Jing Zhang, University of Virginia
Min-max game theory problems for coupled systems of PDEs and associated non-standard Riccati equations
Abstract: We are going to discuss the min-max control problems defined for a large class of PDE models. A
distinct feature of the problems under consideration is the fact that control function (counteracting potential
disturbances in minimizing given objective) acts upon the system distributionally (not functionally). This
happens typically when a control has very small support such as bounded or point controls. Our goal is to
establish well-posedness of a non-standard Riccati equation, where the solution yields a feedback operator
deriving the optimal solution. Our work deals with non-smoothing dynamics as they arise in hyperbolic-like
problems. We shall show that under the assumption of ``singular" estimate imposed on the dynamics (A,
B), (A the generator, B the control).
|eAtB| <
1 /tα , 0 <α< 1.
Well-posedness of Riccati equation is guaranteed and the solution for min-max problem can be derivated by
solving Riccati equation.
The assumption is motivated by a new class of controlled systems that is arising in hyperbolic-parabolic
interacting (coupled system) such as:
-structured acoustic model;
-fluid structure model;
-thermoelastic plate model.
Advisor: Dr. Irena Lasiecka (University of Virginia)