Title:  Optimal Control of Hybrid Dynamical Systems: Theory and Applications

Committee: 

Dr. Egerstedt, Dr. Wardi, Advisors 

Dr. Taylor, Chair

Dr. Yezzi

Abstract: The objective of the proposed research is to solve a class of constrained hybrid optimal control problems by deriving optimality conditions and propose numerical schemes for their efficient computation and demonstrate the utility of the theoretical results by considering their applications to problems in mobile robotics, power aware networks and precision agriculture. Hybrid Dynamical Systems arise in a number of application areas such as robotics, automotive engine control, manufacturing, process control, power electronics 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 and the optimal control of hybrid systems under these constraints is considered in this thesis. We will demonstrate the utility of the general results in few application areas such as power aware networks. The problem of co-optimizing motion and communication energy in multi-agent robotics in fading environments has the structure of hybrid optimal control problem and formulating this as an optimal control problem and subsequently solving them using efficient algorithms in a decentralized manner to achieve co-ordinated tasks will be another focus of the proposed research. We will demonstrate the application of theoretical results on the dwell time problem to a simple version of the above co-optimization problem and to a diverse area of precision agriculture