In this dissertation, we develop feedback control strategies that can be used for evacuating people. Pedestrian models are based on macroscopic or microscopic behavior. We use the macroscopic modeling approach, where pedestrians are treated in an aggregate way and detailed interactions are overlooked. The models representing evacuation dynamics are based on the laws of conservation of mass and momentum and are described by nonlinear hyperbolic partial differential equations. As such the system is distributed in nature. We address the design of feedback control for these models in a distributed setting where the problem of control and stability is formulated directly in the framework of partial differential equations. The control goal is to design feedback controllers to control the movement of people during evacuation and avoid jams and shocks. We design the feedback controllers for both diffusion and advection where the density of people diffuses as well as moves in a specified direction with time. In order to achieve this goal we are assuming that the control variables have no bounds. However, it is practically impossible to have unbounded controls so we modify the controllers in order to take the effect of control saturation into account. We also discuss the feedback control for these models in presence of uncertainties where the goal is to design controllers to minimize the effect of uncertainties on the movement of people during evacuation. The control design technique adopted in all these cases is feedback linearization which includes backstepping for higher order two-equation models, Lyapunov redesign for uncertain models and robust backstepping for two-equation uncertain models. The work also focuses on abstraction of evacuation system which focuses on obtaining models with lesser number of partial differential equations than the original one. The feedback control design of a higher level two-equation model is more difficult than the lower order one-equation model. Therefore, it is desirable to perform control design for a simpler abstracted model and then transform control design back to the original model. / Ph. D.

Stop-and-Go Adaptive Cruise Control (ACC+) is an extension of Adaptive Cruise Control (ACC) that works at low speed as well as normal highway speeds to regulate the speed of the vehicle relative to the vehicle it is following. In this thesis, we design an ACC+ controller for a scale model electric vehicle that ensures the robust performance of the system under various models of uncertainty. We capture the operation of the hybrid system via a state-chart model that performs mode switching between different digital controllers with additional decision logic to guarantee the collision freedom of the system under normal operation. We apply different controller design methods such as Linear Quadratic Regulator (LQR) and H-infinity and perform multiple simulation runs in MATLAB/Simulink to validate the performance of the proposed designs. We compare the practicality of our design with existing formally verified ACC designs from the literature. The comparisons show that the other formally verified designs exhibit unacceptable behaviour in the form of mode thrashing that produces excessive acceleration and deceleration of the vehicle. While simulations provide some assurance of safe operation of the system design, they do not guarantee system safety under all possible cases. To increase confidence in the system, we use Differential Dynamic Logic (dL) to formally state environmental assumptions and prove safety goals, including collision freedom. The verification is done in two stages. First, we identify the invariant required to ensure the safe operation of the system and we formally verify that the invariant preserves the safety property of any system with similar dynamics. This procedure provides a high level abstraction of a class of safe solutions for ACC+ system designs. Second, we show that our ACC+ system design is a refinement of the abstract model. The safety of the closed loop ACC+ system is proven by verifying bounds on the system variables using the KeYmaera verification tool for hybrid systems. The thesis demonstrates how practical ACC+ controller designs optimized for fuel economy, passenger comfort, etc., can be verified by showing that they are a refinement of the abstract high level design. / Thesis / Master of Applied Science (MASc)