By

Kaivalya Bakshi

(Advisor: Prof. Evangelos Theodorou)

2:00 PM, Thursday 12 Nov 2018

Klaus Building, Conference room 2108

LARGE SCALE STOCHASTIC CONTROL: ALGORITHMS, OPTIMALITY

AND STABILITY

Summary:

            Optimal control of large-scale multi-agent networked systems which describe social

networks, macro-economies, traffic and robot swarms is a topic of interest in engineer-

ing, biophysics and economics. A central issue is constructing scalable control-theoretic

frameworks when the number of agents is infinite.

            In this work, we exploit PDE representations of the optimality laws in order to provide

a tractable approach to ensemble (open loop) and closed loop control of such systems. A

centralized open loop optimal control problem of an ensemble of agents driven by jump

noise is solved by a sampling algorithm based on the infinite dimensional minimum prin-

ciple to solve it. The relationship between the infinite dimensional minimum principle and

dynamic programming principles is established for this problem.

            Mean field game (MFG) models expressed as PDE systems are used to describe emer-

gent phenomenon in decentralized feedback optimal control models of a continuum of

interacting agents with stochastic dynamics. However, stability analysis of MFG models

remains a challenging problem, since they exhibit non-unique solutions in the absence of a

monotonicity assumption on the cost function. This thesis addresses the key issue of sta-

bility and control design in MFGs. Specifically, we present detailed results on a models for

flocking and population evolution.

            An interesting connection between MFG models and the imaginary-time Schrödinger

equation is used to obtain explicit stability constraints on the control design in the case

of non-interacting agents. Compared to prior works on this topic which apply only to

agents obeying very simple integrator dynamics, we treat nonlinear agent dynamics and

also provide analytical design constraints.

Committee Members:

Prof. Evangelos Theodorou (Advisor)

Dr. Piyush Grover (Principal Research Scientist, MERL)

Prof. Eric Feron (AE)

Prof. Yongxin Chen (AE)

Prof. Ionel Popescu (MATH)

Prof. Paul Bogdan (EE, USC Viterbi)