Cooperative tracking control of nonlinear multiagent systems using self-structuring neural networks

Filter Pruning Based on Information Capacity and Independence

Filter pruning has gained widespread adoption for the purpose of compressing and speeding up convolutional neural networks (CNNs). However, the existing approaches are still far from practical applications due to biased filter selection and heavy computation cost. This article introduces a new filter pruning method that selects filters in an interpretable, multiperspective, and lightweight manner. Specifically, we evaluate the contributions of filters from both individual and overall perspectives. For the amount of information contained in each filter, a new metric called information capacity is proposed. Inspired by the information theory, we utilize the interpretable entropy to measure the information capacity and develop a feature-guided approximation process. For correlations among filters, another metric called information independence is designed. Since the aforementioned metrics are evaluated in a simple but effective way, we can identify and prune the least important filters with less computation cost. We conduct comprehensive experiments on benchmark datasets employing various widely used CNN architectures to evaluate the performance of our method. For instance, on ILSVRC-2012, our method outperforms state-of-the-art methods by reducing floating-point operations (FLOPs) by 77.4% and parameters by 69.3% for ResNet-50 with only a minor decrease in an accuracy of 2.64%.

Robust Adaptive Leader-Following Formation Control of Nonlinear Multiagents Using Three-Layer Neural Networks

This article studies a formation control problem for a group of heterogeneous, nonlinear, uncertain, input-affine, second-order agents modeled by a directed graph. A tunable neural network (NN) is presented, with three layers (input, two hidden, and output) that can approximate an unknown nonlinearity. Unlike one- or two-layer NNs, this design has the advantage of being able to set the number of neurons in each layer ahead of time rather than relying on trial and error. The NN weights tuning law is rigorously derived using the Lyapunov theory. The formation control problem is tackled using a robust integral of the sign of the error feedback and NNs-based control. The robust integral of the sign of the error feedback compensates for the unknown dynamics of the leader and disturbances in the agent errors, while the NN-based controller accounts for the unknown nonlinearity in the multiagent system. The stability and semi-global asymptotic tracking of the results are proven using the Lyapunov stability theory. The study compares its results with two others to assess the effectiveness and efficiency of the proposed method.

Learning Multi-Agent Cooperation via Considering Actions of Teammates

Recently value-based centralized training with decentralized execution (CTDE) multi-agent reinforcement learning (MARL) methods have achieved excellent performance in cooperative tasks. However, the most representative method among these methods, Q-network MIXing (QMIX), restricts the joint action Q values to be a monotonic mixing of each agent's utilities. Furthermore, current methods cannot generalize to unseen environments or different agent configurations, which is known as ad hoc team play situation. In this work, we propose a novel Q values decomposition that considers both the return of an agent acting on its own and cooperating with other observable agents to address the nonmonotonic problem. Based on the decomposition, we propose a greedy action searching method that can improve exploration and is not affected by changes in observable agents or changes in the order of agents' actions. In this way, our method can adapt to ad hoc team play situation. Furthermore, we utilize an auxiliary loss related to environmental cognition consistency and a modified prioritized experience replay (PER) buffer to assist training. Our extensive experimental results show that our method achieves significant performance improvements in both challenging monotonic and nonmonotonic domains, and can handle the ad hoc team play situation perfectly.

Distributed Adaptive-Neural Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems Subject to Saturated Inputs

In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.

Neural-Network-Based Adaptive Fixed-Time Control for Nonlinear Multiagent Non-Affine Systems

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

Robust Adaptive Self-Structuring Neural Network Bounded Target Tracking Control of Underactuated Surface Vessels

This paper studies the target-tracking problem of underactuated surface vessels with model uncertainties and external unknown disturbances. A composite robust adaptive self-structuring neural-network-bounded controller is proposed to improve system performance and avoid input saturation. An extended state observer is proposed to estimate the uncertain nonlinear term, including the unknown velocity of the tracking target, when only the measurement values of the line-of-sight range and angle can be obtained. An adaptive self-structuring neural network is developed to approximate model uncertainties and external unknown disturbances, which can effectively optimize the structure of the neural network to reduce the computational burden by adjusting the number of neurons online. The input-to-state stability of the total closed-loop system is analyzed by the cascade stability theorem. The simulation results verify the effectiveness of the proposed method.

