Research

My research interests lie broadly in nonlinear control and optimization, complex large-scale systems, privacy in multi-party computation, and ML methods in dynamical systems. Specific topics that I have been dedicated to include:

♢ Control and optimization on manifolds (Intrinsic formation, rigid-body attitude coordination, applications for rigid-body control),

♢ Privacy and security in network control and federated learning,

♢ Moment-based methods for modeling and controlling large-scale systems,

♢ Distributed control and optimization for nonlinear networked systems,

♢ Machine learning algorithms for opinion and crowd dynamics.

Network coordination with privacy

In many Internet of Things applications, privacy is a hotly debated topic, and subject to several regulations in recent years, e.g., GDPR, PIPEDA, and CCPA. When sensitive data is exchanged between parties, there are no guarantees that it stays private, or that it isn't used for nefarious purposes. We study privacy-preserving approaches for network coordination, by which all nodes in a network can achieve the collective goals, such as consensus, collaboratively optimizing a function, and training in federated learning, but without exposing individual privacy to other parties. In contrast to the methods using cryptography, we pursue preserving the participants' privacy in the information exchanges in networks from a perspective of dynamical systems theory, which shows more computation efficiency and application flexibility. [Arxiv], [Arxiv]

Control on manifolds and Intrinsic formation

Control and optimization on manifolds in a distributed manner becomes a timely issues within the context of large-scale systems. It is because by identifying and exploiting the underlying geometric structures in high-dimensional data and states, one can dramatically reduce the complexity of large-scale problems, and therefore make distributed algorithms more informationally efficient and computationally tractable.

We employed this line of work in differentiable manifolds and particularly in n-sphere S^n and Lie group SO(3), which are entailed in numerous rigid-body attitude applications. Based on our study of the distributed algorithms of state consensus (i.e., distributed minimization of deviations between individuals) in non-Euclidean spaces, we further investigated formation problems for multiple rigid bodies.

Unlike most studies in the formation control literature, the new formation mechanism we proposed does not require any shape reference signal pre-given in the control protocol. Instead, the desired formation patterns are constructed based on the geometric properties of the configuration space and the designed connection topology. This type of formation is referred to as Intrinsic Formation Control. Moreover, the research of distributed coordination on manifolds is of not only theoretical but also practical significance in many applications, such as satellite constellation maneuvers, drone cluster coordination, and multi-robot systems control. [Arxiv], [Arxiv], [2017], [2018], [2018].

Modeling and controlling large-scale systems via moment

Large-scale networked systems typically consist of a large number of connected agents, often too large for modeling each agent individually. Moreover, in many cases the agents are exchangeable, and distinguishing each individual may not even be desirable. Therefore, we proposed a novel approach to characterizing the evolution of a network by a sequence of moments. In general, moments represent statistics and also represent realistically measured quantities of a cohort. By properly selecting kernel functions, the corresponding moments carry enough macro-scale information, such that the collective behavior of the networked system can be accordingly reconstructed.

The method provides a tractable approach to building the dynamics for a general moment sequence. In addition, the resulting moment systems typically permit less intricate and lower dimensional dynamics, which considerably reduces computational complexity for controlling and analyzing large-scale systems. The method is applicable to a wide range of applications, such as multi-agent systems, crowd dynamics, opinion dynamics, and many problems pertinent to collective behavior occurring in biology, economy, and social sciences. [Arxiv]

 

My research is supported by WASP, The Wallenberg Foundations, and Digital Futures.