Optimization of second order spatially distributed systems with multiple interconnected actuator/sensor pairs

This work considers the economic aspects in control implementation of second order spatially distributed systems. By opting to use multiple actuator/sensor pairs with limited capacity, instead of a single actuator/sensor pair with higher price and larger capacity, this work provides a first view into the economic, computational and communication aspects. Considering a large number of actuator/sensor pairs and the a priori defined controller architecture of static output feedback along with the collocation assumption of the actuators and sensors, the resulting closed-loop system is expressed in terms of a static output feedback gain matrix that defines the communication amongst the actuator/sensor pairs. The design problem is then to find the values of the static feedback gain matrix in order to optimize a performance measure. Using the energy of the second order infinite dimensional system as the performance measure, the resulting optimization is expressed in terms of the solution to a parameterized operator Lyapunov equation. Simulation studies of the wave PDE in one spatial dimension for different communication topologies, reveal the effects of communication on the performance of the closed loop system.