Finite-Time Consensus Tracking for Incommensurate Fractional-Order Nonlinear Multiagent Systems With Directed Switching Topologies

This article investigates the problem of finite-time consensus tracking for incommensurate fractional-order nonlinear multiagent systems (MASs) with general directed switching topology. For the leader with bounded but arbitrary dynamics, a neighborhood-based saturated observer is first designed to guarantee that the observer's state converges to the leader's state in finite time. By utilizing a fuzzy-logic system to approximate the heterogeneous and unmodeled nonlinear dynamics, an observer-based adaptive parameter control protocol is designed to solve the problem of finite-time consensus tracking of incommensurate fractional-order nonlinear MASs on directed switching topology with a restricted dwell time. Then, the derived result is further extended to the case of directed switching topology without a restricted dwell time by designing an observer-based adaptive gain control protocol. By artfully choosing a piecewise Lyapunov function, it is shown that the consensus tracking error converges to a small adjustable residual set in finite time for both the cases with and without a restricted dwell time. It should be noted that the proposed adaptive gain consensus tracking protocol is completely distributed in the sense that there is no need for any global information. The effectiveness of the proposed consensus tracking scheme is illustrated by numerical simulations.

Robust Tracking Control of the Euler-Lagrange System Based on Barrier Lyapunov Function and Self-Structuring Neural Networks

This article studies the robust tracking control problems of Euler–Lagrange (EL) systems with uncertainties. To enhance the robustness of the control systems, an asymmetric tan-type barrier Lyapunov function (ATBLF) is used to dynamic constraint position tracking errors. To deal with the problems of the system uncertainties, the self-structuring neural network (SSNN) is developed to estimate the unknown dynamics model and avoid the calculation burden. The robust compensator is designed to estimate and compensate neural network (NN) approximation errors and unknown disturbances. In addition, a relative threshold event-triggered strategy is introduced, which greatly saves communication resources. Under the proposed robust control scheme, tracking behavior can be implemented with disturbance and unknown dynamics of the EL systems. All signals in the closed-loop system are proved to be bounded by stability analysis, and the tracking error can converge to the neighborhood near the origin. The numerical simulation results show the effectiveness and the validity of the proposed robust control scheme.

Reinforcement Learning With Task Decomposition for Cooperative Multiagent Systems

In this article, we study cooperative multiagent systems (MASs) with multiple tasks by using reinforcement learning (RL)-based algorithms. The target for a single-agent RL system is represented by its scalar reward signals. However, for an MAS with multiple cooperative tasks, the holistic reward signal consists of multiple parts to represent the tasks, which makes the problem complicated. Existing multiagent RL algorithms search distributed policies with holistic reward signals directly, making it difficult to obtain an optimal policy for each task. This article provides efficient learning-based algorithms such that each agent can learn a joint optimal policy to accomplish these multiple tasks cooperatively with other agents. The main idea of the algorithms is to decompose the holistic reward signal for each agent into multiple parts according to the subtasks, and then the proposed algorithms learn multiple value functions with the decomposed reward signals and update the policy with the sum of distributed value functions. In addition, this article presents a theoretical analysis of the proposed approach. Finally, the simulation results for both discrete decision-making and continuous control problems have demonstrated the effectiveness of the proposed algorithms.

A Novel Connectivity-Preserving Control Design for Rendezvous Problem of Networked Uncertain Nonlinear Systems

This article proposes a novel and robust connectivity-preserving rendezvous control design for a group of uncertain nonlinear multiagent systems with communication constraint where each agent has a limited sensing range. The control design can work under the assumption that the communication network is initially connected and is characterized by two distinguishing features. First, a new potential function is provided not only to maintain the existing and newly added links by the hysteresis rule but also to overcome the difficulty imposed by the nonlinear terms from system dynamics. Second, by constructing a series of lemmas, a connectivity-preserving stabilizing control law is presented to solve the robust stabilization problem with connectivity preservation for a time-varying nonlinear system, which is a special case of the augmented system with both dynamic and static uncertainties obtained via internal model design. After further incorporating the adaptive control technique, regardless of uncertain parameters and external disturbances in the multiple nonlinear subsystems, the leader-following rendezvous with connectivity preservation problem is finally solved by a distributed connectivity-preserving controller with parameter update law.

