Frequency domain methods for optimal sensor placement and scheduling of spatially distributed systems arising in environmental and meteorological applications

We consider the problem of sensor placement (both spatial location and number) for a class of parameter-dependent diffusion-advection processes that model environmental processes. To distinguish between advection and diffusion dominated environmental processes, the Péclet number, Pe, which takes values over a set of a priori defined values, is utilized to optimize the number and spatial location of the sensors required. The minimum number of sensors is defined using system theoretic measures and essentially considers the smallest number of sensors that would render the system observable, thereby facilitating the design of a state observer. The optimization metric is defined with respect to the spatial H₂ norm of the dominant system modes, which may differ for different values of Pe. For each value of Pe, a set of optimal sensor locations and number is found and the associated state estimator is designed. The supervisory scheme then schedules the sensors corresponding to the Péclet number that describes the process at a given time by pouting in sleep mode all sensors associated with a different value of Pe and activating the sensors that are optimal for the current value of Pe. At the same time, the state estimator also switches by using the filter gain corresponding to the current value of the Péclet number and the active sensors. Extensive simulation studies are included to provide further inside on parameter-dependent sensor and observer scheduling for environmental processes.