A Quantum Spatial Graph Convolutional Neural Network Model on Quantum Circuits.

This article proposes a quantum spatial graph convolutional neural network (QSGCN) model that is implementable on quantum circuits, providing a novel avenue to processing non-Euclidean type data based on the state-of-the-art parameterized quantum circuit (PQC) computing platforms. Four basic blocks are constructed to formulate the whole QSGCN model, including the quantum encoding, the quantum graph convolutional layer, the quantum graph pooling layer, and the network optimization. In particular, the trainability of the QSGCN model is analyzed through discussions on the barren plateau phenomenon. Simulation results from various types of graph data are presented to demonstrate the learning, generalization, and robustness capabilities of the proposed quantum neural network (QNN) model.

Pinning Control of Multiplex Dynamical Networks Using Spectral Graph Theory.

Pinning control has been attracting wide attention for the study of various complex networks for decades. This article explores grounded theory on the pinning synchronization of the emerging multiplex dynamical networks. The multiplex dynamical networks under study can describe many real-world scenarios, in which different layers have distinct individual dynamics of node. In this work, we build the bridge between multiplex structures and network dynamics by using the Lyapunov stability theory and the spectral graph theory. Furthermore, by analyzing spectral properties of the grounded super-Laplacian matrices, we set up several graph-based synchronization criteria for multiplex networks via pinning control. In addition, we overcome the difficulties induced by distinct node dynamics in different layers, and find that interlayer coupling strengths promote intralayer synchronization of multiplex networks. Finally, a collection of numerical simulations verifies the effectiveness of theoretical results.

Adaptive Fuzzy Tracking Control With Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems.

For strict-feedback systems with mismatched uncertainties, adaptive fuzzy control techniques are developed to provide global prescribed performance with prescribed-time convergence. First, a class of prescribed-time prescribed performance functions are designed to quantify the performance constraints of the tracking error. Additionally, a novel error transformation function is provided to eliminate the initial value limitations and resolve the singularity issue in previous research. To ensure the convergence of the tracking error into a prescribed bounded region within a prescribed time and satisfactory transient performance, controllers with or without approximating structures are established. Notably, the settling time and initial condition of the prescribed performance function are completely independent of the initial tracking error and system parameters, thereby improving upon existing results. Furthermore, the disadvantage of the semi-global boundedness of tracking error induced by dynamic surface control can be eliminated through the use of a novel Lyapunov-like energy function. Finally, the effectiveness of the proposed strategies is validated through numerical simulations performed on practical examples.

Finite-Time Time-Varying Formation Tracking for Heterogeneous Nonlinear Multiagent Systems Using Adaptive Output Regulation.

The finite-time output time-varying formation tracking (TVFT) problem for heterogeneous nonlinear multiagent system (MAS) is investigated in this article, where the dynamics of the agents can be nonidentical, and leader's input is unknown. The target of this article is that the outputs of followers need to track leader's output and realize the desired formation in finite time. First, for removing the assumption that all agents are required to know the information of leader's system matrices and the upper boundary of its unknown control input in previous studies, a kind of finite-time observer is constructed by exploiting the neighboring information, which can estimate not only the leader's state and system matrices but also can compensate for the effects of unknown input. On the basis of the developed finite-time observers and adaptive output regulation method, a novel finite-time distributed output TVFT controller is proposed with the help of the technique of coordinate transformation by introducing an extra variable, which removes the assumption that the generalized inverse matrix of follows' input matrix needs to be found in the existing results. By means of the Lyapunov and finite-time stability theory, it is proven that the expected finite-time output TVFT can be realized by the considered heterogeneous nonlinear MASs within a finite time. Finally, simulation results demonstrate the efficacy of the proposed approach.

Optimal Containment Control of a Quadrotor Team With Active Leaders via Reinforcement Learning.

