Applied Mathematics
http://hdl.handle.net/10012/9926
2023-10-02T17:31:26ZFormation Control of Multi-agent Systems via Impulsive Strategy
http://hdl.handle.net/10012/19850
Formation Control of Multi-agent Systems via Impulsive Strategy
Liang, Zhanlue
Multi-agent systems (MASs) involving cooperative control problems such as consensus tracking of distributed networks, flocking control with obstacle avoidance, and attitude alignment have received a considerable amount of interest over the past few decades because of their broad real-time applications in various fields. As one of the most significant aspects of cooperative control, the formation stabilization process has been studied extensively in relation to cooperative surveillance, unmanned aerial vehicles, spacecraft coordination, autonomous underwater vehicles, etc. In formation tracking control, the fundamental goal is to reach a desired configuration and align with the formation leader from any arbitrary starting position. This can be achieved using various types of distributed control protocols in practice, which facilitate efficient communication and information exchange among agents. To begin with, we discuss the design of hybrid impulsive control protocols for the formation stabilization of multi-agent systems. By taking various sizes of time delay into account, some sufficient formation stabilization criteria are established via the Razumikhin technique and Lyapunov functional method. It is important to emphasize that the guarantee of stabilization is largely determined by the impulsive strength, the size of the time delays, and the length of the impulsive intervals. In the meantime, the general structure of collision avoidance mechanisms using artificial potential fields (APFs) or braking/gyroscopic forces is also discussed since they are critical for ensuring safety and reducing accident risk in a variety of applications. In comparison, the approach of braking and gyroscopic forces provides better performance by preventing undesired local minima. Moreover, one should realize that the inclusion of such mechanisms will raise the complexity of asymptotic formation stabilization under delay-dependent impulses. Thus, we further consider treating the collision avoidance mechanism as an external input and investigate input-to-state formation stabilization with respect to different impulse classes. In this way, stabilization can still be achieved once environmental obstacles are out of sensing range. Some sufficient conditions benefiting from stabilizing control impulses are derived by employing the Lyapunov Krasovskii functional and impulsive comparison principle. The hybrid impulsive control framework will be kept using throughout the rest of this thesis. Then, on top of the hybrid impulsive control framework, we extend our formation stabilization results into the following aspects. Multi-group formation stabilization for heterogeneous MASs with different dynamics order is investigated. In this setup, each subgroup can pursue its own control objectives, while group-wise coordination can be established via directed inter-group communication links. The stabilization is then dependent on the overall topological structure of the network. The hybrid event-triggered impulsive formation stabilization associated with non-linearity strength of intrinsic dynamics is considered. By incorporating pinning mechanisms and delayed control inputs, the corresponding event-triggered strategies are developed. Based on the Lyapunonv-Razumikhin technique regarding delayed impulsive systems, some novel results for maintaining local formation stabilization are obtained. We also investigate the finite-time formation tracking control of multi-agents via aperiodic intermittent communication under the hybrid impulsive control framework. In addition, the concepts of average impulsive interval and state-dependent intermittent control width are also implemented. The finite-time stabilization results illustrate the effectiveness of the proposed control protocol on the basis of the weak Lyapunov inequality condition. Furthermore, we investigate the formation stabilization of vehicle platoons using switching control, which is a trending application of multi-agent systems. Based on time-dependent switching between stable and unstable control inputs, or state-dependent switching utilizing convex switching regions and chatter-free switching rules, exponential stabilization results are obtained. Finally, numerical simulations are provided to demonstrate the effectiveness and performance of our analytical results.
2023-09-08T00:00:00ZTheory and Mitigation of Crosstalk on Quantum Information Processors
http://hdl.handle.net/10012/19848
Theory and Mitigation of Crosstalk on Quantum Information Processors
Winick, Adam
Successfully implementing large-scale quantum computation has proven to be an exceptionally arduous task. Decoherence and imperfect control limit the coherent manipulation of large ensembles of particles. While quantum error correction provides robust schemes for executing quantum algorithms on error-prone systems, the methods usually assume that the errors are well-behaved and lie below some threshold. The burden of QEC can be substantial, and reaching error rates well below these thresholds can dramatically improve the processing capabilities of a device.
A hierarchy of error processes exists with increasingly desirable properties at the cost of realism and generality. For example, quantum circuits subject to Markovian errors typically have higher error thresholds than those under general errors. We can further divide Markovian errors into coherent and incoherent processes, with the former having much lower thresholds.
This thesis examines crosstalk, a type of coherent error process, and mainly studies its role in superconducting quantum computing devices.
