Kernel Controllers: A Systems-Theoretic Approach for Data-Driven Modeling and Control of Spatiotemporally Evolving Processes

摘要

We consider the problem of modeling, estimating, and controlling the latentstate of a spatiotemporally evolving continuous function using very few sensormeasurements and actuator locations. Our solution to the problem consists oftwo parts: a predictive model of functional evolution, and feedback basedestimator and controllers that can robustly recover the state of the model anddrive it to a desired function. We show that layering a dynamical systems priorover temporal evolution of weights of a kernel model is a valid approach tospatiotemporal modeling that leads to systems theoretic, control-usable,predictive models. We provide sufficient conditions on the number of sensorsand actuators required to guarantee observability and controllability. Theapproach is validated on a large real dataset, and in simulation for thecontrol of spatiotemporally evolving function.