Remote Ph.D. Dissertation Defense: Sheng Cheng
Thursday, May 13, 2021
Zoom link: https://umd.zoom.us/j/2109330813?pwd=SVlSeEtaRlVvcWxGcWFYdFN2cXlLdz09
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ANNOUNCEMENT: Remote Ph.D. Dissertation Defense
Name: Sheng Cheng
Professor Derek A. Paley, Chair/Advisor
Professor John S. Baras,
Professor Andre L. Tits,
Professor Pratap Tokekar,
Professor Nikhil Chopra
Date & Time: Thursday, May 13th, 2021 at 10:00 am
Title: Estimation and Control of a Distributed Parameter System by a Team of Mobile Sensors and Actuators
In the first part of this dissertation, an optimization framework is proposed to control a DPS modeled by a 2D diffusion-advection equation using a team of mobile actuators. The framework simultaneously seeks optimal control of the DPS and optimal guidance of the mobile actuators such that a cost function associated with both the DPS and the mobile actuators is minimized subject to the dynamics of each. We establish conditions for the existence of a solution to the proposed problem. Since computing an optimal solution requires approximation, we also establish the conditions for convergence to the exact optimal solution of the approximate optimal solution. That is, when evaluating these two solutions by the original cost function, the difference becomes arbitrarily small as the approximation gets finer. Two numerical examples demonstrate the performance of the optimal control and guidance obtained from the proposed approach.
In the second part of this dissertation, an optimization framework is proposed to design guidance for a possibly heterogeneous team of multiple mobile sensors to estimate a DPS modeled by a 2D diffusion-advection process. Owing to the abstract linear system representation of the process, we apply the Kalman-Bucy filter for estimation, where the sensors' measurement innovates the estimate through the covariance operator. We propose an optimization problem that minimizes the sum of the trace of the covariance operator of the Kalman-Bucy filter and a generic mobility cost of the mobile sensors, subject to the sensors' motion modeled by linear dynamics. We establish the existence of a solution to this problem. Moreover, we prove convergence to the exact optimal solution of the approximate optimal solution. That is, when evaluating these two solutions using the original cost function, the difference becomes arbitrarily small as the approximation gets finer. To compute the approximate solution, we use Pontryagin's minimum principle after approximating the infinite-dimensional terms originating from the diffusion-advection process.
The approximate solution is applied in simulation to analyze how a single mobile sensor's performance depends on two important parameters: sensor noise variance and mobility penalty. We also illustrate the application of the framework to multiple sensors, particularly the performance of a heterogeneous team of sensors.
In the third part of this dissertation, a framework of cooperative estimation and control of a 2D diffusion process using collocated mobile sensors and actuators is proposed. Guidance and actuation of the actuators are computed from an optimization problem originated from the first part of the dissertation with additional constraints on the maximum speed and maximum actuation of the mobile actuators. Early lumping is applied such that the optimization problem is solved using a nonlinear programming solver. The sensors' measurement is fed to a Kalman filter to estimate state subject to Gaussian state and measurement noise. The estimation is periodically fed to the optimization problem to compute optimal actuation and guidance in a receding horizon manner. Extensive numerical studies have been conducted to analyze and evaluate the performance of the proposed framework with both parameter sweep on the nondimensional parameters of the optimization problem and Monte Carlo simulations of the entire framework. The framework is demonstrated on an outdoor multi-quadrotor testbed at the Fearless Flight Facility of the University of Maryland.