Seminars

Abstract: In the first part of this talk, we investigate team optimal decentralized control of a system with one major and multiple minor agents. The major agent affects the state evolution of the minor agent but not vice-versa. We assume that the major agent perfectly observes its state; the minor agents perfectly observe the state of the major player but observe their local state corrupted by non-Gaussian noise. As far as we are aware, decentralized control of linear quadratic systems with non-Gaussian noise has not been considered in the literature. 

Our main result is to show that the optimal strategy has a certainty equivalence structure. In particular, the optimal control action at the major player is a linear function of its own state and its estimate of the states of the minor players. The optimal control action at the minor agent is a linear function of the major agent's estimate of the state of all minor agents and the "innovation'' of the estimate of its own state based on locally observed data. The corresponding gains are obtained by solving n+1 decoupled Riccati equations. It is worth highlighting that the "innovation'' is obtained via non-linear filtering. So, the control action is a non-linear function of the observations.

In the second part of this talk, motivated by estimation problems arising in autonomous vehicles and decentralized control of unmanned aerial vehicles, we consider multi-agent estimation and filtering problems in which multiple agents generate state estimates based on decentralized information and the objective is to minimize a coupled mean-squared error which we call team mean-square error. We call the resulting estimates as minimum team mean-squared error (MTMSE) estimates. We show that MTMSE estimates are different from minimum mean-squared error (MMSE) estimates. We derive closed-form expressions for MTMSE estimates, which are a linear function of the observations where the corresponding gain depends on the weight matrix that couples the estimation error. We then consider a filtering problem where a linear stochastic process is monitored by multiple agents that can share their observations (with delay) over a communication graph. We derive expressions to recursively compute the MTMSE estimates. To illustrate the effectiveness of the proposed scheme we consider an example of estimating the distances between vehicles in the platoon and show that MTMSE estimates significantly outperform MMSE estimates and consensus Kalman filtering estimates.

Bio: Mohammad Afshari received the B.S. and the M.S. degrees in Electrical Engineering from the Isfahan University of Technology, Isfahan, Iran, in 2010 and 2012, respectively. He is currently working towards the Ph.D. degree in Electrical and Computer Engineering at McGill University, Montreal, Canada. His current area of research is decentralized stochastic control, team theory, and reinforcement learning. Mr. Afshari is a member of the McGill Center of Intelligent Machines (CIM) and a member of the Research Group in Decision Analysis (GERAD). He is currently a research intern at MILA Lab where he is working on Inverse Reinforcement Learning. Mohammad has also been a research intern at the University of Southern California in Fall 2019.