Average Consensus and Stability Analysis in Networked Dynamic Systems

This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is a high dimensional vector as a solution of the highly nonlinear first order dynamics with and without drift terms. This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is high Under the proposed interaction rules, agreements as a common average value or an average trajectory are reached, solving finitetime average consensus and the multisystem equilibrium is controlled leading to the finitetime stability of each system origin. Sufficient conditions are achieved using the Lyapunov techniques and the graph theory. In networked dynamic systems, the theoretical results of the paper cover a large class of underactuated autonomous systems as formation flight, multivehicle coordination, and heterogeneous multisystem behaviors. Some examples are introduced in simulation which approves the proposed protocols.

Topological sampling through windings

We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

Iterative Learning Consensus Control for Nonlinear Partial Difference Multiagent Systems with Time Delay

This paper considers the consensus control problem of nonlinear spatial-temporal hyperbolic partial difference multiagent systems and parabolic partial difference multiagent systems with time delay. Based on the system’s own fixed topology and the method of generating the desired trajectory by introducing virtual leader, using the consensus tracking error between the agent and the virtual leader agent and neighbor agents in the last iteration, an iterative learning algorithm is proposed. The sufficient condition for the system consensus error to converge along the iterative axis is given. When the iterative learning number k approaches infinity, the consensus error in the sense of the L 2 norm between all agents in the system will converge to zero. Furthermore, simulation results illustrate the effectiveness of the algorithm.

Modeling of Photovoltaic Module

A Photovoltaic (PV) cell is a device that converts sunlight or incident light into direct current (DC) based electricity. Among other forms of renewable energy, PV-based power sources are considered a cleaner form of energy generation. Due to lower prices and increased efficiency, they have become much more popular than any other renewable energy source. In a PV module, PV cells are connected in a series and parallel configuration, depending on the voltage and current rating, respectively. Hence, PV modules tend to have a fixed topology. However, in the case of partial shading, mismatching or failure of a single PV cell can lead to many anomalies in a PV module’s functioning. If proper attention is not given, it can lead to the forward biasing of healthy PV cells in the module, causing them to consume the electricity instead of producing it, hence reducing the PV module’s overall efficiency. Hence, to further the PV module research, it is essential to have an approximate way to model them. Doing so allows for understanding the design’s pros and cons before deploying the PV module-based power system in the field. In the last decade, many mathematical models for PV cell simulation and modeling techniques have been proposed. The most popular among all the techniques are diode based PV modeling. In this book chapter, the author will present a double diode based PV cell modeling. Later, the PV module modeling will be presented using these techniques that incorporate mismatch, partial shading, and open/short fault. The partial shading and mismatch are reduced by incorporating a bypass diode along with a group of four PV cells. The mathematical model for showing the effectiveness of bypass diode with PV cells in reducing partial shading effect will also be presented. Additionally, in recent times besides fixed topology of series–parallel, Total Cross-Tied (TCT), Bridge Link (BL), and Honey-Comb (H-C) have shown a better capability in dealing with partial shading and mismatch. The book chapter will also cover PV module modeling using TCT, BL, and H-C in detail.

Local genetic context shapes the function of a gene regulatory network

Gene expression levels are influenced by multiple coexisting molecular mechanisms. Some of these interactions such as those of transcription factors and promoters have been studied extensively. However, predicting phenotypes of gene regulatory networks (GRNs) remains a major challenge. Here, we use a well-defined synthetic GRN to study in Escherichia coli how network phenotypes depend on local genetic context, i.e. the genetic neighborhood of a transcription factor and its relative position. We show that one GRN with fixed topology can display not only quantitatively but also qualitatively different phenotypes, depending solely on the local genetic context of its components. Transcriptional read-through is the main molecular mechanism that places one transcriptional unit (TU) within two separate regulons without the need for complex regulatory sequences. We propose that relative order of individual TUs, with its potential for combinatorial complexity, plays an important role in shaping phenotypes of GRNs.

Consensus Control of Multi-agent Robot System with State Delay Based on Fractional-Order Iterative Learning Control Algorithm

This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDα). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation.