Research projects

Uncertainty and Robustness in Central Banking

[2019, with Prof. Roberto Rigobon and Prof. Munther A. Dahleh]

After the 2008 Global Financial Crisis, Central Banks around the developed world embarked on a large easing of monetary policy. They started relying on the monetary policy tool they have been using for decades: open market operations; lowering the interest rate in the short run. Very soon interest rates got close to zero, and in many countries, it became exactly zero. Under the assumption that negative rates were unfeasible or inconvenient, central Banks started to expand their monetary policy arsenal using unorthodox interventions. Almost all of them relied on 'forward guidance' (Equivalent operations include, but not limited to “Operation Twist” by the Reserve Bank of India and targeted longer-term refinancing operations (TLTRO) by European Central Bank)

One key assumption in creating more policy tools is that more tools is always make a system easier to control. However, this research shows that, when model uncertainty and expectation channels are presented at the same time, more tools could result in worse control. Moreover, information advantage of the central bank (if there is any) could potentially destabilize the market.

Contingent Financial Networks

[2017, with Prof. Roberto Rigobon and Prof. Munther A. Dahleh]

Several papers have studied how the financial networks propagate shocks either because their liabilities or assets are interconnected. From the policy point of view the reaction to the financial crisis also paid attention to systemic considerations. Today, most financial regulators assess the aggregate consequences different financial institutions might incur. Therefore, banks and insurance companies are classified either as systemically important or not. Most of this process takes a network approach. Interestingly, the empirical literature and most of the theoretical literature assumes that the network is stable. However, it is obvious that different financial institutions might exhibit different behavior depending on the shock that hits the system. For instance, two banks could be exposed to the same real estate risk but might lend to different manufacturing sectors. In this setting, the two banks might be very highly correlated when a shock to the real estate market hits the economy, but those same banks might be quite unrelated if there is a shock to the industry where one is exposed and the other is not. Therefore, in principle, the nature of the network might differ conditional on the shock. This project empirically estimates the different linear networks that might affect the US banking system. We propose an identification method to estimate multiple unobserved networks, and propose a test for the number of minimum number of linear network.

Coalitional game with opinion exchange

[2016, with Prof. Munther A. Dahleh and Dr. Mardavij Roozbehani]

This project proposes a new framework considering coalitional games with unrealized subset payoff function. In a coalitional game, if different participants hold different opinions about the payoff function corresponding to each subset of the coalition, the traditional coalitional game theory cannot apply. This paper proposes a framework where players exchange opinions about their view of payoff functions and then decide the value distribution of the grand coalition. With all players being rational, the model implies that if influential players are risk-averse, then an efficient distributed data fusion is achieved at pure strategy Nash equilibrium. Also, removing the assumption that all players are rational, each player can adopt an algorithmic R-learning process, which gives the same result with the pure strategy Nash equilibrium with rational players.

3D mobile sensor network localization using distance-only measurements

[2015, with Prof. Brian D.O. Anderson, and Dr. Hatem Hman]

For a group of UAVs, aligning coordinate systems among each other is a key task. This project studies the coordinate-alignment problem for a group of UAVs flying in 3D space when distance measurements are the only type of inter-agent sensing that is available. A requirement for the minimum number of distance measurements in the multi-agent 3D case is formally established for the first time. The derivation of the conditions is based on graph rigidity theory.

Higher order Voronoi based mobile coverage control

[2014, with Prof. Brian D.O. Anderson, Dr. Zhiyong Sun]

Most current results on Voronoi based coverage control using mobile sensors require that one partitioned cell is the sole responsibility of one sensor. However, many localization and detection techniques require more than one agents in different locations cooperatively monitoring one area. Examples of these methods include bistatic radar detection, TDOA localization, bearing only localization, etc. In the above cases, the current framework is not applicable.

In order to solve this problem, we consider a class of generalized Voronoi coverage control problems by using higher order Voronoi partitions. We introduce a framework depending on a coverage performance function incorporating higher order Voronoi cells and then design a gradient-based controller which allows the multi-sensor system to achieve a local equilibrium in a distributed manner. We also give several real world examples to justify our model.

Optimal Path Planning and Sensor Placement for Mobile Target Detection

[2013, with Prof. Brian D.O. Anderson, Dr. Adrian N. Bishop and Dr. Sam P. Drake]

This is an applications problem originating from Australia’s Defence Science and Technology Organization (DSTO). The primary goal of this project is, but not limited to, computing the least-probability-of-detection path through a field of heterogeneous detectors. The computation burden should be very low such that the algorithm can be implemented on Unmanned Aerial Vehicles (UAVs) such as quadrotors.

While most of the previous optimization models aim to minimize the cumulative radar exposure, we derived a model that can directly minimize the probability of being detected. In addition, a homotopy method with exceptionally low computational complexity is derived, allowing UAVs adjusting the optimal path on board when the detection rate function changes. Finally, we also show how to apply a convex optimization method to find optimal positions of detectors when vehicles can do path planning.

Velocity consensus and formation shape control using distance-only measurements

[2012, with Prof. Brian D.O. Anderson and Dr. Mohammad Deghat]

In 2011, the Australian government Defence Science and Technology Organization (DSTO) decided to explore formation control of mobile vehicles using restricted sensing. The topic I got is to design a strategy allowing mobile vehicles achieving formation shape control with only one distance sensor on each agent. The task seems to be impossible because each agent’s motion on a 2D plane has two degree of freedom while distance sensor can only restrict one. That is to say, if the motion of agents have full arbitrary, it is not possible to infer the position using only distance data.

To solve this problem, we let each agent in a formation move in a small neighbourhood, namely circular motion, around its nominal trajectory, then collect distance information over an interval to infer direction and relative velocity. Fourier transform is used to infer the information and the method is very robust against measurement noise.

In addition, because we let agents collect information for a time interval to infer neighbour's position and velocity, we need a discretized formation shape control and flocking algorithm. We gave such a control algorithm and proved its stability using Malkin Theorem.