Coordination and Control of Distributed Discrete Event Systems under Actuator and Sensor Faults

We investigate the coordination and control problems of distributed discrete event systems that are composed of multiple subsystems subject to potential actuator and/or sensor faults. We model actuator faults as local controllability loss of certain actuator events and sensor faults as observability failure of certain sensor readings, respectively. Starting from automata-theoretic models that characterize behaviors of the subsystems in the presence of faulty actuators and/or sensors, we establish necessary and sufficient conditions for the existence of actuator and sensor fault tolerant supervisors, respectively, and synthesize appropriate local post-fault supervisors to prevent the post-fault subsystems from jeopardizing local safety requirements. Furthermore, we apply an assume-guarantee coordination scheme to the controlled subsystems for both the nominal and faulty subsystems so as to achieve the desired specifications of the system. A multi-robot coordination example is used to illustrate the proposed coordination and control architecture.Comment: 33 pages; 20 figures; 1 tabl

Lepton-antilepton Annihilation in the Massless Schwinger Model

We evaluate the next-to-leading order radiative corrections to a process in the massless Schwinger model that is the analogue of the $e^+e^-$ inclusive annihilation into hadrons process in QCD. We then carry out an asymptotic expansion of the calculable exact result and find that it agrees with the perturbative answer. However, we also find that higher orders in the asymptotic expansion involve terms that depend on the logarithm of the strong coupling constant.Comment: (9 pages

Distributed Byzantine Tolerant Stochastic Gradient Descent in the Era of Big Data

The recent advances in sensor technologies and smart devices enable the collaborative collection of a sheer volume of data from multiple information sources. As a promising tool to efficiently extract useful information from such big data, machine learning has been pushed to the forefront and seen great success in a wide range of relevant areas such as computer vision, health care, and financial market analysis. To accommodate the large volume of data, there is a surge of interest in the design of distributed machine learning, among which stochastic gradient descent (SGD) is one of the mostly adopted methods. Nonetheless, distributed machine learning methods may be vulnerable to Byzantine attack, in which the adversary can deliberately share falsified information to disrupt the intended machine learning procedures. Therefore, two asynchronous Byzantine tolerant SGD algorithms are proposed in this work, in which the honest collaborative workers are assumed to store the model parameters derived from their own local data and use them as the ground truth. The proposed algorithms can deal with an arbitrary number of Byzantine attackers and are provably convergent. Simulation results based on a real-world dataset are presented to verify the theoretical results and demonstrate the effectiveness of the proposed algorithms

Mixture Gaussian Signal Estimation with L_infty Error Metric

We consider the problem of estimating an input signal from noisy measurements in both parallel scalar Gaussian channels and linear mixing systems. The performance of the estimation process is quantified by the $\ell_\infty$ norm error metric. We first study the minimum mean $\ell_\infty$ error estimator in parallel scalar Gaussian channels, and verify that, when the input is independent and identically distributed (i.i.d.) mixture Gaussian, the Wiener filter is asymptotically optimal with probability 1. For linear mixing systems with i.i.d. sparse Gaussian or mixture Gaussian inputs, under the assumption that the relaxed belief propagation (BP) algorithm matches Tanaka's fixed point equation, applying the Wiener filter to the output of relaxed BP is also asymptotically optimal with probability 1. However, in order to solve the practical problem where the signal dimension is finite, we apply an estimation algorithm that has been proposed in our previous work, and illustrate that an $\ell_\infty$ error minimizer can be approximated by an $\ell_p$ error minimizer provided the value of $p$ is properly chosen

On the Privacy Guarantees of Gossip Protocols in General Networks

Recently, the privacy guarantees of information dissemination protocols have attracted increasing research interests, among which the gossip protocols assume vital importance in various information exchange applications. In this work, we study the privacy guarantees of gossip protocols in general networks in terms of differential privacy and prediction uncertainty. First, lower bounds of the differential privacy guarantees are derived for gossip protocols in general networks in both synchronous and asynchronous settings. The prediction uncertainty of the source node given a uniform prior is also determined. For the private gossip algorithm, the differential privacy and prediction uncertainty guarantees are derived in closed form. Moreover, considering that these two metrics may be restrictive in some scenarios, the relaxed variants are proposed. It is found that source anonymity is closely related to some key network structure parameters in the general network setting. Then, we investigate information spreading in wireless networks with unreliable communications, and quantify the tradeoff between differential privacy guarantees and information spreading efficiency. Finally, considering that the attacker may not be present at the beginning of the information dissemination process, the scenario of delayed monitoring is studied and the corresponding differential privacy guarantees are evaluated

