Actuator switching for vibration control of spatially distributed systems

In this paper we define a switching strategy for hybrid systems where both the actuating devices and the corresponding control signals are changing at the onset of a given time interval. This actuator-plus-controller switching is dictated by the need to address spatiotemporally varying disturbances in spatially distributed systems. Stability measures utilizing Lyapunov functions are employed to define the switching strategy at each time interval. To introduce a certain level of optimality, these Lyapunov functions are chosen as the optimal values of associated linear quadratic regulator functionals. To avoid the computational burden associated with an optimal strategy for a finite horizon quadratic functional, a suboptimal quadratic index is considered instead which takes the form of a cost-to-go of an infinite horizon index with a changing lower limit. This immediately imposes the solution to algebraic as opposed to differential Riccati equations. Due to this suboptimal measures, the proposed policy is applicable to linear systems with spatiotemporally varying disturbances. To validate the proposed switching policy, a flexible structure with multiple piezoceramic patches as actuators is considered. The objective then becomes that of suppressing the plate vibration that is subjected to spatiotemporally varying disturbances. Extensive simulation studies are performed to exhibit the viability of using actuator-plus-controller switching to minimize the effects of spatiotemporally varying disturbances.