| PhD Viva

Name of the Speaker: Mr. Aniruddha Roy (EE18D031)
Guide: Dr. Puduru Viswanadha Reddy
Venue: Online
Online meeting link: https://meet.google.com/diw-tizy-rvm
Date/Time: 5th July 2024(Friday), at 2PM
Title: Guaranteed cost equilibria in infinite horizon linear-quadratic differential games

Abstract :

The study of multi-agent systems (MAS) and related control architectures is becoming increasingly popular in emerging engineering systems such as power grids, multi-robot systems, IoT (Internet of Things) systems, and sensor networks. These systems are large-scale and characterized by the presence of multiple interdependent decision-making entities or agents, which are networked and heterogeneous in nature. This work deals with the distributed control of networked MAS with linear time-invariant dynamics and quadratic performance measures. As the MAS is networked, an agent has access only to the state information of its neighbors, also referred to as local or output feedback information structure. As a consequence, full-state feedback controllers are not implementable. Using a game-theoretic framework, we model the distributed control problem as a networked differential game. Existing research works assume complete state information, which is not feasible in practical scenarios, and the local state information or outputs are available when agents are networked. We illustrate that, even for low-dimensional problems, computing an output feedback Nash equilibrium (OFNE) is difficult. In particular, finding an OFNE is related to solving coupled algebraic Riccati equations (CARE). However, solving CARE becomes complicated as the number of players increases. Even though iterative methods exist to solve CARE, their efficacy depends on proper initialization, and their convergence is not guaranteed. As a result, the existence of an OFNE is not verifiable due to the structural constraints induced by the network topology. To address this, we develop the notion of output feedback guaranteed cost equilibrium (GCE). The output feedback GCE controllers achieve a given upper bound on the individual cost of agents while retaining an equilibrium property. We derive several properties associated with a GCE. In particular, we show that the set of GCE controllers is monotone with respect to the cost profile. We also derive a uniform price of stability bound associated with a set of GCE. We provide sufficient conditions for the verification of GCE given cost and strategy profiles of the players. Further, we also derive sufficient conditions for the existence of a guaranteed cost response. We formulate linear matrix inequality (LMI)-based conditions for the existence of these equilibria and an algorithm for synthesizing them. Next, we focus on the control of MAS under the effect of an external deterministic disturbance signal. Despite the significance of robustness in control theory, there is a lack of research on differential games that are influenced by uncertainties or disturbances. We introduce the concept of soft-constrained output feedback guaranteed cost equilibrium (SCOGCE) assuming the external disturbances are quadratically bounded. We provide sufficient conditions for the existence of SCOGCE controllers and an iterative LMI-based algorithm for synthesizing them.