Dissertation
Flocking Dynamics and Multi-Fidelity Learning in Non-Dissipative Multi-Agent Systems
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000006342
Abstract
Modeling collective motion in multi-agent systems has gained much attention in recent years. In particular, of interest are the conditions under which flocking dynamics emerges. We present a generalization of the multi-agent model of Olfati--Saber with non-linear navigational feedback virtual forces. As opposed to the original model, our model is, in general, not dissipative. This makes obtaining sufficient conditions for flocking challenging due to the absence of an obvious choice of a Lyapunov function. By means of an alternative argument, we show that our model possesses a global attractor when the navigational feedback forces are bounded perturbations of the linear ones. We further demonstrate that, under mild conditions, the dynamics of the group converges to a complete velocity agreement at an exponential rate. We show that the attractor of a dissipative system can contain non-equilibrium solutions. We construct explicit examples of such solutions and obtain conditions under which they cannot exist. In addition, we present a case study of the energy efficiency of our model. We show how non-linear navigational feedback forces, which possess flexibility that linear forces lack, can be used to reduce on-board energy consumption.
Analytically determining the optimal configuration of the virtual forces is often a hard problem. Meanwhile, an accurate numerical solution will require a substantial number of high-fidelity simulations, which can be computationally expensive. However, one can obtain a large amount of biased and noisy results with fast low-fidelity simulations. We propose a generic algorithm that can efficiently learn a surrogate model of a system described by computational models of varying fidelity. The algorithm performs online training of a neural network-based surrogate model using stochastic gradient descent. By means of importance sampling, our algorithm allows efficient exploration of the domain of the model, which reduces the number of costly data source evaluations as compared to random exploration approaches. We demonstrate the efficiency of our algorithm on synthetic examples. We use the algorithm to approximate the average energy consumption function for the proposed model of collective motion. The resulting surrogate model can then be minimized at a low computational cost.
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Details
- Title
- Flocking Dynamics and Multi-Fidelity Learning in Non-Dissipative Multi-Agent Systems
- Creators
- Oleksandr Dykhovychnyi
- Contributors
- Alexander Panchenko (Advisor)Robert H Dillon (Committee Member)Nikolaos Voulgarakis (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 151
- Identifiers
- 99901087336501842
- Language
- English
- Resource Type
- Dissertation