Research Communication | Open Access
Volume 2021 | Communication ID 184
Volume 2021 | Communication ID 184
| Bilinear Boundary Control Problem of Hyperbolic Systems |
Abdelhak Bouhamed, Hassane Bouzahir
Received |
Accepted |
Published |
January 30, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: This work presents an optimal control problem of hyperbolic systems with bilinear boundary control. The functional cost is taken as the combination of the energy and the difference between the solution of the hyperbolic system at final time, and a desired state on L^2 norm. For a closed convex set, we prove existence of an optimal control that minimizes the functional cost using priori estimates. Then, using the differentiability of the cost functional with respect of the control, we establish the characterization by deriving necessary conditions that an optimal control must satisfy.