Optimal Control for Switched Distributed Parameter Systems with Application to the Guidance of a Moving Actuator

The present study considers a hybrid controller scheme for the optimal switching of a moving (or scanning) actuator (MA) for a class of distributed parameter systems (DPS). The proposed hybrid controller switches both the location and control signal of the actuator at the beginning of a time interval and remains unchanged over the duration of the time-interval. As time progresses, the above policy is repeated over a sequence of “time windows”, thus generating an algorithmic procedure which results in the actuator/controller switching policy. Guiding the MA at certain a priori selected actuator positions at different timeintervals is made possible by solving a double optimization problem. The decision method for actuator switching utilizes a finite-horizon LQR optimal control policy and, using optimality criteria, the associated optimal control problem is solved backwards-in-time for several time subintervals. A numerical example with simulation results is presented. Copyright c ©2005 IFAC.