Control Design and Model Validation for Applications in Nonlinear Vessel Dynamics
In recent decades, computational models have become critical to how engineers and mathematicians understand nature; as a result they have become an integral part of the design process in most engineering disciplines. Moore's law anticipates computing power doubling every two years; a prediction that has historically been realized. As modern computing power increases, problems that were previously too complex to solve by hand or by previous computing abilities become tractable. This has resulted in the development of increasingly complex computational models simulating increasingly complex dynamics. Unfortunately, this has also resulted in increased challenges in fields related to model development, such as model validation and model based control, which are needed to make models useful in the real world.
Much of the validation literature to date has focused on spatial and spatiotemporal simulations; validation approaches are well defined for such models. For most time series simulations, simulated and experimental trajectories can be directly compared negating the need for specialized validation tools. In the study of some ship motion behavior, chaos exists, which results in chaotic time series simulations. This presents novel challenges for validation; direct comparison may not be the most apt approach. For these applications, there is a need to develop appropriate metrics for model validation. A major thrust of the current work seeks to develop a set of validation metrics for such chaotic time series data. A complementary but separate portion of work investigates Non-Intrusive Polynomial Chaos as an approach to reduce the computational costs associated with uncertainty analysis and other stochastic investigations into the behavior of nonlinear, chaotic models.
A final major thrust of this work focuses on contributing to the control of nonlinear marine systems, specifically the autonomous recovery of an unmanned surface vehicle utilizing motion prediction information. The same complexity and chaotic nature that makes the validation of ship motion models difficult can also make the development of reliable, robust controllers difficult as well. This body of work seeks to address several facets of this broad need that has developed due to our increased computational abilities by providing validation metrics and robust control laws.