Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Distributed averaging over communication networks:Fragility, robustness and opportunities

Distributed averaging, a canonical operation among many natural interconnected systems, has found applications in a tremendous variety of applied fields, including statistical physics, signal processing, systems and control, communication and social science. As information exchange is a central part of distributed averaging systems, it is of practical as well as theoretical importance to understand various properties/limitations of those systems in the presence of communication constraints and devise new algorithms to alleviate those limitations. We study the fragility of a popular distributed averaging algorithm when the information exchange among the nodes is limited by communication delays, fading connections and additive noise. We show that the otherwise well studied and benign multi-agent system can generate a collective global complex behavior. We characterize this behavior, common to many natural and human-made interconnected systems, as a collective hyper-jump diffusion process and as a L\\u27{e}vy flights process in a special case. We further describe the mechanism for its emergence and predict its occurrence, under standard assumptions, by checking the Mean Square instability of a certain part of the system. We show that the strong connectivity property of the network topology guarantees that the complex behavior is global and manifested by all the agents in the network, even though the source of uncertainty is localized. We provide novel computational analysis of the MS stability index under spatially invariant structures and gain certain qualitative as well as quantitative insights of the system. We then focus on design of agents\u27 dynamics to increase the robustness of distributed averaging system to topology variations. We provide a general structure of distributed averaging systems where individual agents are modeled by LTI systems. We show the problem of designing agents\u27 dynamics for distributed averaging is equivalent to an $\mathcal{H}_{\infty}$ minimization problem. In this way, we could use tools from robust control theory to build the distributed averaging system where the design is fully distributed and scalable with the size of the network. It is also shown that the agents could be used in different fixed networks and networks with speical time varying interconnections. We develop new iterative distributed averaging algorithms which allow agents to compute the average quantity in the presence of additive noise and random changing interconnections. The algorithm relaxes several previous restrictive assumptions on distributed averaging under uncertainties, such as diminishing step size rule, doubly stochastic weights, symmetric link switching styles, etc, and introduces novel mechanism of network feedback to mitigate effects of communication uncertainties on information aggregation. Based on the robust distributed averaging algorithm, we propose continuous as well as discrete time computation models to solve the distributed optimization problem where the objective function is formed by the summation of convex functions of the same variable. The algorithm shows faster convergence speed than existing ones and exhibits robustness to additive noise, which is the main source of limitation on algorithms based on convex mixing. It is shown that agents with simple dynamics and gradient sensing abilities could collectively solve complicated convex optimization problems. Finally, we generalize this algorithm to build a general framework forconstrained convex optimization problems. This framework is shown to be particularly effective to derive solutions for distributed decision making problems and lead to a systems perspective for convex optimization