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abstract: 'We consider the problem of modeling, estimating, and controlling the latent state of a spatiotemporally evolving continuous function using very few sensor measurements and actuator locations. Our solution to the problem consists of two parts: a predictive model of functional evolution, and feedback based estimator and controllers that can robustly recover the state of the model and drive it to a desired function. We show that layering a dynamical systems prior over temporal evolution of weights of a kernel model is a valid approach to spatiotemporal modeling that leads to systems theoretic, control-usable, predictive models. We provide sufficient conditions on the number of sensors and actuators required to guarantee observability and controllability. The approach is validated on a large real dataset, and in simulation for the control of spatiotemporally evolving function.'
author:
- 'Hassan A. Kingravi, Harshal Maske and Girish Chowdhary [^1]'
title: ' Kernel Controllers: A Systems-Theoretic Approach for Data-Driven Modeling and Control of Spatiotemporally Evolving Processes '
---

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Introduction {#sec:intro}
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Modeling, control, and estimation of spatiotemporally varying systems is a challenging area in controls research. These systems are characterized by dynamic evolution in both the spatial and temporal variables. Some examples of relevant problems 