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

TL;DR

This paper introduces a systems-theoretic framework for modeling, estimating, and controlling spatiotemporal processes using minimal sensors and actuators, leveraging kernel-based models with proven observability and controllability.

Contribution

It proposes a novel layered kernel control approach that integrates dynamical systems priors with functional evolution for data-driven control of spatiotemporal processes.

Findings

Validates the approach on real and simulated datasets.

Provides conditions for sensor and actuator placement.

Demonstrates effective control of evolving functions.

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.