On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results

Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network

This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, a distributed optimization algorithm is proposed based on the internal model principle in which the internal model term can effectively compensate for external environmental disturbances. Secondly, the relationship between the optimal solution and the equilibrium point of the system is discussed through the properties of the Laplacian matrix and graph theory. Some sufficient conditions are derived by using the Lyapunov–Razumikhin theory, which ensures all agents asymptotically reach the optimal value of the distributed optimization problem. Moreover, an aperiodic sampled-data control protocol is proposed, which can be well transformed into the proposed time-varying delay protocol and analyzed by using the Lyapunov–Razumikhin theory. Finally, an example is given to verify the effectiveness of the results

Safe consensus control of cooperative-competitive multi-agent systems via differential privacy

summary:This paper investigates a safe consensus problem for cooperative-competitive multi-agent systems using a differential privacy (DP) approach. Considering that the agents simultaneously interact cooperatively and competitively, we propose a novel DP bipartite consensus algorithm, which guarantees that the DP strategy only works on competitive pairs of agents. We then prove that the proposed algorithm can achieve the mean square bipartite consensus and $(p,r)$-accuracy. Furthermore, a differential privacy analysis is conducted, which shows that the performance of privacy protection is positively correlated with the number of neighbors. Thus, a practical method is established for the agents to select their own privacy levels. Finally, the simulation results are presented to demonstrate the validity of the proposed safe consensus algorithm

Distributed Delay-Tolerant Strategies for Equality-Constraint Sum-Preserving Resource Allocation

This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at all-times. The proposed solutions can address various model nonlinearities, for example, due to quantization and/or saturation. Further, it allows to reach faster convergence or to robustify the solution against impulsive noise or uncertainties. We prove convergence over weakly connected networks using convex analysis and Lyapunov theory. Our findings show that convergence can be reached for general sign-preserving odd nonlinearity. We further propose delay-tolerant mechanisms to handle general bounded heterogeneous time-varying delays over the communication network of agents while preserving all-time feasibility. This work finds application in CPU scheduling and coverage control among others. This paper advances the state-of-the-art by addressing (i) possible nonlinearity on the agents/links, meanwhile handling (ii) resource-demand feasibility at all times, (iii) uniform-connectivity instead of all-time connectivity, and (iv) possible heterogeneous and time-varying delays. To our best knowledge, no existing work addresses contributions (i)-(iv) altogether. Simulations and comparative analysis are provided to corroborate our contributions

A Study on the Hierarchical Control Structure of the Islanded Microgrid

The microgrid is essential in promoting the power system’s resilience through its ability to host small-scale DG units. Furthermore, the microgrid can isolate itself during main grid faults and supply its demands. However, islanded operation of the microgrid is challenging due to difficulties in frequency and voltage control. In islanded mode, grid-forming units collaborate to control the frequency and voltage. A hierarchical control structure employing the droop control technique provides these control objectives in three consecutive levels: primary, secondary, and tertiary. However, challenges associated with DG units in the vicinity of distribution networks limit the effectiveness of the islanded mode of operation.In MV and LV distribution networks, the X/R ratio is low; hence, the frequency and voltage are related to the active and reactive power by line parameters. Therefore, frequency and voltage must be tuned for changes in active or reactive powers. Furthermore, the line parameters mismatch causes the voltage to be measured differently at each bus due to the different voltage drops in the lines. Hence, a trade-off between voltage regulation and reactive power-sharing is formed, which causes either circulating currents for voltage mismatch or overloading for reactive power mismatch. Finally, the economic dispatch is usually implemented in tertiary control, which takes minutes to hours. Therefore, an estimation algorithm is required for load and renewable energy quantities forecasting. Hence, prediction errors may occur that affect the stability and optimality of the control. This dissertation aims to improve the power system resilience by enhancing the operation of the islanded microgrid by addressing the above-mentioned issues. Firstly, a linear relationship described by line parameters is used in droop control at the primary control level to accurately control the frequency and voltage based on measured active and reactive power. Secondly, an optimization-based consensus secondary control is presented to manage the trade-off between voltage regulation and reactive power-sharing in the inductive grid with high line parameters mismatch. Thirdly, the economic dispatch-based secondary controller is implemented in secondary control to avoid prediction errors by depending on the measured active and reactive powers rather than the load and renewable energy generation estimation. The developed methods effectively resolve the frequency and voltage control issues in MATLAB/SIMULINK simulations