This article proposes an optimal controller for a team of underactuated quadrotors with multiple active leaders in containment control tasks. The quadrotor dynamics are underactuated, nonlinear, uncertain, and subject to external disturbances. The active team leaders have control inputs to enhance the maneuverability of the containment system. The proposed controller consists of a position control law to guarantee the achievement of position containment and an attitude control law to regulate the rotational motion, which are learned via off-policy reinforcement learning using historical data from quadrotor trajectories. The closed-loop system stability can be guaranteed by theoretical analysis. Simulation results of cooperative transportation missions with multiple active leaders demonstrate the effectiveness of the proposed controller.

Practical Output Containment of Heterogeneous Nonlinear Multiagent Systems Under External Disturbances.

The practical output containment problem for heterogeneous nonlinear multiagent systems under external disturbances generated by an exosystem is investigated in this article. It is required that the outputs of followers converge to the predefined convex combination of leaders' outputs. One of the major challenges in solving such a problem lies in dealing with the coupling among different nonlinearities, state dimensions, and system matrices of heterogeneous agents. To overcome the aforementioned challenge, a distributed observer-based control protocol is developed and employed. First, an adaptive state observer for estimating the states of all the leaders is constructed based on the neighboring interactions. Second, two new classes of observers are constructed for each follower exploiting the output information of the follower, in which the adaptive neural networks (NNs)-based approximation is exploited to compensate for the unknown nonlinearity in the followers' dynamics. A practical output containment control protocol is then generated by the proposed observers, where the control parameters are determined by an algorithm including two steps. Furthermore, with the help of the Lyapunov stability theory and the output regulation method, the practical output containment criteria for the considered closed-loop system under the influences of external disturbances are derived on the basis of the presented control protocol. Finally, the derived theoretical results are illustrated by a simulation example.

Toward Better Structure and Constraint to Mine Negative Sequential Patterns.

Nonoccurring behavior (NOB) studies have attracted the growing attention of scholars as a crucial part of behavioral science. As an effective method to discover both NOB and occurring behaviors (OB), negative sequential pattern (NSP) mining is successfully used in analyzing medical treatment and abnormal behavior patterns. At this time, NSP mining is still an active and challenging research domain. Most of the algorithms are inefficient in practice. Briefly, the key weaknesses of NSP mining are: 1) an inefficient positive sequential pattern (PSP) mining process, 2) a strict constraint of negative containment, and 3) the lack of an effective Negative Sequential Candidate (NSC) generation method. To address these weaknesses, we propose a highly efficient algorithm with improved techniques, named sc-NSP, to mine NSP efficiently. We first propose an improved PrefixSpan algorithm in the PSP mining process, which connects to a bitmap storage structure instead of the original structure. Second, sc-NSP loosens the frequency constraint and exploits the NSC generation method of positive and negative sequential patterns mining (PNSP) (a classic NSP mining method). Furthermore, a novel pruning strategy is designed to reduce the computational complexity of sc-NSP. Finally, sc-NSP obtains the support of NSC by using the most efficient bitwise-based calculation operation. Theoretical analyses show that sc-NSP performs particularly well on data sets with a large number of elements and items in sequence. Comparison and extensive experiments along with case studies on health data show that sc-NSP is 10 times more efficient than other state-of-the-art methods, and the number of NSPs obtained is 5 times greater than other methods.

Distributed Nash Equilibrium Seeking in Consistency-Constrained Multicoalition Games.

The distributed Nash equilibrium (NE) seeking problem for multicoalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This article considers a class of networked games among multiple coalitions where each coalition contains multiple agents that cooperate to minimize the sum of their costs, subject to the demand of reaching an agreement on their state values. Furthermore, the underlying network topology among the agents does not need to be balanced. To achieve the goal of NE seeking within such a context, two estimates are constructed for each agent, namely, an estimate of partial derivatives of the cost function and an estimate of global state values, based on which, an iterative state updating law is elaborately designed. Linear convergence of the proposed algorithm is demonstrated. It is shown that the consistency-constrained multicoalition games investigated in this article put the well-studied networked games among individual players and distributed optimization in a unified framework, and the proposed algorithm can easily degenerate into solutions to these problems.

Synchronous Spatiotemporal Graph Transformer: A New Framework for Traffic Data Prediction.