Cooperative Adaptive Output Regulation for Lower Triangular Nonlinear Multi-Agent Systems Subject to Jointly Connected Switching Networks

The cooperative global robust output regulation problem for multi-agent systems is a generalization of the leader-following consensus problem. The problem has been studied for various multi-agent systems over connected static networks and for some special classes of nonlinear multi-agent systems over jointly connected switching networks. In this paper, we further consider the same problem for a class of heterogeneous lower triangular nonlinear multi-agent systems over jointly connected switching networks. This class of systems is quite general in that it contains inverse dynamics, is of any order, and its subsystems can have different relative degrees. We will integrate the adaptive distributed observer and the distributed internal model approach to come up with a recursive approach to deal with our problem. We will also apply our approach to a leader-following consensus problem for a group of hyperchaotic Lorenz systems.

Distributed Fault-Tolerant Control of Multiagent Systems: An Adaptive Learning Approach

This paper focuses on developing a distributed leader-following fault-tolerant tracking control scheme for a class of high-order nonlinear uncertain multiagent systems. Neural network-based adaptive learning algorithms are developed to learn unknown fault functions, guaranteeing the system stability and cooperative tracking even in the presence of multiple simultaneous process and actuator faults in the distributed agents. The time-varying leader's command is only communicated to a small portion of follower agents through directed links, and each follower agent exchanges local measurement information only with its neighbors through a bidirectional but asymmetric topology. Adaptive fault-tolerant algorithms are developed for two cases, i.e., with full-state measurement and with only limited output measurement, respectively. Under certain assumptions, the closed-loop stability and asymptotic leader-follower tracking properties are rigorously established.

Practical Time-Varying Formation Tracking for Second-Order Nonlinear Multiagent Systems With Multiple Leaders Using Adaptive Neural Networks

Practical time-varying formation tracking problems for second-order nonlinear multiagent systems with multiple leaders are investigated using adaptive neural networks (NNs), where the time-varying formation tracking error caused by time-varying external disturbances can be arbitrarily small. Different from the previous work, there exists a predefined time-varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the dynamics of each agent has both matched/mismatched heterogeneous nonlinearities and disturbances simultaneously. First, a practical time-varying formation tracking protocol using adaptive NNs is proposed, which is constructed using only local neighboring information. The proposed control protocol can process not only the matched/mismatched heterogeneous nonlinearities and disturbances, but also the unknown control inputs of the leaders. Second, an algorithm with three steps is introduced to design the practical formation tracking protocol, where the parameters of the protocol are determined, and the practical time-varying formation tracking feasibility condition is given. Third, the stability of the closed-loop multiagent system is proven by using the Lyapunov theory. Finally, a simulation example is showed to illustrate the effectiveness of the obtained theoretical results.

Distributed Adaptive Containment Control for a Class of Nonlinear Multiagent Systems With Input Quantization

This paper is devoted to distributed adaptive containment control for a class of nonlinear multiagent systems with input quantization. By employing a matrix factorization and a novel matrix normalization technique, some assumptions involving control gain matrices in existing results are relaxed. By fusing the techniques of sliding mode control and backstepping control, a two-step design method is proposed to construct controllers and, with the aid of neural networks, all system nonlinearities are allowed to be unknown. Moreover, a linear time-varying model and a similarity transformation are introduced to circumvent the obstacle brought by quantization, and the controllers need no information about the quantizer parameters. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the containment errors into an arbitrarily small residual set. The simulation results illustrate the effectiveness of the scheme.

LMI Conditions for Global Stability of Fractional-Order Neural Networks

Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

Consensus Control of Nonlinear Multiagent Systems With Time-Varying State Constraints

In this paper, we present a novel adaptive consensus algorithm for a class of nonlinear multiagent systems with time-varying asymmetric state constraints. As such, our contribution is a step forward beyond the usual consensus stabilization result to show that the states of the agents remain within a user defined, time-varying bound. To prove our new results, the original multiagent system is transformed into a new one. Stabilization and consensus of transformed states are sufficient to ensure the consensus of the original networked agents without violating of the predefined asymmetric time-varying state constraints. A single neural network (NN), whose weights are tuned online, is used in our design to approximate the unknown functions in the agent's dynamics. To account for the NN approximation residual, reconstruction error, and external disturbances, a robust term is introduced into the approximating system equation. Additionally in our design, each agent only exchanges the information with its neighbor agents, and thus the proposed consensus algorithm is decentralized. The theoretical results are proved via Lyapunov synthesis. Finally, simulations are performed on a nonlinear multiagent system to illustrate the performance of our consensus design scheme.

