Optimal control and controller location for distributed parameter elastic systems

A class of systems governed by second order partial differential equations and driven by controllers located at points ri, i = 1,..., k, is considered. A cost functional quadratic in the time derivative of the state and the control is associated with the system. The optimal controller locations are defined as the ones which minimize the maximum of the cost over all possible initial states. An analytical solution to the associated Riccati equation is presented providing a convenient expression for determining the optimal locations.