| PhD Seminar

Name of the Speaker: Mr. Aniruddhar Roy (EE18D031)
Guide: Dr. Puduru Viswanadha Reddy
Venue: CSD-308 (Conference Hall)
Date/Time: 14th February 2024 (Wednesday), 3:30 PM
Title: Soft-constrained output feedback guaranteed cost equilibria in infinite horizon uncertain linear-quadratic differential games

Abstract

The study of multi-agent systems (MAS) and related control architectures is gaining popularity in emerging engineering applications like power grids, multi-robot systems, IoT systems, and sensor networks. These systems are large-scale and characterized by the presence of multiple, interdependent decision-making players or agents, which are networked and heterogeneous in nature. In the first seminar, we considered distributed control of networked MAS in a deterministic setting. Using a game theoretical framework, we modelled the distributed control problem as a networked linear quadratic differential game. The concept of feedback guaranteed cost equilibria (GCE) using local or output feedback information structure was presented. The existence of GCE controllers and a synthesis algorithm was presented.

In this seminar, we will present on the robust control of multi-agent systems in the presence of unmodeled uncertainties. Despite the significance of robustness in control theory, there is a lack of research on differential games involving model uncertainties. We assume that the nominal dynamics is linear and influenced by unbounded disturbances. Further, we assume that the risk attitudes of the players are described by a soft-constrained quadratic cost criterion defined over an infinite horizon. We illustrate difficulties associated with computing a soft-constrained output feedback Nash equilibrium. To address this, we introduce the concept of soft-constrained output feedback guaranteed cost equilibrium (SCOGCE). At a SCOGCE, the players' worst-case costs are upper-bounded by a given cost profile while retaining the equilibrium property. We obtain the Price of Stability (PoS) bound associated with SCOGCE. We show that sufficient conditions for the existence of SCOGCE controllers are related to solvability of a set of coupled bi-linear matrix inequalities. Using semi-definite programming relaxations, we provide linear matrix inequality based iterative algorithms for the synthesis of SCOGCE. We illustrate the proposed design approach using numerical experiments.