Vikas Yadav

Stabilization of nested systems with uncertain subsystem communication channels

This paper addresses the design of stabilizing controllers for a nested control system where the controller is realized in a distributed manner, considering uncertainty not only in the controller-to-plant and plant-to-controller channels but also in the nest-to-nest, subcontroller-to-subcontroller communication. An input-output approach is taken. Two appropriate controller architectures that stabilize the entire system with the various components subject to uncertainty and noise are addressed. We present controller synthesis procedures to address deterministic uncertainty and stochastic uncertainty, that model packet-loss in the Internet.

Phase Transitions on Fixed Connected Graphs and Random Graphs in the Presence of Noise

In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected graph or a random graph process, and each agent, taking bipolar value either +1 or -1, updates its value according to its previous value and the noisy measurements of the values of the agents connected to it. We present proofs for the occurrence of the following phase transition behavior: At a noise level higher than some threshold, the system generates symmetric behavior (vapor or melt of magnetization) or disagreement; whereas at a noise level lower than the threshold, the system exhibits spontaneous symmetry breaking (solid or magnetization) or consensus. The threshold is found analytically. The phase transition occurs for any dimension. Finally, we demonstrate the phase transition behavior and all analytic results using simulations. This result may be found useful in the study of the collective behavior of complex systems under communication constraints.

Distributed Architectures and Implementations of Observer Based Controllers for Performance Optimization

In this paper we address the problem of synthesizing controllers that have to be implemented distributively and have structure. The effect of sub-controller to sub-controller communication noise on stability and performance is considered. Using an observer based controller parameterization, we provide suitable stabilizing sub-controller architectures that directly take into account the effect of communication noise on performance. In particular, the overall performance optimization can be cast as a convex problem in the Youla-Kucera parameter Q. Similar results hold for banded controller structures, i.e., when there is also a delay in the subsystem to subsystem communication

Architectures for Distributed Controller With Sub-Controller Communication Uncertainty

Recent technology has led to systems with architectures that distribute the controller effort over sub-controllers to respect information flow and/or resource constraints. The associated communication uncertainty between sub-controllers partly governs the performance of the controller. The related controller synthesis methodology has to address internal stability concerns and has to incorporate the effect of communication uncertainty into the performance metric. In this article, it is demonstrated that different canonical distributed architectures derived from a centralized design can result in appreciably different performance. Architectures of information flow that result in convex optimization problems are developed and synthesis methods to incorporate robustness with respect to model uncertainty of communication channels are obtained. The efficacy of the approach is demonstrated on application problems.

Distributed architectures and implementations of observer based controllers for performance optimization

In this paper we address the problem of synthesizing controllers that have to be implemented distributively and have structure. The effect of sub-controller to sub-controller communication noise on stability and performance is considered. Using an observer based controller parameterization, we provide suitable stabilizing sub-controller architectures that directly take into account the effect of communication noise on performance. In particular, the overall performance optimization can be cast as a convex problem in the Youla-Kucera parameter Q. Similar results hold for banded controller structures, i.e., when there is also a delay in the subsystem to subsystem communication.

Architectures for distributed control for performance optimization in presence of sub-controller communication noise

In this paper, we use state space approach to give a sufficient condition for internal stability of the closed loop system when the centralized stabilizing controller is implemented in a distributive manner. Using this condition, we show that the centralized stabilizing controller for a 2-nest system can be split into two sub-controllers without affecting the internal stability. The effect of sub-controller to sub-controller communication noise on the performance is considered along with the constraint on strength of sub-controller to sub-controller communication signal. We take an input-output approach. In a 2-nest case, we obtain a sufficient condition for splitting the stabilizing controller such that the overall performance optimization can be cast as a convex problem in the Youla-Kucera parameter Q. We also present an architecture for distributive implementation of banded structure controllers such that all closed loop maps are affine in Q