Differential Riccati equation for the active control of a problem in structural acoustics
In this paper, we provide results concerning the optimal feedback control of a system of partial differential equations which arises within the context of modeling a particular fluid/structure interaction seen in structural acoustics, this application being the primary motivation for our work. This system consists of two coupled PDEs exhibiting hyperbolic and parabolic characteristics, respectively, with the control action being modeled by a highly unbounded operator. We rigorously justify an optimal control theory for this class of problems and further characterize the optimal control through a suitable Riccati equation. This is achieved in part by exploiting recent techniques in the area of optimization of analytic systems with unbounded inputs, along with a local microanalysis of the hyperbolic part of the dynamics, an analysis which considers the propagation of singularities and optimal trace behavior of the solutions.
Journal of Optimization Theory and Applications
Avalos, G., & Lasiecka, I. (1996). Differential Riccati equation for the active control of a problem in structural acoustics. Journal of Optimization Theory and Applications, 91 (3), 695-728. https://doi.org/10.1007/BF02190128