Prescribed Performance for Bipartite Tracking Control of Nonlinear Multiagent Systems With Hysteresis Input Uncertainties

Adaptive Critic Learning-Based Optimal Bipartite Consensus for Multiagent Systems With Prescribed Performance

Developing a distributed bipartite optimal consensus scheme while ensuring user-predefined performance is essential in practical applications. Existing approaches to this problem typically require a complex controller structure due to adopting an identifier-actor-critic framework and prescribed performance cannot be guaranteed. In this work, an adaptive critic learning (ACL)-based optimal bipartite consensus scheme is developed to bridge the gap. A newly designed error scaling function, which defines the user-predefined settling time and steady accuracy without relying on the initial conditions, is then integrated into a cost function. The backstepping framework combines the ACL and integral reinforcement learning (IRL) algorithm to develop the adaptive optimal bipartite consensus scheme, which contributes a critic-only controller structure by removing the identifier and actor networks in the existing methods. The adaptive law of the critic network is derived by the gradient descent algorithm and experience replay to minimize the IRL-based residual error. It is shown that a compute-saving learning mechanism can achieve the optimal consensus, and the error variables of the closed-loop system are uniformly ultimately bounded (UUB). Besides, in any bounded initial condition, the evolution of bipartite consensus is limited to a user-prescribed boundary under bounded initial conditions. The illustrative simulation results validate the efficacy of the approach.

Adaptive fuzzy fixed-time bipartite consensus control for stochastic nonlinear multi-agent systems with performance constraints

This paper investigates the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) with performance constraints. A constraint scaling function is proposed to model the performance constraints with user-predefined steady-state accuracy and settling time without relying on the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable using the constraint scaling function and an error transformation function before being used to design the controller. To achieve fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to guarantee the prescribed performance. Then, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and one adaptive parameter needs to be estimated online. It is shown that the closed-loop system has practical fixed-time stability in probability, and the antagonistic network's consensus error evolves within user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.

Event-triggered predictive control for cooperation-competition multi-agent systems under DoS attacks

This paper concerns the bipartite consensus problem of multi-agent systems(MASs) with competitive- cooperative network topology under denial-of-service (DoS) attacks. Firstly, this work extensively analyzes the competitive phenomena that may exist in the information interchange of agents in contrast to the single cooperative behavior between agents. Based on this, some necessary conditions are provided for the system to attain the bipartite consensus. In addition, the event-triggered mechanism (ETM) effectively lowers unnecessary information sharing between agents and eliminates Zeno behavior. Furthermore, the predictive method provides the system with exceptional resistance against common energy-limited DoS attacks and the ability to compensate for information loss caused by DoS attacks. Finally, a numerical simulation proves that the proposed approach is feasible.

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.

Data-Driven Adaptive Iterative Learning Bipartite Consensus for Heterogeneous Nonlinear Cooperation-Antagonism Networks

Heterogeneous dynamics, strongly nonlinear and nonaffine structures, and cooperation-antagonism networks are considered together in this work, which have been considered as challenging problems in the output consensus of multiagent systems. A heterogeneous linear data model (LDM) is presented to accommodate the nonlinear nonaffine structure of the heterogeneous agent. It also builds an I/O dynamic relationship of the agents along the iteration-dimensional direction to make it possible to learn control experience from previous iterations to improve the transient consensus performance. Then, an adaptive update algorithm is developed for the estimation of the uncertain parameters of the LDM to compensate for the unknown heterogeneous dynamics and model structures. To address the problem of cooperation and antagonism, an adaptive learning consensus protocol is proposed considering two signed graphs, which are structurally balanced and unbalanced, respectively. The learning gain can be regulated using the proposed adaptive updating law to enhance the adaptability to the uncertainties. With rigorous analysis, the bipartite consensus is proven in the case that the graph is structurally balanced, and the convergence of the agent output to zero is also proven in the case that the graph is unbalanced in its structure. The presented bipartite consensus method is data-based without the use of any explicit model information. The theoretical results are demonstrated through simulations.

