Minimum Number of Probes for Brain Dynamics Observability

In this paper, we address the problem of placing sensor probes in the brain such that the system dynamics' are generically observable. The system dynamics whose states can encode for instance the fire-rating of the neurons or their ensemble following a neural-topological (structural) approach, and the sensors are assumed to be dedicated, i.e., can only measure a state at each time. Even though the mathematical description of brain dynamics is (yet) to be discovered, we build on its observed fractal characteristics and assume that the model of the brain activity satisfies fractional-order dynamics. Although the sensor placement explored in this paper is particularly considering the observability of brain dynamics, the proposed methodology applies to any fractional-order linear system. Thus, the main contribution of this paper is to show how to place the minimum number of dedicated sensors, i.e., sensors measuring only a state variable, to ensure generic observability in discrete-time fractional-order systems for a specified finite interval of time. Finally, an illustrative example of the main results is provided using electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720

A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z)

In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. Firstly, a vector matroid is defined over F(z). Secondly, the full rank conditions of [sI-A|B] are derived in terms of the concept related to matroid theory, such as rank, base and union. Then the sufficient condition for the linear system and composite system over F(z) to be structurally controllable is obtained. Finally, this paper gives several examples to demonstrate that the married-theoretic approach is simpler than other existing approaches

State Omniscience for Cooperative Local Catalog Maintenance of Close Proximity Satellite Systems

Resiliency in multi-agent system navigation is reliant on the inherent ability of the system to withstand, overcome, or recover from adverse conditions and disturbances. In large part, resiliency is achieved through reducing the impact of critical failure points to the success and/or performance of the system. In this view, decentralized multi-agent architectures have become an attractive solution for multi-agent navigation, but decentralized architectures place the burden of information acquisition directly on the agents themselves. In fact, the design of distributed estimators has been a growing interest to enable complex multi-sensor/multi-agent tasks. In such scenarios, it is important that each local estimator converges to the true global system state - a quality known as state omniscience. Most previous related work has focused on the design of such systems under varying assumptions on the graph topology with simplified information fusion schemes. Contrarily, this work introduces characterizations of state omniscience under generalized graph topologies and generalized information fusion schemes. State omniscience is discussed analogously to observability from classical control theory; and a collection of necessary and sufficient conditions for a distributed estimator to be state omniscient are presented. This dissertation discusses this phenomena in terms of an on-orbit scenarios dubbed the local catalog maintenance problem and the cooperative local catalog maintenance problem. The goal of each agent is to maintain their catalog of all bodies (objects and agents) within this neighborhood through onboard angles-only measurements and cooperative communication with the other agents. A central supervisor selects the target body for each agent, a local controller tracks the selected target body for each agent, and a local estimator coalesces both an agent\u27s measurements and state estimates provided by neighboring agents within the communication graph. Numerical results are provided to demonstrate the supervisor\u27s ability to select an appropriate target subject to an uncertainty threshold, the controller\u27s ability to track the selected target, and the estimator\u27s ability to maintain an accurate and precise estimate of each of the bodies in the local environment

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page