Real-time optimal distributed estimation and control of spatiotemporal processes using multi-domain methods and optimally-guided mobile sensors
Abstract
The goal of this project is to develop an advanced theoretical and computational approach that enables the real-time estimation of spatiotemporal processes modelled by partial differential equations (PDEs) using mobile sensors. Under the proposed approach, the spatial domain of interest is decomposed into an inner domain surrounding the mobile sensor and an outer domain. The theoretical framework includes an optimal Kalman filter for the inner domain, a simplified naïve observer for the outer domain, and time-varying transmission conditions due to the mobile sensors. This domain decomposition approach results in a hybrid estimator and reduces the computational cost needed for real-time implementation of a Kalman filter by restricting the solution of the differential Riccati equation to the inner domain. The hybrid estimator kernel in the inner domain is developed so that its support vanishes in the outer domain. Such a constraint ensures that no residual innovation terms appear in the outer domain filter thereby acting as an exogenous input. The proposed approach ensures that the optimality of the domain decomposition filter matches that of the Kalman filter designed for a single domain. In the proposed approach, the mobile sensors provide point measurements of the spatiotemporal field and are guided to optimal locations of the domain to minimize the estimation error. The proposed hybrid estimator is implemented numerically with a parallelized, non-overlapping, domain-decomposition method using structured and uniform grids. The hybrid estimator is discretized in space with a finite-volume total variation diminishing method. The transmission conditions are implemented on the interfaces between adjacent subdomains for data communication. The time integration of the resulting semi-discrete equations is performed using a multi-step Runge-Kutta scheme with sub-cycling for the mobile sensor motion.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 14, 2024
- Source ID
- FA95502310756
Entities
People
- Michael Demetriou
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- Worcester Polytechnic Institute