Title:  Optimal Control of Constrained Hybrid Dynamical Systems: Theory, Computation and Applications

Committee:

Dr. Magnus Egerstedt, ECE, Chair , Advisor

Dr. Yorai Wardi, ECE, Co-Advisor

Dr. David Taylor, ECE

Dr. Anthony Yezzi, ECE

Dr. Erik Verriest, ECE

Dr. Evangelos Theodorou, AE

Abstract:

Hybrid Dynamical Systems arise in a number of application areas such as mobile and humanoid robotics, automotive engine control, manufacturing, power converters, hybrid cars etc. to name a few and as such the optimal control of these systems has been an area of active research. These systems are characterized by two components; subsystems with continuous dynamics and subsystems with discrete dynamics that interact with each other. The control parameters for these systems includes a switching law which determines which system is active at a given time and an external input. While in theory, we can switch infinitely many times between different modes in a finite amount of time, most physical systems have to spend some minimum time in a mode before they can switch to another mode due to mechanical reasons, power constraints, information delays, stability considerations etc. This minimum time is known as the dwell time, a term first used in the context of stability of hybrid systems, and the optimal control of hybrid systems under these constraints is the main focus of this thesis. Another main thrust of this thesis is a class of constrained hybrid optimal control problems inspired by power aware mobile robotic networks that are subject to various con- straints on inputs and states. Finally, we propose a multiple shooting based gradient descent techniques to solve a class of complex optimal control problems with large time horizons, which otherwise are hard to solve due to numerical problems arising from instability issues associated with the state or co-state equation and consider its application to solve large multi-agent problem in power aware robotic networks.