Practical Stabilization of Systems With Countable Set of Actions: A Nearest Action Selection Approach

The control and stabilization of systems, whose inputs can only take values from finite countable sets, is studied and analyzed in this thesis. Such systems arise in a number of engineering systems, including a renewable energy storage system that is modeled and presented in the latter part of the thesis. In the first part of the thesis, a simple input-quantization method based on the nearest action selection approach, namely the nearest action control (NAC), is proposed and analyzed. The proposed control methods are applied to both single- and multi-agent systems, with a particular focus on the class of passive nonlinear systems. Practical stability analysis is shown for both classes of systems where the convergence region can be related to the property of the countable input sets. A strategy to achieve exponential convergence rate is also presented by expanding the input sets in a logarithmic fashion. In the second part of this thesis, the modeling of the ocean grazer wave energy converter (OG-WEC) system in the port-Hamiltonian framework is given. The model contains the hydrodynamic interaction among the floating bodies of OG-WEC via Cummin's equation and the mechanical prime-mover systems of OG-WEC. The developed multi-domain model using port-Hamiltonian systems is validated using existing numerical models of OG-WEC systems.