The first part of our work details a systematic framework for modeling crosstalk that occurs during the operation of a quantum computer, i.e., what happens on the device while performing gates. We break this crosstalk down into local and nonlocal effects. We show how to model local crosstalk on a digital computer without approximations efficiently. Unlike local crosstalk, nonlocal crosstalk cannot be modeled efficiently on a digital computer without approximations. Thus, we develop a framework for approximating the effect of nonlocal crosstalk. We observed a negligible difference between our approximation and the exact system dynamics in typical systems.
The second part of this thesis details our attempts to characterize and efficiently mitigate crosstalk on fixed-frequency superconducting qubits experimentally. The first obstacle we encountered was learning the crosstalk affecting a system. When the crosstalk is weak, existing methods prove difficult, so we developed a new approach to measure crosstalk. The second problem we needed to address was verifying that our model was correct. Using the results from our first measurements, we compare predicted evolutions with experimental data in a setting much different than the measurement procedure. We see excellent agreement between experiment and theory, indicating the model is reasonable. The last outstanding puzzle piece in this investigation is using this model to mitigate crosstalk, and our research is ongoing.
2023-09-08T00:00:00ZA comparison of the Kalman filter and recurrent neural networks for state estimation of dynamical systems
http://hdl.handle.net/10012/19807
A comparison of the Kalman filter and recurrent neural networks for state estimation of dynamical systems
Takigawa, Akihiro
The study of dynamical systems is of great interest in many fields, with a wide range of applications. In some cases, these dynamical systems may be affected by noise and the availability of measurements may be limited. State estimations methods which can account for these challenges are valuable tools in analyzing these systems. While for linear systems the standard method is by using an algorithm called the Kalman filter, data-driven methods employing the versatility of artificial neural networks have also been proposed. In this thesis, we first introduce state estimation using the Kalman filter. Next, we provide an overview of a type of artificial neural network called recurrent neural networks (RNNs), which are particularly suited for tasks on time series data. We finally present the results of implementing RNN-based estimators for a number of dynamical systems with comparisons
to Kalman filtering.
2023-08-30T00:00:00ZMathematical Modeling of the Vaporization of Encapsulated Perfluorocarbon Nanodroplets using Chirp Ultrasound
http://hdl.handle.net/10012/19795
Mathematical Modeling of the Vaporization of Encapsulated Perfluorocarbon Nanodroplets using Chirp Ultrasound
Jiang, Kaiwen
Ultrasound imaging is the use of sound waves beyond the human frequency range to construct images of human tissue. This is carried out through the measurement of reflected and scattered waves from the interfaces between tissues of differing acoustic impedances. Conventional ultrasound imaging faces limitations when imaging tissue microvasculature, resulting in poor resolution between blood and the surrounding tissue. This can be remedied using microbubbles which oscillate under ultrasound stimulation and thus provide an enhanced backscattered signal. Free gas bubbles however have a short half-life in the bloodstream as they are removed by the lungs. Therefore, phase-change contrast agents (PCCAs) have been introduced as an alternative which has better longevity in the body. An example of a PCCA is encapsulated perfluorocarbon nanodroplets. These nanodroplets are in liquid form when introduced into the body, but under exposure to ultrasound waves in the target tissue, undergo vaporization to form micrometer-scale bubbles. Therefore achieving a similar level of contrast enhancement to microbubbles. The encapsulation also confers them increased stability in circulation.
Typical use of ultrasound in medical imaging involves pulses of several wave cycles at constant frequency. Higher frequency ultrasound results in better axial resolution but a reduced penetrative depth as it undergoes a larger degree of attenuation within tissues. Coded excitation schemes where the outgoing ultrasound waveform is either frequency-modulated or phase-modulated can be utilized to increase axial resolution without sacrificing transmitted power and penetrative depth. One example of a coded excitation scheme is a linear chirp where the frequency of the ultrasound pulse increases linearly from the beginning to the end of the pulse.
The acoustic droplet vaporization of encapsulated perfluorocarbon nanodroplets under chirp ultrasound was investigated and it was found that although the increase in frequency over the course of the ultrasound pulse inhibits direct vaporization, if the stiffness of the encapsulating shell can be kept relatively low, there are feasible ultrasound parameters (amplitude, starting frequency and chirp bandwidth) which can still cause direct vaporization. This represents an improvement since the nanodroplets still fulfill their role as phase-change contrast agents and the chirp ultrasound fulfills its role of enhancing the axial resolution of the image.
2023-08-29T00:00:00Z