My work lies at the intersection of Control, Communications, and Distributed Algorithms. My PhD and MS research topics are described below.
Linear Iterative Strategies for Information Dissemination and Processing
in Distributed Systems
Consider an arbitrary network of interconnected agents where each agent has some value, and the objective is to enable a subset of the agents to calculate some function of these values in a distributed manner. This scenario arises in a multitude of settings:
- A sink node in a sensor network might be tasked with computing the average measurement value of all the sensors
- A tabulator might be interested in determining the results of a vote
- A set of mobile robots might wish to communicate with each other in order to maintain a consistent formation
Our work focuses on the analysis and design of linear iterative strategies to enable information dissemination and function calculation in distributed systems. In linear iterative strategies, each agent repeatedly updates its value to be a weighted linear combination of its own previous value and those of its neighbors; such strategies have received a great deal of attention in the control systems community for the purpose of reaching asymptotic consensus (whereby all of the agents converge to the same value after an infinite number of iterations). The contribution of our work has been to show that, despite their simplicity, these linear iterative strategies are substantially more powerful than previously recognized. Using concepts from linear system theory, we demonstrate that such strategies actually allow any agent in the network to obtain the initial value of any other agent after a finite number of iterations, thereby allowing any agent to calculate any arbitrary function of the initial values. Furthermore, even if a set of agents conspiratorially decide to spread misinformation about the values of other agents, our analysis reveals that linear iterative strategies provide every agent in the network with sufficient information to overcome this disruptive behavior (as long as the underlying network topology satisfies some fundamental limitations, in the form of network connectivity). Surprisingly, the constraints imposed upon the network topology by linear strategies are no more stringent than the requirements imposed by any other strategy, and thus our work essentially establishes that linear strategies are viable and effective methods for distributing information in networks with malicious agents.
Delayed Observers for Linear Systems with Unknown Inputs
In practice, many physical systems can be modeled as having both known inputs (such as control inputs and reference signals) and unknown inputs (such as faults, disturbances, and parametric uncertainties). For such systems, it may be necessary to estimate the internal states and unknown inputs in order to achieve certain control objectives. In our research, we analyze and design observers to estimate these quantities for linear systems. In particular, we study delayed observers, which estimate states and inputs from the past based on output measurements up to the present. This capability enlarges the class of systems for which state and input estimation is possible.
Our analysis provides necessary and sufficient conditions for the existence of delayed state and input observers, as well as a characterization of the minimum delay required to reconstruct the states and inputs. When it is not possible to estimate all of the states and inputs, we study the problem of partial state and input observers. Our approach characterizes the set of all linear functions of the states and inputs that can be reconstructed through a linear observer with a given delay, and directly produces the corresponding observer.
We also consider the case where the system states and outputs are affected by noise, and present a method for constructing optimal state estimators. Specifically, we consider minimum variance unbiased estimators (MVUEs), which satisfy the following properties:
- On average, the estimation error is zero,
- The variance of the estimation error is minimized.
Once again, our design provides a characterization of estimators with delay, which eases the established necessary conditions for existence of unbiased estimators with zero-delay.
The observers produced by our research can be used in a variety of applications, including fault diagnosis, robust control design, decentralized control, and communication systems.