Modeling the spatiotemporal relationship (STR) of traffic data is important yet challenging for existing graph networks. These methods usually capture features separately in temporal and spatial dimensions or represent the spatiotemporal data by adopting multiple local spatial-temporal graphs. The first kind of method mentioned above is difficult to capture potential temporal-spatial relationships, while the other is limited for long-term feature extraction due to its local receptive field. To handle these issues, the Synchronous Spatio-Temporal grAph Transformer (S2TAT) network is proposed for efficiently modeling the traffic data. The contributions of our method include the following: 1) the nonlocal STR can be synchronously modeled by our integrated attention mechanism and graph convolution in the proposed S2TAT block; 2) the timewise graph convolution and multihead mechanism designed can handle the heterogeneity of data; and 3) we introduce a novel attention-based strategy in the output module, being able to capture more valuable historical information to overcome the shortcoming of conventional average aggregation. Extensive experiments are conducted on PeMS datasets that demonstrate the efficacy of the S2TAT by achieving a top-one accuracy but less computational cost by comparing with the state of the art.

An Augmented Game Approach for Design and Analysis of Distributed Learning Dynamics in Multiagent Games.

In this article, an augmented game approach is proposed for the formulation and analysis of distributed learning dynamics in multiagent games. Through the design of the augmented game, the coupling structure of utility functions among all the players can be reformulated into an arbitrary undirected connected network while the Nash equilibria are preserved. In this case, any full-information game learning dynamics can be recast into a distributed form, and its convergence can be determined from the structure of the augmented game. We apply the proposed approach to generate both deterministic and stochastic distributed gradient play and obtain several negative convergent results about the distributed gradient play: 1) a Nash equilibrium is convergent under the classic gradient play, yet its corresponding augmented Nash equilibrium may be not convergent under the distributed gradient play and, on the other side, 2) a Nash equilibrium is not convergent under the classic gradient play, yet its corresponding augmented Nash equilibrium may be convergent under the distributed gradient play. In particular, we show that the variational stability structure (including monotonicity as a special case) of a game is not guaranteed to be preserved in its augmented game. These results provide a systematic methodology about how to formulate and then analyze the feasibility of distributed game learning dynamics.

Predefined-Time Bounded Consensus of Multiagent Systems With Unknown Nonlinearity via Distributed Adaptive Fuzzy Control.

This article investigates uniformly predefined-time bounded consensus of leader-following multiagent systems (MASs) with unknown system nonlinearity and external disturbance via distributed adaptive fuzzy control. First, uniformly predefined-time-bounded stability is analyzed and a sufficient condition is derived for the system to achieve semiglobally (globally) uniformly predefined-time-bounded consensus. Therein, the settling time is independent of initial conditions and can be defined in advance. Then, for first-order MASs, distributed adaptive fuzzy controllers are designed by combining neighboring consensus errors to drive all following agents to globally track the leader's state within predefined time. For second-order MASs, by formulating filtered errors, the consensus errors between following agents and the leader are shown to be bounded if the filtered errors are bounded. Furthermore, with the distributed controllers designed based on filtered errors, second-order MASs achieve semiglobally uniformly predefined-time-bounded leader-following consensus. Finally, two numerical examples are simulated, including: 1) a first-order leader-following MAS and 2) a second-order Lagrangian system consisting of single-link manipulators, to demonstrate the performance of the proposed controllers.

Neuroadaptive Output Formation Tracking for Heterogeneous Nonlinear Multiagent Systems With Multiple Nonidentical Leaders.

This article investigates the practical time-varying output formation tracking (TVOFT) problem for heterogeneous nonlinear multiagent systems (MASs) having multiple leaders, where agents herein could have heterogeneous dynamics and interact with each other under event-triggered communications. It is required that the outputs of followers not only track the predefined convex combination of multiple leaders but also achieve the desired time-varying formation simultaneously. The existing works on formation tracking problems for MASs with multiple leaders depend on the assumption that each follower is a well-informed or uninformed follower, where the well-informed follower is required to have all the leaders as its neighbor. To remove the limitation, a fully distributed observer-based formation tracking control protocol is developed and employed. First, an adaptive state observer with an edge-based event-triggered mechanism for estimating the states of multiple leaders is proposed based on the neighboring interactions, which eliminates the unexpected Zeno behavior. Second, a novel observer is constructed for each follower by exploiting the output information of the follower, in which the adaptive neural network (NN)-based approximation is exploited to compensate for the unknown nonlinearity. A practical TVOFT control protocol is then generated by the proposed observers, where the parameters are determined by an algorithm including five steps. With the help of Lyapunov stability theory and output regulation method, a practical TVOFT criterion for the considered closed-loop system is derived. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example.

A Timestamp-Based Inertial Best-Response Dynamics for Distributed Nash Equilibrium Seeking in Weakly Acyclic Games.

In this article, we consider the problem of distributed game-theoretic learning in games with finite action sets. A timestamp-based inertial best-response dynamics is proposed for Nash equilibrium seeking by players over a communication network. We prove that if all players adhere to the dynamics, then the states of players will almost surely reach consensus and the joint action profile of players will be absorbed into a Nash equilibrium of the game. This convergence result is proven under the condition of weakly acyclic games and strongly connected networks. Furthermore, to encounter more general circumstances, such as games with graphical action sets, state-based games, and switching communication networks, several variants of the proposed dynamics and its convergent results are also developed. To demonstrate the validity and applicability, we apply the proposed timestamp-based learning dynamics to design distributed algorithms for solving some typical finite games, including the coordination games and congestion games.

Fixed-Time Synchronization of Complex Dynamical Networks: A Novel and Economical Mechanism.

Fixed-time synchronization of complex networks is investigated in this article. First, a completely novel lemma is introduced to prove the fixed-time stability of the equilibrium of a general ordinary differential system, which is less conservative and has a simpler form than those in the existing literature. Then, sufficient conditions are presented to realize synchronization of a complex network (with a target system) within a settling time via three different kinds of simple controllers. In general, controllers designed to achieve fixed-time stability consist of three terms and are discontinuous. However, in our mechanisms, the controllers only contain two terms or even one term and are continuous. Thus, our controllers are simpler and of more practical applicability. Finally, three examples are provided to illustrate the correctness and effectiveness of our results.

Intralayer Synchronization of Multiplex Dynamical Networks via Pinning Impulsive Control.

These days, the synchronization of multiplex networks is an emerging and important research topic. Grounded framework and theory about synchronization and control on multiplex networks are yet to come. This article studies the intralayer synchronization on a multiplex network (i.e., a set of networks connected through interlayer edges), via the pinning impulsive control method. The topologies of different layers are independent of each other, and the individual dynamics of nodes in different layers are different as well. Supra-Laplacian matrices are adopted to represent the topological structures of multiplex networks. Two cases are considered according to impulsive sequences of multiplex networks: 1) pinning controllers are applied to all the layers simultaneously at the instants of a common impulse sequence and 2) pinning controllers are applied to each layer at the instants of distinct impulse sequences. Using the Lyapunov stability theory and the impulsive control theory, several intralayer synchronization criteria for multiplex networks are obtained, in terms of the supra-Laplacian matrix of network topology, self-dynamics of nodes, impulsive intervals, and the pinning control effect. Furthermore, the algorithms for implementing pinning schemes at every impulsive instant are proposed to support the obtained criteria. Finally, numerical examples are presented to demonstrate the effectiveness and correctness of the proposed schemes.

Consensus of Stochastic Dynamical Multiagent Systems in Directed Networks via PI Protocols.

With the rapid development of swarm intelligence, the consensus of multiagent systems (MASs) has attracted substantial attention due to its broad range of applications in the practical world. Inspired by the considerable gap between control theory and engineering practices, this article is aimed at addressing the mean square consensus problems for stochastic dynamical nonlinear MASs in directed networks by designing proportional-integral (PI) protocols. In light of the general algebraic connectivity, consensus underlying PI protocols for a directed strongly connected network is investigated, and due to the M -matrix approaches, consensus with PI protocols for a directed network containing a spanning tree is studied. By constructing appropriate Lyapunov functions, combining with the stochastic analysis technique and LaSalle's invariant principles, some sufficient conditions are derived under which the stochastic dynamical MASs realize consensus in mean square. Numerical simulations are finally presented to illustrate the validity of the main results.

