Optimization of an integrated actuator placement and robust control scheme for distributed parameter processes subject to worst-case spatial disturbance distribution

In many works, the location and placement of actuating devices in systems governed by distributed parameter systems is primarily based on either controllability or performance based criteria. Locations that yield enhanced controllability, i.e., rendering systems "more controllable" or enhance a performance-based criterion (usually LQR-type) are considered optimal. The control signal is subsequently calculated using an optimal or robust functional based on those actuator choices. While the resulting control with this "optimal" location provides improved performance, it nonetheless ignores the spatial variation of the disturbance distribution function. A way to enhance control robustness is to place the actuators in locations that provide optimality with respect to worst-case spatial distributions of disturbances. Once this is achieved, a robust controller may then be designed accounting for a worst-case temporal disturbance function. This idea is implemented in a class of parabolic distributed parameter systems where it is observed that locations that might yield an optimal location using solely performance measures might produce poor robustness with respect to spatiotemporal disturbances. Computational issues regarding the robustness measure for placing actuators subject to a "worst-case" disturbance are examined and a numerical example is presented to support the theoretical findings of this work.