Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty

Motivated by the massive deployment of power-hungry data centers for service provisioning, we examine the problem of routing in optical networks with the aim of minimizing traffic-driven power consumption. To tackle this issue, routing must take into account energy efficiency as well as capacity considerations; moreover, in rapidly-varying network environments, this must be accomplished in a real-time, distributed manner that remains robust in the presence of random disturbances and noise. In view of this, we derive a pricing scheme whose Nash equilibria coincide with the network's socially optimum states, and we propose a distributed learning method based on the Boltzmann distribution of statistical mechanics. Using tools from stochastic calculus, we show that the resulting Boltzmann routing scheme exhibits remarkable convergence properties under uncertainty: specifically, the long-term average of the network's power consumption converges within $\varepsilon$ of its minimum value in time which is at most $\tilde O(1/\varepsilon^2)$, irrespective of the fluctuations' magnitude; additionally, if the network admits a strict, non-mixing optimum state, the algorithm converges to it - again, no matter the noise level. Our analysis is supplemented by extensive numerical simulations which show that Boltzmann routing can lead to a significant decrease in power consumption over basic, shortest-path routing schemes in realistic network conditions.Comment: 24 pages, 4 figure

CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systems

The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the analytical form of our CaRT safety filter formally ensures safe maneuvers of nonlinear multi-agent systems, optimally with minimal deviation from the learning-based policy. Second, in off-nominal settings, the analytical form of our CaRT robust filter optimally tracks the certified safe trajectory, generated by the previous layer in the hierarchy, the CaRT safety filter. We show using contraction theory that CaRT guarantees safety and the exponential boundedness of the trajectory tracking error, even under the presence of deterministic and stochastic disturbance. Also, the hierarchical nature of CaRT enables enhancing its robustness for safety just by its superior tracking to the certified safe trajectory, thereby making it suitable for off-nominal scenarios with large disturbances. This is a major distinction from conventional safety function-driven approaches, where the robustness originates from the stability of a safe set, which could pull the system over-conservatively to the interior of the safe set. Our log-barrier formulation in CaRT allows for its distributed implementation in multi-agent settings. We demonstrate the effectiveness of CaRT in several examples of nonlinear motion planning and control problems, including optimal, multi-spacecraft reconfiguration.Comment: IEEE Conference on Decision and Control (CDC), Preprint Version, Accepted July, 202

Smart Distributed Generation System Event Classification using Recurrent Neural Network-based Long Short-term Memory

High penetration of distributed generation (DG) sources into a decentralized power system causes several disturbances, making the monitoring and operation control of the system complicated. Moreover, because of being passive, modern DG systems are unable to detect and inform about these disturbances related to power quality in an intelligent approach. This paper proposed an intelligent and novel technique, capable of making real-time decisions on the occurrence of different DG events such as islanding, capacitor switching, unsymmetrical faults, load switching, and loss of parallel feeder and distinguishing these events from the normal mode of operation. This event classification technique was designed to diagnose the distinctive pattern of the time-domain signal representing a measured electrical parameter, like the voltage, at DG point of common coupling (PCC) during such events. Then different power system events were classified into their root causes using long short-term memory (LSTM), which is a deep learning algorithm for time sequence to label classification. A total of 1100 events showcasing islanding, faults, and other DG events were generated based on the model of a smart distributed generation system using a MATLAB/Simulink environment. Classifier performance was calculated using 5-fold cross-validation. The genetic algorithm (GA) was used to determine the optimum value of classification hyper-parameters and the best combination of features. The simulation results indicated that the events were classified with high precision and specificity with ten cycles of occurrences while achieving a 99.17% validation accuracy. The performance of the proposed classification technique does not degrade with the presence of noise in test data, multiple DG sources in the model, and inclusion of motor starting event in training samples

Resilient Autonomous Control of Distributed Multi-agent Systems in Contested Environments

An autonomous and resilient controller is proposed for leader-follower multi-agent systems under uncertainties and cyber-physical attacks. The leader is assumed non-autonomous with a nonzero control input, which allows changing the team behavior or mission in response to environmental changes. A resilient learning-based control protocol is presented to find optimal solutions to the synchronization problem in the presence of attacks and system dynamic uncertainties. An observer-based distributed H_infinity controller is first designed to prevent propagating the effects of attacks on sensors and actuators throughout the network, as well as to attenuate the effect of these attacks on the compromised agent itself. Non-homogeneous game algebraic Riccati equations are derived to solve the H_infinity optimal synchronization problem and off-policy reinforcement learning is utilized to learn their solution without requiring any knowledge of the agent's dynamics. A trust-confidence based distributed control protocol is then proposed to mitigate attacks that hijack the entire node and attacks on communication links. A confidence value is defined for each agent based solely on its local evidence. The proposed resilient reinforcement learning algorithm employs the confidence value of each agent to indicate the trustworthiness of its own information and broadcast it to its neighbors to put weights on the data they receive from it during and after learning. If the confidence value of an agent is low, it employs a trust mechanism to identify compromised agents and remove the data it receives from them from the learning process. Simulation results are provided to show the effectiveness of the proposed approach