Adaptive control systems.

Systems with time delays have a broad range of applications not only in control
systems but also in many other disciplines such as mathematical biology, financial
economics, etc. The time delays cause more complex behaviours of the systems. It
requires more sophisticated analysis due to the infinite dimensional structure of the
space spaces. In this thesis we investigate stability properties associated with output
functions of delay systems.
Our primary target is the equivalent Lyapunov characterization of input-tooutput
stability (ios). A main approach used in this work is the Lyapuno Krasovskii
functional method. The Lyapunov characterization of the so called output-Lagrange
stability is technically the backbone of this work, as it induces a Lyapunov description
for all the other output stability properties, in particular for ios. In the study, we
consider two types of output functions. The first type is defined in between Banach
spaces, whereas the second type is defined between Euclidean spaces. The Lyapunov
characterization for the first type of output maps provides equivalence between the
stability properties and the existence of the Lyapunov-Krasovskii functionals. On the
other hand, as a special case of the first type, the second type output renders flexible Lyapunov descriptions that are more efficient in applications. In the special case
when the output variables represent the complete collection of the state variables,
our Lyapunov work lead to Lyapunov characterizations of iss, complementing the
current iss theory with some novel results.
We also aim at understanding how output stability are affected by the initial
data and the external signals. Since the output variables are in general not a full
collection of the state variables, the overshoots and decay properties may be affected
in different ways by the initial data of either the state variables or just only the output
variables. Accordingly, there are different ways of defining notions on output stability,
making them mathematically precisely. After presenting the definitions, we explore
the connections of these notions. Understanding the relation among the notions is
not only mathematically necessary, it also provides guidelines in system control and
design.

As humans explore greater depths of Earth’s oceans, there is a growing need for the installation of subsea structures. 71% of the earth’s surface is ocean but there are limitations inherent in current detection instruments for marine applications leading to the need for the development of underwater platforms that allow research of deeper subsea areas. Several underwater platforms including Autonomous Underwater Vehicles (AUVs), Remote Operated Vehicles (ROVs), and wave gliders enable more efficient deployment of marine structures.
Deployable structures are able to be compacted and transported via AUV to their destination then morph into their final form upon arrival. They are a lightweight, compact solution. The wrapped package includes the deployable structure, underwater pump, and other necessary instruments, and the entire package is able to meet the payload capability requirements. Upon inflation, these structures can morph into final shapes that are a hundred times larger than their original volume, which extends the detection range and also provides long-term observation capabilities.
This dissertation reviews underwater platforms, underwater acoustics, imaging sensors, and inflatable structure applications then proposes potential applications for the inflatable structures. Based on the proposed applications, a conceptual design of an underwater tubular structure is developed and initial prototypes are built for the study of the mechanics of inflatable tubes. Numerical approaches for the inflation process and bending loading are developed to predict the inflatable tubular behavior during the structure’s morphing process and under different loading conditions. The material properties are defined based on tensile tests. The numerical results are compared with and verified by experimental data. The methods used in this research provide a solution for underwater inflatable structure design and analysis. Several ocean morphing structures are proposed based on the inflatable tube analysis.

In this research, a wind feedforward (FF) controller has been developed to augment closed loop feedback controllers for the position and heading station keeping control of Unmanned Surface Vehicles (USVs). The performance of the controllers was experimentally tested using a 16 foot USV in an outdoor marine environment. The FF controller was combined with three nonlinear feedback controllers, a Proportional–Derivative (PD) controller, a Backstepping (BS) controller, and a Sliding mode (SM) controller, to improve the station-keeping performance of the USV. To address the problem of wind model uncertainties, adaptive wind feedforward (AFF) control schemes are also applied to the FF controller, and implemented together with the BS and SM feedback controllers. The adaptive law is derived using Lyapunov Theory to ensure stability. On-water station keeping tests of each combination of FF and feedback controllers were conducted in the U.S. Intracoastal Waterway in Dania Beach, FL USA. Five runs of each test condition were performed; each run lasted at least 10 minutes. The experiments were conducted in Sea State 1 with an average wind speed of between 1 to 4 meters per second and significant wave heights of less than 0.2 meters. When the performance of the controllers is compared using the Integral of the Absolute Error (IAE) of position criterion, the experimental results indicate that the BS and SM feedback controllers significantly outperform the PD feedback controller (e.g. a 33% and a 44% decreases in the IAE, respectively). It is also found that FF is beneficial for all three feedback controllers and that AFF can further improve the station keeping performance. For example, a BS feedback control combined with AFF control reduces the IAE by 25% when compared with a BS feedback controller combined with a non-adaptive FF controller. Among the eight combinations of controllers tested, SM feedback control combined with AFF control gives the best station keeping performance with an average position and heading error of 0.32 meters and 4.76 degrees, respectively.