Wiener Filters in Gaussian Mixture Signal Estimation with Infinity-Norm Error

Consider the estimation of a signal ${\bf x}\in\mathbb{R}^N$ from noisy observations ${\bf r=x+z}$, where the input~${\bf x}$ is generated by an independent and identically distributed (i.i.d.) Gaussian mixture source, and ${\bf z}$ is additive white Gaussian noise (AWGN) in parallel Gaussian channels. Typically, the $\ell_2$-norm error (squared error) is used to quantify the performance of the estimation process. In contrast, we consider the $\ell_\infty$-norm error (worst case error). For this error metric, we prove that, in an asymptotic setting where the signal dimension $N\to\infty$, the $\ell_\infty$-norm error always comes from the Gaussian component that has the largest variance, and the Wiener filter asymptotically achieves the optimal expected $\ell_\infty$-norm error. The i.i.d. Gaussian mixture case is easily applicable to i.i.d. Bernoulli-Gaussian distributions, which are often used to model sparse signals. Finally, our results can be extended to linear mixing systems with i.i.d. Gaussian mixture inputs, in settings where a linear mixing system can be decoupled to parallel Gaussian channels.Comment: To appear in IEEE Trans. Inf. Theor

SEARCHING FOR HIGGS BOSONS ON LHC USING bb-TAGGING

We demonstrate that the detection of the SM and MSSM Higgs bosons will be possible at the LHC via t\anti t b\anti b and b\anti b b\anti b final state, provided $b$-tagging can be performed with good efficiency and purity.Comment: Talk presented at BEYOUND THE STANDARD MODEL IV conference; Taho City, 12/19/94, 3 pages

Distributed Communication-aware Motion Planning for Networked Mobile Robots under Formal Specifications

Control and communication are often tightly coupled in motion planning of networked mobile robots, due to the fact that robotic motions will affect the overall communication quality, and the quality of service (QoS) of the communication among the robots will in turn affect their coordination performance. In this paper, we propose a control theoretical motion planning framework for a team of networked mobile robots in order to accomplish high-level spatial and temporal motion objectives while optimizing communication QoS. Desired motion specifications are formulated as Signal Temporal Logic (STL), whereas the communication performances to be optimized are captured by recently proposed Spatial Temporal Reach and Escape Logic (STREL) formulas. Both the STL and STREL specifications are encoded as mixed integer linear constraints posed on the system and/or environment state variables of the mobile robot network, where satisfactory control strategies can be computed by exploiting a distributed model predictive control (MPC) approach. To the best of the authors' knowledge, we are the first to study controller synthesis for STREL specifications. A two-layer hierarchical MPC procedure is proposed to efficiently solve the problem, whose soundness and completeness are formally ensured. The effectiveness of the proposed framework is validated by simulation examples

Distributed Communication-aware Motion Planning for Multi-agent Systems from STL and SpaTeL Specifications

In future intelligent transportation systems, networked vehicles coordinate with each other to achieve safe operations based on an assumption that communications among vehicles and infrastructure are reliable. Traditional methods usually deal with the design of control systems and communication networks in a separated manner. However, control and communication systems are tightly coupled as the motions of vehicles will affect the overall communication quality. Hence, we are motivated to study the co-design of both control and communication systems. In particular, we propose a control theoretical framework for distributed motion planning for multi-agent systems which satisfies complex and high-level spatial and temporal specifications while accounting for communication quality at the same time. Towards this end, desired motion specifications and communication performances are formulated as signal temporal logic (STL) and spatial-temporal logic (SpaTeL) formulas, respectively. The specifications are encoded as constraints on system and environment state variables of mixed integer linear programs (MILP), and upon which control strategies satisfying both STL and SpaTeL specifications are generated for each agent by employing a distributed model predictive control (MPC) framework. Effectiveness of the proposed framework is validated by a simulation of distributed communication-aware motion planning for multi-agent systems.Comment: Submitted for publication on 2017 IEEE Conference on Decision and Control (CDC2017

Communication-aware Motion Planning for Multi-agent Systems from Signal Temporal Logic Specifications

We propose a mathematical framework for synthesizing motion plans for multi-agent systems that fulfill complex, high-level and formal local specifications in the presence of inter-agent communication. The proposed synthesis framework consists of desired motion specifications in temporal logic (STL) formulas and a local motion controller that ensures the underlying agent not only to accomplish the local specifications but also to avoid collisions with other agents or possible obstacles, while maintaining an optimized communication quality of service (QoS) among the agents. Utilizing a Gaussian fading model for wireless communication channels, the framework synthesizes the desired motion controller by solving a joint optimization problem on motion planning and wireless communication, in which both the STL specifications and the wireless communication conditions are encoded as mixed integer-linear constraints on the variables of the agents' dynamical states and communication channel status. The overall framework is demonstrated by a case study of communication-aware multi-robot motion planning and the effectiveness of the framework is validated by simulation results.Comment: 6 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.1025