CISE Seminar: September 25, 2020 – Lili Wang, SE Post Doctoral Associate

Distributed computation and estimation across a network allow each agent in the network to deal with situations, like limited sensing capacity, constrained computation ability, and so on. This talk discusses three problems in distributed computation and estimation of a network of autonomous agents: the distributed state estimation and control problem, the distributed linear equation solver problem, and the distributed modulus consensus problem. Neighbor relations are characterized by a directed graph called a neighbour graph whose vertices correspond to agents and whose arcs depict neighbor relations.

The distributed state estimation and control problem is to develop observers, one for each agent, to estimate the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a network. The state is simultaneously estimated by the group of agents assuming each agent receives appropriately defined data from each of its neighbors’ observers. The benefit of distributed state estimation is that each agent can reconstruct the full state with a limited sensing ability. Three different observers are discussed in this talk.

First, a time-invariant, linear, distributed observer is described for solving the distributed state estimation problem with the assumption that the neighbor graph is constant and strongly connected. The spectrum of the overall distributed observer can be freely assigned using results from classical decentralized control theory. The result is extended to the case when the neighbor graph is consisting of strong connected components.

Second, a hybrid observer is described for solving the distributed state estimation problem with the assumption that the neighbor graph is strongly connected but time-varying. It is shown that the hybrid observer can estimate the system exponentially fast with preassigned convergence rate. The result still holds when there is an abrupt change in the network.

Third, a simply structured distributed observer is described when the neighbor graph is time-varying but always strongly connected. By exploiting several well-known properties of invariant subspaces, and the observers can estimate the system state exponentially fast with preassigned convergence rate. Correspondingly, a discrete-time distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system by exploiting several well-known properties of invariant subspace.

Using the result of the distributed state estimation problem, an observer-based control system which is implemented in a distributed manner is proposed to solve the basic distributed feedback control problem for a multi-channel linear system assuming only that the system is jointly controllable, jointly observable and has an associated neighbor graph which is strongly connected. Using these ideas, a solution is also given to the distributed set-point control problem for a multi-channel linear system in which each and every agent with access to the system is able to independently adjust its controlled output to any desired set-point value.

A distributed linear equation solver is to solve a system of linear algebraic equations of the form Ax = b which has a solution by a group of agents across a time-varying network assuming that each agent knows only a subset of the rows of the partitioned matrix [A b]. A consensus-based algorithm is proposed which can cause all agents’ estimates to converge exponentially fast to one solution of Ax = b provided the neighbor graph is l-repeatedly jointly strongly connected. The proposed algorithm leads naturally to a more general class of distributed algorithms for solving certain types of nonlinear equations.

Lastly, the distributed modulus consensus problem in opinion dynamics is considered. A discrete-time modulus consensus model is considered in which the interaction among a family of networked agents is described by a neighbor graph whose arcs are assigned complex numbers from a cyclic group. Limiting behavior of the model is studied using a graphical approach. It is shown that, under appropriate connectedness, a certain type of clustering will be reached exponentially fast for almost all initial conditions if and only if the sequence of gain graphs is “repeatedly jointly structurally balanced” corresponding to that type of clustering, where the number of clusters is at most the order of a cyclic group. It is also shown that the model will reach a consensus asymptotically at zero if the sequence of gain graphs is repeatedly jointly strongly connected and structurally unbalanced.

Lili Wang received the B.E. and M.S. degrees in electrical engineering from Zhejiang University, Zhejiang, China, in 2011 and 2014, respectively. She received the Ph.D. degree from Yale University, New Haven, CT, USA, in 2020. She is currently a Postdoctoral Associate at Boston University.

Her research interests include the topics of cooperative multiagent systems, distributed computation and estimation, and distributed control.

Faculty Host: Christos Cassandras
Student Host: Erfan Aasi