5 research outputs found
Optimality conditions for differential system of Petrowsky type with infinite number of variables and boundary control
AbstractIn this paper, we study the optimal control problem for an n×n coupled Petrowsky type system involving a 2ℓ-th order self-adjoint elliptic operator with an infinite number of variables and constrained boundary control acting through Neumann conditions. Also, we derived the necessary and sufficient conditions of optimality for two types of performance index (quadratic one, general integral form).By using standard Lions’s arguments [J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, vol. 170, Springer-Verlag, 1971] we proved the existence of a solution to the n×n coupled Petrowsky system and we derived optimality conditions for the optimal control problem with a quadratic performance index. In the case of the general integral form of the performance index we applied Dubovitskii–Milyutin’s formalism earlier used in Kotarski [W. Kotarski, Some problems of optimal and pareto optimal control for distributed parameter systems, Reports of Silesian University Katowice, Poland, 1997, no. 1668]. Finally, we provided some special cases
Optimal control of a system governed by Petrowsky type equation with an infinite number of variables
Indirect stabilization of weakly coupled systems with hybrid boundary conditions
We investigate stability properties of indirectly damped systems of evolution
equations in Hilbert spaces, under new compatibility assumptions. We prove
polynomial decay for the energy of solutions and optimize our results by
interpolation techniques, obtaining a full range of power-like decay rates. In
particular, we give explicit estimates with respect to the initial data. We
discuss several applications to hyperbolic systems with {\em hybrid} boundary
conditions, including the coupling of two wave equations subject to Dirichlet
and Robin type boundary conditions, respectively
Reports to the President
A compilation of annual reports for the 1999-2000 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans