Channel Coupling Dynamics of Deep-Lying Orbitals in Molecular High-Harmonic Generation.

Investigation on structures in the high-harmonic spectrum has provided profuse information of molecular structure and dynamics in intense laser fields, based on which techniques of molecular ultrafast dynamics imaging have been developed. Combining ab initio calculations and experimental measurements on the high-harmonic spectrum of the CO_{2} molecule, we find a novel dip structure in the low-energy region of the harmonic spectrum which is identified as fingerprints of participation of deeper-lying molecular orbitals in the process and decodes the underlying attosecond multichannel coupling dynamics. Our work sheds new light on the ultrafast dynamics of molecules in intense laser fields.

Pinning-Based Neural Control for Multiagent Systems With Self-Regulation Intermediate Event-Triggered Method.

A pinning-based self-regulation intermediate event-triggered (ET) funnel tracking control strategy is proposed for uncertain nonlinear multiagent systems (MASs). Based on the backstepping framework, a pinning control strategy is designed to achieve the tracking control objective, which only uses the communication weight between the agents without additional feedback parameters. Moreover, by designing a self-regulation triggered condition based on the tracking error, the intermediate triggered signal is calculated to replace the continuous signal in the controller, so as to achieve the goal of discontinuous update of the controller signal, and this mechanism does not need to add additional compensation function to the controller signal. At the same time, the funnel method is adopted to restrict the error of step n and avoid the possible negative impact caused by control signal. Furthermore, the nonlinear noncontinuous faults are compensated by the disturbance observer. Then, the Lyapunov stability theorem is used to prove that all signals of the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, some simulation results confirm the effectiveness of the proposed control scheme.

Neuroadaptive Performance Guaranteed Control for Multiagent Systems With Power Integrators and Unknown Measurement Sensitivity.

This article investigates the adaptive performance guaranteed tracking control problem for multiagent systems (MASs) with power integrators and measurement sensitivity. Different from the structural characteristics of existing results, the dynamic of each agent is a power exponential function. A method called adding a power integrator technique is introduced to guarantee that the consensus is achieved of the MASs with power integrators. Different from existing prescribed performance tracking control results for MASs, a new performance guaranteed control approach is proposed in this article, which can guarantee that the relative position error between neighboring agents can converge into the prescribed boundary within preassigned finite time. By utilizing the Nussbaum gain technique and neural networks, a novel control scheme is proposed to solve the unknown measurement sensitivity on the sensor, which successfully relaxes the restrictive condition that the unknown measurement sensitivity must be within a specific range. Based on the Lyapunov functional method, it is proven that the relative position error between neighboring agents can converge into the prescribed boundary within preassigned finite time. Finally, a simulation example is proposed to verify the availability of the control strategy.

Observer-Based Dynamic Event-Triggered Control for Multiagent Systems With Time-Varying Delay.

This article is concerned with the dynamic event-triggered-based adaptive output-feedback tracking control problem of nonlinear multiagent systems with time-varying input delay. By utilizing the approximation capability of neural network (NN), a low-gain nonlinear observer is first established to estimate the immeasurable states. To mitigate the effect of time-varying input delay, an auxiliary system with communication information is designed to generate the compensation signals. Then, a distributed adaptive composite NN dynamic surface control (DSC) strategy is proposed to acquire the satisfactory tracking accuracy, where the filter errors are compensated by the introduced serial-parallel estimation model. Moreover, an effective switching dynamic event-triggered mechanism is developed to determine the communication instants and reduce the update frequency of the controller. It is proven that the consensus tracking error converges to a residual set of the origin. Finally, simulation results are presented to demonstrate the effectiveness of the proposed composite NN DSC scheme.

Neural-Network-Based Predefined-Time Adaptive Consensus in Nonlinear Multi-Agent Systems With Switching Topologies.

A predefined-time adaptive consensus control strategy is developed for a class of multi-agent systems containing unknown nonlinearity. The unknown dynamics and switching topologies are simultaneously considered to adapt to actual scenarios. The time required for tracking error convergence can be easily adjusted using the proposed time-varying decay functions. An efficient method is proposed to determine the expected convergence time. Subsequently, the predefined time is adjustable by regulating the parameters of the time-varying functions (TVFs). The neural network (NN) approximation technique is used to address the issue of unknown nonlinear dynamics through predefined-time consensus control. The Lyapunov stability theory testifies that the predefined-time tracking error signals are bounded and convergent. The feasibility and effectiveness of the proposed predefined-time consensus control scheme are demonstrated through the simulation results.

Dissipativity-Based Consensus Tracking Control of Nonlinear Multiagent Systems With Generally Uncertain Markovian Switching Topologies and Event-Triggered Strategy.

This article focuses on the dissipativity-based consensus tracking control (DBCTC) problems of time-varying delayed leader-following nonlinear multiagent systems (LFNMASs) with the event-triggered transmission strategy. The switching topologies of the LFNMASs are subject to the uncertain and partially unknown generally Markovian jumping process. The control inputs of the following agents are updated according to the proposed event-triggered transmission strategy, which could reduce the communication burden. Based on the event-triggered transmission condition and distributed consensus protocol, some dissipativity-based criteria obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII) are proposed to guarantee the LFNMAS consensus. The validity of the main results is verified by two simulation examples.

Adaptive Bipartite Tracking Control of Nonlinear Multiagent Systems With Input Quantization.

This article studies the bipartite tracking control problem of distributed nonlinear multiagent systems with input quantization, external disturbances, and actuator faults. We use the radial basis function (RBF) neural networks (NNs) to model unknown nonlinearities. Due to the fact that the upper bounds of disturbances and the number of actuator faults are unknown, an intermediate control law is designed based on a backstepping strategy, where a compensation term is introduced to eliminate external disturbances and actuator faults. Meanwhile, a novel smooth function is incorporated into the real distributed controller to reduce the effect of quantization on the virtual controller. The proposed distributed controller not only realizes the bipartite tracking control but also ensures that all signals are bounded in the closed-loop systems and the outputs of all followers converge to a neighborhood of the leader output. Finally, simulation results demonstrate the effectiveness of the proposed control algorithm.

Neural-Network-Based Event-Triggered Adaptive Control of Nonaffine Nonlinear Multiagent Systems With Dynamic Uncertainties.

This article addresses the adaptive event-triggered neural control problem for nonaffine pure-feedback nonlinear multiagent systems with dynamic disturbance, unmodeled dynamics, and dead-zone input. Radial basis function neural networks are applied to approximate the unknown nonlinear function. A dynamic signal is constructed to deal with the design difficulties in the unmodeled dynamics. Moreover, to reduce the communication burden, we propose an event-triggered strategy with a varying threshold. Based on the Lyapunov function method and adaptive neural control approach, a novel event-triggered control protocol is constructed, which realizes that the outputs of all followers converge to a neighborhood of the leader's output and ensures that all signals are bounded in the closed-loop system. An illustrative simulation example is applied to verify the usefulness of the proposed algorithms.

Cooperative Adaptive Dynamic Surface Control for a Class of High-Order Stochastic Nonlinear Multiagent Systems.

This article investigates the consensus tracking problem for high-order stochastic pure-feedback nonlinear multiagent systems (MASs) with dead zones. It should be pointed out that each follower's virtual and actual control items are the power-exponential functions with positive odd numbers instead of linear items. Because of the structural characteristics of the followers' dynamics, a technique called adding a power integrator is used, which effectively overcomes the difficulties of states and dead zone with power-exponential functions. Furthermore, radial basis function neural networks are employed to estimate unknown nonlinear functions and solve the problem of algebraic loop caused by the pure-feedback structure of MASs. Meanwhile, the problems of "explosion of complexity" caused by repeated differentiations of the virtual controller are solved by using the tracking differentiators. Based on the Lyapunov stability theorem, it is proved that all signals of the closed-loop systems are semiglobally uniformly ultimately bounded in probability, and the tracking errors can converge to a small neighborhood of the origin. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Prescribed Performance Adaptive Fuzzy Containment Control for Nonlinear Multiagent Systems Using Disturbance Observer.

This article focuses on the containment control problem for nonlinear multiagent systems (MASs) with unknown disturbance and prescribed performance in the presence of dead-zone output. The fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear function, and a nonlinear disturbance observer is used to estimate unknown external disturbances. Meanwhile, a new distributed containment control scheme is developed by utilizing the adaptive compensation technique without assumption of the boundary value of unknown disturbance. Furthermore, a Nussbaum function is utilized to cope with the unknown control coefficient, which is caused by the nonlinearity in the output mechanism. Moreover, a second-order tracking differentiator (TD) is introduced to avoid the repeated differentiation of the virtual controller. The outputs of the followers converge to the convex hull spanned by the multiple dynamic leaders. It is shown that all the signals are semiglobally uniformly ultimately bounded (SGUUB), and the local neighborhood containment errors can converge into the prescribed boundary. Finally, the effectiveness of the approach proposed in this article is illustrated by simulation results.

Prescribed Performance Cooperative Control for Multiagent Systems With Input Quantization.

This paper studies the quantized cooperative control problem for multiagent systems with unknown gains in the prescribed performance. Different from the finite-time control, a speed function is designed to realize that the tracking errors converge to a prescribed compact set in a given finite time for multiagent systems. Meanwhile, we consider the problem of unknown gains and input quantization, which can be addressed by using a lemma and Nussbaum function in cooperative control. Moreover, the fuzzy logic systems are proposed to approximate the nonlinear function defined on a compact set. A distributed controller and adaptive laws are constructed based on the Lyapunov stability theory and backstepping method. Finally, the effectiveness of the proposed approach is illustrated by some numerical simulation results.

Event-Triggered Adaptive Tracking Control for Multiagent Systems With Unknown Disturbances.

This paper considers the event-triggered tracking control problem of nonlinear multiagent systems with unknown disturbances. The event-triggering mechanism is considered in the controller update, which decreases the amount of communication and reduces the frequency of the controller update in practice. By designing a disturbance observer, the unknown external disturbances are estimated. Moreover, a part of adaptive parameters are only dependent on the number of followers, which weakens the computational burden. It is shown that all the signals are bounded, and the consensus tracking errors are located in a small neighborhood of the origin based on the Lyapunov stability theory and backstepping approach. Finally, the effectiveness of the approach proposed in this paper is proved by simulation results.

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Sampled-Data Synchronization Analysis of Markovian Neural Networks With Generally Incomplete Transition Rates.

This paper investigates the problem of sampled-data synchronization for Markovian neural networks with generally incomplete transition rates. Different from traditional Markovian neural networks, each transition rate can be completely unknown or only its estimate value is known in this paper. Compared with most of existing Markovian neural networks, our model is more practical because the transition rates in Markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors. In addition, the time-dependent Lyapunov-Krasovskii functional is proposed to synchronize drive system and response system. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay. Moreover, the desired sampled-data controllers are obtained. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Optimal Output Regulation for Heterogeneous Multiagent Systems via Adaptive Dynamic Programming.

In this paper, the optimal output regulation problem for partially model-free heterogeneous linear multiagent systems with disturbance generated by an exosystem is addressed by using adaptive dynamic programming and double compensator method. The topology graph for the information exchange of the agents has a spanning tree. The dynamic of individual agent is assumed to be nonidentical and of different dimensions. One distributed compensator is designed to deal with the nonidentical agents, and the other compensator is used to handle the optimal performance index. By constructing the double compensator, the distributed feedback control laws are designed to make the output of each agent synchronize with the reference output and minimize the energy of the output error simultaneously. To overcome the lack of the dynamics knowledge of each agent, a novel online policy iteration algorithm is developed to obtain the optimal feedback gain matrix. Finally, two examples are presented to illustrate the effectiveness of our results.

Distributed-observer-based cooperative control for synchronization of linear discrete-time multi-agent systems.

This paper considers output synchronization of discrete-time multi-agent systems with directed communication topologies. The directed communication graph contains a spanning tree and the exosystem as its root. Distributed observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct the observer-based protocols. In light of the discrete-time algebraic Riccati equation and internal model principle, synchronization problem is completed. At last, numerical simulation is provided to verify the effectiveness of the theoretical results.

Mode-Dependent Stochastic Synchronization for Markovian Coupled Neural Networks With Time-Varying Mode-Delays.

This paper investigates the stochastic synchronization problem for Markovian hybrid coupled neural networks with interval time-varying mode-delays and random coupling strengths. The coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is proposed, where some terms involving triple or quadruple integrals are considered, which makes the LKF matrices mode-dependent as much as possible. This gives significant improvement in the synchronization criteria, i.e., less conservative results can be obtained. In addition, by applying an extended Jensen's integral inequality and the properties of random variables, new delay-dependent synchronization criteria are derived. The obtained criteria depend not only on upper and lower bounds of mode-delays but also on mathematical expectations and variances of the random coupling strengths. Finally, two numerical examples are provided to demonstrate the feasibility of the proposed results.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.