Optimal Actuator Design for Nonlinear Partial Differential Equations

Abstract For systems modeled by partial differential equations, the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator location is a special case of optimal design. For linear partial differential equations (PDEs), the existence of an optimal actuator location for a number of cost functions has been established. However, many dynamics are affected by nonlinearities and linearization of the PDE can neglect some important aspects of the model. This paper describes recent results establishing conditions for existence of optimal actuator design and control for important classes of nonlinear PDEs.