Quantized Zeroth-Order Gradient Tracking Algorithm for Distributed Nonconvex Optimization Under Polyak- [Formula: see text] ojasiewicz Condition.

This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak- [Formula: see text] ojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.

The female germ unit is essential for pollen tube funicular guidance in Arabidopsis thaliana.

In angiosperm, two immotile sperm cells are delivered to the female gametes for fertilization by a pollen tube, which perceives guidance cues from ovules at least at two critical sites, micropyle for short-distance guidance and funiculus for comparably longer distance guidance. Compared with the great progress in understanding pollen tube micropylar guidance, little is known about the signaling for funicular guidance. Here, we show that funiculus plays an important role in pollen tube guidance and report that female gametophyte (FG) plays a critical role in funicular guidance by analysis of a 3-dehydroquinate synthase (DHQS) mutant. Loss function of DHQS in FG interrupts pollen tube funicular guidance, suggesting that the guiding signal is generated from FG. We show the evidence that the capacity of funicular guidance is established during FG functional specification after the establishment of cell identity. Specific expression of DHQS in the synergid cells, central cells, or egg cells can rescue funicular guidance defect in dhqs/+, indicating all the female germ unit cells are involved in the funicular guidance. The finding reveals that the attracting signal of pollen tube funicular guidance was generated at a site and stage manner and provides novel clue to locate and search for the signal.

Semiglobal Suboptimal Output Regulation for Heterogeneous Multi-Agent Systems With Input Saturation via Adaptive Dynamic Programming.

This article considers the semiglobal cooperative suboptimal output regulation problem of heterogeneous multi-agent systems with unknown agent dynamics in the presence of input saturation. To solve the problem, we develop distributed suboptimal control strategies from two perspectives, namely, model-based and data-driven. For the model-based case, we design a suboptimal control strategy by using the low-gain technique and output regulation theory. Moreover, when the agents' dynamics are unknown, we design a data-driven algorithm to solve the problem. We show that proposed control strategies ensure each agent's output gradually follows the reference signal and achieves interference suppression while guaranteeing closed-loop stability. The theoretical results are illustrated by a numerical simulation example.

Pull-Based Distributed Event-Triggered Consensus for Multiagent Systems With Directed Topologies.

This paper mainly investigates consensus problem with a pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time, and the next triggering time of this agent is determined by its in-neighbors' information. The general directed topologies, including irreducible and reducible cases, are investigated. The scenario of distributed continuous communication is considered first. It is proved that if the network topology has a spanning tree, then the event-triggered coupling algorithm can realize the consensus for the multiagent system. Then, the results are extended to discontinuous communication, i.e., self-triggered control, where each agent computes its next triggering time in advance without having to observe the system's states continuously. The effectiveness of the theoretical results is illustrated by a numerical example finally.

Stability of Analytic Neural Networks With Event-Triggered Synaptic Feedbacks.

In this paper, we investigate stability of a class of analytic neural networks with the synaptic feedback via event-triggered rules. This model is general and include Hopfield neural network as a special case. These event-trigger rules can efficiently reduces loads of computation and information transmission at synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of the other neurons at its latest triggering time but changes at its next triggering time, which is determined by a certain criterion. It is proved that every trajectory of the analytic neural network converges to certain equilibrium under this event-triggered rule for all the initial values except a set of zero measure. The main technique of the proof is the Lojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the efficiency of the theoretical results.