To execute a variety of collaborative tasks, the cooperation for unmanned aerial vehicles (UAVs) with complicated interactions under dynamic environments is a challenging and critical issue. This paper studies the cooperation issue for UAVs under dynamic environments through an approach of game theory-reinforcement learning (GT-RL) approach, which combines the advantages of both game theory and reinforcement learning. First, to cope with the complicated interactions of UAVs, the cluster of UAVs is modeled as a public goods game with asymmetrical environmental feedback. Then, reinforcement learning is adopted to optimize decision-making of UAVs under unknown and dynamic environments through comparing the dynamic behaviors of UAVs, where a novel dynamics system offers a more comprehensive understanding on cooperative behavior among UAVs. Finally, the simulation results show that the GT-RL approach can effectively promote cooperation among UAVs in completing the collaborative tasks.

This article investigates the global predefined-time consensus (PTC) of multiagent system (MAS) via constructing a duplex communication network. Unlike the traditional finite-/fixed-time convergence, our method allows the upper-bound of settling-time to be an explicit constant, which is tunable and can be set beforehand without relating with the network information, controlling parameters, and initial conditions. In particular, our approach uses a smooth, nonchattering consensus scheme that avoids conventional discontinuous functions like signum and absolute value functions. By the Lyapunov stability analysis, the sufficient criterion is deduced for ensuring the PTC of MAS. Finally, simulations confirm the effectiveness of our proposed nonchattering scheme.

Vertex cover problem is a typical nondeterministic polynomial combinatorial optimization problem with wide applications. In order to seek a near-optimal solution in finite time, this article achieves the goal from the perspective of serial potential game optimization. Specifically, we present the vertex cover problem as a potential game, where the corresponding potential function minimizers are equivalent to the minimum vertex cover state. Then, we propose a novel polynomial-based serial game distributed algorithm, and prove that the algorithm can guarantee that strategies of all vertices converge to a $\epsilon$ -minimum vertex cover ( $\epsilon$ -MVC) state in finite time. Compared with the existing representative optimization algorithms on networks and standard benchmarks, numerical simulations demonstrate our proposed algorithm can effectively balance solution efficiency and computation time. We hope this work provides insight for decision-makers designing a reasonable algorithm when solving nondeterministic polynomial optimization problems, so as to guarantee both solution quality and computation time. Note to Practitioners —Vertex cover problem has a wide range of practical applications. Many distributed optimization algorithms for the vertex cover problem are available in the existing literatures. However, those algorithms mainly pursue high-quality solutions in infinite time. Thus, one of the main challenges is to design a distributed algorithm that guarantees both solution quality and computation time. This article design a polynomial-based serial game algorithm, and prove that it can converge to the $\epsilon$ -MVC state in finite time. This article can serve as a supplement to the existing optimization algorithms for solving the vertex cover problem.

Recently, as an emerging signal processing technology, the semi-tensor product compressed sensing (STP-CS) has attracted widespread attention in the fields of image processing, communications, and bioinformatics. This paper reviews the theoretical foundations, algorithmic designs, and practical applications of STP-CS. It begins by revisiting the basic concepts of compressed sensing (CS) and the definition of the semi-tensor product (STP), followed by a detailed discussion on the theoretical model of STP-CS, optimization of the measurement matrix, and reconstruction algorithms. Furthermore, the paper explores the practical applications of STP-CS in areas such as sensor nodes, visual security, image encryption, and spectrum sensing, analyzing its performance advantages and potential challenges in these fields. A comprehensive analysis indicates that STP-CS offers significant benefits in saving storage space, reducing computational complexity, and enhancing data security, making it a promising technology in the field of signal processing.

Vertex covering a static network has received much attention in the past few years, while vertex covering a dynamical network has rarely been reviewed. In this paper, we newly establish a vertex cover game model of dynamical networks with integrating prospect theory, and design an adaptive evolution scheme for network structure and vertices' strategies to achieve the adaptive covering of a dynamical network concurrently. We define a Nash equilibrium state of the network structure and vertices' strategies. Subsequently, we prove that given the reference point in the active region, the designed adaptive evolution scheme can drive the network structure and vertices' strategies to a Nash cover equilibrium (NCE) state with probability one. Intensive examples verify the effectiveness of the designed adaptive evolution scheme to the vertex covering of dynamical networks, presenting that in the NCE states, the less the average number of covered vertices, the less the average clustering coefficient and the ratio of the average degree of covered vertices to the average degree of uncovered vertices.

The vertex cover of networks is a classical combinatorial optimization problem. In this paper, we investigate the vertex cover problem solved by the memory-based best response update rule, which can not converge to a strict Nash equilibrium (SNE) with memory length m =3D 1. To overcome this shortcoming, a bounded rational behavioral (BRB) update rule is newly proposed in this paper. We prove that the BRB with m =3D 1 can guarantee that the whole vertices' state converges to a SNE. The simulation is carried out to verify that the performance of the proposed BRB update rule on representative networks. Moreover, we also find that a better SNE will be achieved by increasing the selection intensity.