INFINITE HORIZON QUADRATIC COST PROBLEMS FOR BOUNDARY CONTROL PROBLEMS.
The authors present an abstract dynamical model and show that it covers not only second-order hyperbolic equations with both Dirichlet or Neumann boundary control, but also the Euler-Bernoulli type of equations, likewise with control action exercised on the boundary of the spatial domain (or part thereof). The emphasis on situations in which the space of maximal regularity of the solutions coincides with the space of exact controllability of them (in finite time). Thus, in the associated study of quadratic cost problems over an infinite horizon, if penalization is introduced for the solution on the corresponding space of maximal regularity (the natural space) then as a consequence of the exact controllability property being fulfilled, it is obtained a fortiori that the finite cost condition is automatically satisfied for all these dynamics. Hence, previously published abstract results on the algebraic Riccati equations and resulting stabilizing feedback controls in terms of Riccati operators are applicable and provide uniform stabilization results on the natural state space of the corresponding boundary feedback systems.
Proceedings of the IEEE Conference on Decision and Control
Lasiecka, I., & Triggiani, R. (1987). INFINITE HORIZON QUADRATIC COST PROBLEMS FOR BOUNDARY CONTROL PROBLEMS.. Proceedings of the IEEE Conference on Decision and Control, 1005-1010. https://doi.org/10.1109/cdc.1987.272548