ESTIMATION AND CONTROL OF A DISTRIBUTED PARAMETER SYSTEM BY A TEAM OF MOBILE SENSORS AND ACTUATORS

The recent development of mobile robots has dramatically extended the scenarios where robots can be deployed to complete tasks autonomously. One of the tasks is monitoring and controlling large-scale spatiotemporal processes, e.g., oil spills and forest fires, which is mainly conducted by human operators. These tasks can pose health threats, cause severe environmental issues, and incur substantial financial costs. Autonomous robots can free human operators from danger and complete tasks in a timely and economically efficient manner. In this dissertation, estimation and control of spatiotemporal processes using mobile sensors and actuators are studied. Spatiotemporal processes vary in both space and time, whose dynamics can be characterized by partial differential equations (PDEs). Since the state space of a PDE is infinite-dimensional, a system with PDE dynamics is also known as a distributed parameter system (DPS). The performance of the estimation and control of a DPS can be enhanced (compared to stationary sensors and actuators) due to the additional degree of freedom induced from the mobility of the sensors and actuators. However, the vehicles carrying sensors and actuators usually have limited onboard resources (e.g., fuels and batteries) whose usage requires judicious decisions. Hence, we propose a new optimization framework that addresses the goal of estimation and control of a spatiotemporal process while considering the limited onboard resources. 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 spatiotemporal process 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 provide linear outputs. 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, in particular the performance of a heterogeneous team of sensors. In the third part of this dissertation, a cooperative framework for estimating and controlling a spatiotemporal process using collocated mobile sensors and actuators is proposed. We model the spatiotemporal process by a 2D diffusion equation that represents the dynamics. Measurement and actuation of the process dynamics are performed by mobile agents whose motion is described by single-integrator dynamics. The estimation and control framework is formulated using a Kalman filter and an optimization problem. The former uses sensor measurements to reconstruct the process state, while the latter uses the estimated state to plan the actuation and guidance of the mobile agents. The optimization problem seeks the actuation and guidance that minimize the sum of the quadratic costs of the process state, actuation input, and guidance effort. Constraints include the process and agent dynamics as well as actuation and speed bounds. The framework is implemented with the optimization problem solved periodically using a nonlinear program solver. Numerical studies analyze and evaluate the performance of the proposed framework using a nondimensional parameterization of the optimization problem. The framework is also implemented on an outdoor multi-quadrotor testbed with a simulated spatiotemporal process and synthetic measurement and actuation