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms.

Observer-Based Adaptive Backstepping Consensus Tracking Control for High-Order Nonlinear Semi-Strict-Feedback Multiagent Systems

Combined with backstepping techniques, an observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form. By constructing the neural network-based state observer for each follower, the proposed consensus control method solves the unmeasurable state problem of high-order nonlinear multiagent systems. The control algorithm can guarantee that all signals of the multiagent system are semi-globally uniformly ultimately bounded and all outputs can synchronously track a reference signal to a desired accuracy. A simulation example is carried out to further demonstrate the effectiveness of the proposed consensus control method.

Robust Consensus of Nonlinear Multiagent Systems With Switching Topology and Bounded Noises

Consensus of multiagent systems (MASs) is an intriguing topic in recent years due to its widely used application in robotics, biology, computer, and social science. In the real world, the evolution of MAS is inevitably involved in dynamical environments and the recent development of MAS calls for novel tools for the analysis of MAS with dynamic topology. In addition, the interactions between agents are generally nonlinear and environmental noises are ubiquitous in the communication channels between agents. However, the existing investigation on MAS places little attention on nonlinear models and the inner relationship between external disturbance and consensus is still unclear. Facing these problems, this paper considers an MAS in which the interactions between agents are nonlinear and the communication between agents are infected by environmental noises. By using a novel method of nonsmooth Lyapunov candidate, it has been demonstrated that such an MAS can realize robust consensus under the conditions of jointly (sequentially) connected topology and bounded noises. Finally, simulation results validate the effectiveness of these criteria.

Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions

This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols.

Consensus Control With Failure--Wait or Abandon?

This paper introduces and solves a decision-making problem under the context of consensus control with failure. We study an optimal consensus control problem in which n autonomous agents try to arrive at a target at the same time. One of the agents suddenly fails and the rest n - 1 agents can either wait or abandon the failed agent. If they wait, they must slow down and delay the consensus time. If they abandon the failed agent, they can reach consensus earlier at the cost of losing one agent at consensus. This cost is an added delay to the consensus time. The decision problem is to decide whether to wait or abandon and, if abandon, when? To solve this problem, we derive analytical expressions and establish structural properties for target distance functions. We use numerical examples and simulation examples to demonstrate the applications of the derived formulas and results.

Adaptive Robust Output Feedback Control for a Marine Dynamic Positioning System Based on a High-Gain Observer

This paper develops an adaptive robust output feedback control scheme for dynamically positioned ships with unavailable velocities and unknown dynamic parameters in an unknown time-variant disturbance environment. The controller is designed by incorporating the high-gain observer and radial basis function (RBF) neural networks in vectorial backstepping method. The high-gain observer provides the estimations of the ship position and heading as well as velocities. The RBF neural networks are employed to compensate for the uncertainties of ship dynamics. The adaptive laws incorporating a leakage term are designed to estimate the weights of RBF neural networks and the bounds of unknown time-variant environmental disturbances. In contrast to the existing results of dynamic positioning (DP) controllers, the proposed control scheme relies only on the ship position and heading measurements and does not require a priori knowledge of the ship dynamics and external disturbances. By means of Lyapunov functions, it is theoretically proved that our output feedback controller can control a ship's position and heading to the arbitrarily small neighborhood of the desired target values while guaranteeing that all signals in the closed-loop DP control system are uniformly ultimately bounded. Finally, simulations involving two ships are carried out, and simulation results demonstrate the effectiveness of the proposed control scheme.

Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions

This paper presents an adaptive output-feedback neural network (NN) control scheme for a class of stochastic nonlinear time-varying delay systems with unknown control directions. To make the controller design feasible, the unknown control coefficients are grouped together and the original system is transformed into a new system using a linear state transformation technique. Then, the Nussbaum function technique is incorporated into the backstepping recursive design technique to solve the problem of unknown control directions. Furthermore, under the assumption that the time-varying delays exist in the system output, only one NN is employed to compensate for all unknown nonlinear terms depending on the delayed output. Moreover, by estimating the maximum of NN parameters instead of the parameters themselves, the NN parameters to be estimated are greatly decreased and the online learning time is also dramatically decreased. It is shown that all the signals of the closed-loop system are bounded in probability. The effectiveness of the proposed scheme is demonstrated by the simulation results.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.