim with the control is to prevent transition from laminar to turbulent flows. A linear model-based feedback control approach, that minimizes an objective function which measures the...

We consider the tracking problem for parabolic systems with boundary control. Assuming that the reference signal is bounded and measurable, we prove various regularity results as well representation formulas for the optimal control and the optimal trajectory.

In this paper, we investigate optimal control problems for Allen–Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace– Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribe...

We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the u...

In this paper, we rst study an optimal boundary control problem governed by the Stokes system with point pressure observations on the boundary. A constrained LQR approach with some hydrostatic potential theory, boundary integral equations and a variational inequality in a Banach space setting is applied to establish a state feedback characterization of the optimal control. Since a hyper-singula...