Time-Varying Group Formation-Containment Tracking Control for General Linear Multiagent Systems With Unknown Inputs.

Time-varying group formation-containment tracking problems for general linear multiagent systems with unknown control input are investigated. Agents are classified into tracking leaders, formation leaders, and followers and assigned in groups. Tracking leaders with unknown control inputs provide unpredictable trajectories as macroscopic moving references. Formation leaders accomplish desired subformations while following the trails of tracking leaders. At the same time, followers converge into different convex hulls spanned by formation leaders. First, formation-containment tracking protocols are designed with neighboring relative information and effects of unknown input of tracking leaders. Then, the design of group division is analyzed by adjusting the properties in Laplacian matrices, which represent interaction relationships. An algorithm to determine the parameters in control protocols is proposed, and the formation tracking feasible constraint is presented. Next, it is proved that the general linear multiagent system can achieve time-varying group formation-containment control effectively with errors uniformly asymptotically converging to zero under designed protocols. Finally, a numerical simulation is given to verify the effectiveness of obtained theoretical results.

Learning From Architectural Redundancy: Enhanced Deep Supervision in Deep Multipath Encoder-Decoder Networks.

Deep encoder-decoders are the model of choice for pixel-level estimation due to their redundant deep architectures. Yet they still suffer from the vanishing supervision information issue that affects convergence because of their overly deep architectures. In this work, we propose and theoretically derive an enhanced deep supervision (EDS) method which improves on conventional deep supervision (DS) by incorporating variance minimization into the optimization. A new structure variance loss is introduced to build a bridge between deep encoder-decoders and variance minimization, and provides a new way to minimize the variance by forcing different intermediate decoding outputs (paths) to reach an agreement. We also design a focal weighting strategy to effectively combine multiple losses in a scale-balanced way, so that the supervision information is sufficiently enforced throughout the encoder-decoders. To evaluate the proposed method on the pixel-level estimation task, a novel multipath residual encoder is proposed and extensive experiments are conducted on four challenging density estimation and crowd counting benchmarks. The experimental results demonstrate the superiority of our EDS over other paradigms, and improved estimation performance is reported using our deeply supervised encoder-decoder.

Topology Identification of Multilink Complex Dynamical Networks via Adaptive Observers Incorporating Chaotic Exosignals.

Topology identification of complex networks is an important and meaningful research direction. In recent years, the topology identification method based on adaptive synchronization has been developed rapidly. However, a critical shortcoming of this method is that inner synchronization of a network breaks the precondition of linear independence and leads to the failure of topology identification. Hence, how to identify the network topology when possible inner synchronization occurs within the network has been a challenging research issue. To solve this problem, this article proposes improved topology identification methods by regulating the original network to synchronize with an auxiliary network composed of isolated chaotic exosystems. The proposed methods do not require the sophisticated assumption of linear independence. The topology identification observers incorporating a series of isolated chaotic exosignals can accurately identify the network structure. Finally, numerical simulations show that the proposed methods are effective to identify the structure of a network even with large weights of edges and abundant connections between nodes.

Distributed Adaptive Finite-Time Consensus for Second-Order Multiagent Systems With Mismatched Disturbances Under Directed Networks.

In this paper, the finite-time output consensus problem is considered for a class of second-order multiagent systems (MASs), where the mismatched disturbance exists in the dynamics of each agent, and the communication topology is directed. First of all, a basic backstepping control protocol is proposed to solve the finite-time consensus problem without mismatched disturbance. Then, a finite-time disturbance observer is designed to estimate the mismatched disturbance, based on which, two adaptive finite-time consensus protocols are proposed to solve the finite-time output consensus and tracking consensus problems without using any global information with respect to the communication topology. Finally, two simulation examples are illustrated to verify the theoretical results.