Plume Source Localization and Boundary Prediction

Plume location and prediction using mobile sensors is the main contribution of this thesis. Plume concentration values measured by chemical sensors at different locations are used to estimate the source of the plume. This is achieved by employing a stochastic approximation technique to localize the source and compare its performance to the nonlinear least squares method. The source location is then used as the initial estimate for the boundary tracking problem. Sensor measurements are used to estimate the parameters and the states of the state space model of the dynamics of the plume boundary. The predicted locations are the reference inputs for the LQR controller. Measurements at the new locations (after the correction of the prediction error) are added to the set of data to refine the next prediction process. Simulations are performed to demonstrate the viability of the methods developed. Finally, interpolation using the sensors locations is used to approximate the boundary shape

Control Oriented Nonlinear Model Reduction for Distributed Parameter Systems

The development of model reduction techniques for physical systems modeled by partial differential equations (PDEs) has been a very active research area. Large number of states is needed to accurately capture the dynamics of such systems which makes them unsuitable for control design. The order of the system must be reduced prior to control design. In this dissertation, new methods that generalize the popular proper orthogonal decomposition (POD) to nonlinear PDEs are investigated. In particular, cluster based POD algorithms are developed and applied to the one and two dimensional Burgers equations that govern a nonlinear convective ow. Each cluster contains relatively close in distance dynamic behavior within itself, and considerably far with respect to other clusters. Three different clustering schemes in time, space and space-time are proposed. A complete and detailed approach for the Orthogonal Locality Preserving Projections (OLPP) modes computation for the incompressible Navier-Stokes PDE that governs the dynamics of the NACA 0015 airfoil fluid flow is presented. Close snapshots in the full order model are forced to stay close in the reduced order model by defining an optimization problem that preserves local distances. Optimal boundary control laws are derived based on the proposed nonlinear reduced order models, and applied to various distributed parameter systems including: Nonlinear convection, temperature control in energy efficient buildings systems governed by the heat equation, power and voltage control in large electromechanical oscillations in the power grid governed by the wave equation, and ow separation control for fluid flows governed by the Navier-Stokes equations