Discretized Distributed Optimization over Dynamic Digraphs

We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic networks under switching topologies, e.g., in mobile multi-agent systems and volatile networks due to link failures. Compared to many existing lines of work, there is no need for bi-stochastic weight designs on the links. The existing literature mostly needs the link weights to be stochastic using specific weight-design algorithms needed both at the initialization and at all times when the topology of the network changes. This paper eliminates the need for such algorithms and paves the way for distributed optimization over time-varying digraphs. We derive the bound on the gradient-tracking step-size and discrete time-step for convergence and prove dynamic stability using arguments from consensus algorithms, matrix perturbation theory, and Lyapunov theory. This work, particularly, is an improvement over existing stochastic-weight undirected networks in case of link removal or packet drops. This is because the existing literature may need to rerun time-consuming and computationally complex algorithms for stochastic design, while the proposed strategy works as long as the underlying network is weight-symmetric and balanced. The proposed optimization framework finds applications to distributed classification and learning

Back-Pressure Traffic Signal Control in the Presence of Noisy Queue Information

In this paper, we consider decentralized traffic signal control policies using the max-weight algorithm when the queue size measurement is noisy. We first show analytically that the standard max-weight algorithm is throughput optimal even under noisy queue measurements. However, the average steady-state queue lengths and subsequently the average delays are increased. In order to alleviate the effect of these noisy measurements we add filtering to the max-weight algorithm; more specifically, we propose the Filtered-max-weight algorithm, which is based on particle filtering. We demonstrate via simulations that the Filtered-max-weight algorithm performs better than the standard max-weight algorithm in the presence of noisy measurements

Reduced-order damping controller design for power systems via frequency-weighted model reduction

A damping controller is essential for the smooth operation of power systems. Different types of disturbances result in low-frequency oscillations, which propagate in all the interconnected machines. A safe operation of an interconnected power system requires sufficient damping of these oscillations. Otherwise, there are high chances of blackouts. As the order of the interconnected power system model increases, the analytical controller design procedures result in a high-order controller, which is impractical to implement. In this paper, we demonstrate that the frequency-weighted model order reduction can be used to effectively design a reduced-order loop shaping damping controller. To that end, we design an H-Infinity damping controller for the interconnection of the New England test system (NETS) with the New York power system (NYPS) with an additional constraint of pole-placement. The time-domain simulations of disturbed system with and without controller are performed using MATLAB. Results show that the designed controller successfully removes the low frequency oscillations, maintains synchronism among generators, and guarantees the stability of the power system