Optimal Actuator Location in Semi-linear PDEs
Finding the best actuator location to control a distributed parameter system can improve performance and significantly reduce the cost of the control. The existence of an optimal actuator location has been established for linear partial differential equations (PDEs) with various cost functions.
Nonlinearities can have a significant effect on dynamics, and such systems cannot be accurately modeled by linear models. Hence, a controller design and actuator location strategy should take nonlinear behavior into consideration.
In this talk, we consider the theory for a semi-linear system on a reflexive Banach space.The control operator depends on a parameter r that takes values in a some set K. The parameter r typically has interpretation as possible actuator designs. The simplest case is actuator location, but the theory also applies to optimization of the shape.There are few theoretical studies on concurrent optimal actuator and controller design in nonlinear systems.
The research also extends previous work on optimal control of nonlinear PDEs in that the linear part of the partial differential equation is not constrained to be the generator of an analytic semigroup. It is shown that the problem has an optimal control and actuator design. Under additional assumptions, optimality equations explicitly characterizing the optimal control and actuator are obtained.
The results are applied to optimal actuator and controller design in a railway track model as well as semi-linear wave models.