Reduced-Order Observer-Based Output-Feedback Tracking Control for Nonlinear Time-Delay Systems With Global Prescribed Performance

In this article, the output-feedback tracking control problem is considered for a class of nonlinear time-delay systems in a strict-feedback form. Based on a state observer with reduced order, a novel output-feedback control scheme is proposed using the backstepping approach, which is able to guarantee the system transient and steady-state performance within a prescribed region. Different from existing works on prescribed performance control (PPC), the present method can relax the restriction that the initial value must be given within a predefined region, say, PPC semiglobally. In the case that the upper bound functions for nonlinear time-delay functions are unknown, based on the approximate capacity of fuzzy-logic systems, an adaptive fuzzy approximation control strategy is proposed. When the upper bound functions are known in prior, or in a product form with unknown parameters and known functions, an output-feedback tracking controller is designed, under which the closed-loop signals are globally ultimately uniformly bounded, and tracking control with global prescribed performance can be achieved. Simulation results are given to substantiate our method.

Distributed Control Problems on Signed Networks Under Mixed Static and Dynamic Protocols

This article aims at exploring the dynamic behaviors of signed networks under the mixed static and dynamic control protocols, which reflect the existence of two classes of communication channels. An extended leader-follower framework admitting multiple dynamic leaders is established to identify the roles of all nodes in signed networks, depending on the union of two related signed digraphs. It is shown that bipartite containment tracking is achieved for signed networks despite any topology conditions. To be specific, every leader group realizes modulus consensus and the leaders dominate the dynamic evolutions of signed networks such that all followers converge within the bounded zone spanned by the leaders' converged states and their symmetric states. Furthermore, conditions on the zero convergence of dynamic control inputs are exploited, together with those on the (interval) bipartite consensus of signed networks. Simulation examples are given to demonstrate the convergence behaviors of signed networks with respect to the mixed static and dynamic control protocols.

Robust bipartite tracking consensus of multi-agent systems via neural network combined with extended high-gain observer

In this paper, the robust bipartite tracking consensus problem for second-order multi-agent systems has been addressed in the presence of lumped disturbances and unknown velocity information. The leader's dynamics are modeled by uncertain fractional-order equality based on the neural network (NN), and the followers can only obtain the position information of the leader under the signed networks. A novel robust bipartite tracking consensus control scheme is developed by combining the NN approximators, the continuous sliding mode control (SMC) strategy, and the improved extended high-gain observer (EHGO). The improved EHGO is used to compensate for and estimate each agent's lumped disturbances and unknown velocity information in the controller design process. Moreover, NN is constructed to approximate the velocity and acceleration of the uncertain leader's dynamics for generating the feedforward signal of controllers, and the adaptive update laws of estimation parameters are generated online based on the Lyapunov function. Finally, the effectiveness of the proposed control strategy is verified by some numerical simulations.

Prescribed Performance Bipartite Consensus Control for Stochastic Nonlinear Multiagent Systems Under Event-Triggered Strategy

In this article, the event-triggered bipartite consensus problem for stochastic nonlinear multiagent systems (MASs) with unknown dead-zone input under the prescribed performance is studied. To surmount the influence of the dead-zone input, the dead-zone model is transformed into a linear term and a disturbance term. Meanwhile, the prescribed tracking performance is realized by developing a speed function, which means that all tracking errors of MASs can converge to a predefined set in a given finite time. Moreover, the unknown nonlinear dynamics are approximated by fuzzy-logic systems. By combining the dynamic surface approach and the Lyapunov stability theory, we design an adaptive event-triggered control algorithm, such that the bipartite consensus problem of stochastic nonlinear MASs can be achieved, and all signals are semiglobally uniformly ultimately bounded in probability of the closed-loop systems. Finally, simulation examples are proposed to verify the feasibility of the algorithm.

Asynchronous Tracking Control of Leader-Follower Multiagent Systems With Input Uncertainties Over Switching Signed Digraphs

Signed digraphs with both positive and negative weighted edges are widely applied to explain cooperative and competitive interactions arising from various social, biological, and physical systems. This article formulates and solves the asynchronous tracking control problem of multiagent systems with input uncertainties on switching signed digraphs. In the interaction setting, we assume that the leader moves at a time-varying acceleration that cannot be measured by the followers accurately, and further suppose that each agent receives its neighbors' states information at certain instants determined by its own clock, which is not necessary to be synchronized with those of other agents. Using dynamically changing spanning subdigraphs of signed digraphs to describe graphically asynchronous interactions, the asynchronous tracking problem is equivalently transformed into a convergence problem of products of general substochastic matrices (PGSSM), in which the matrix elements are not necessarily non-negative and the row sums are less than or equal to 1. With the help of the matrix analysis technique and the composition of binary relations, we propose a new and original method to deal with the convergence problem of PGSSM, and further establish a spanning tree condition for asynchronous tracking control. Finally, the validity of the theoretical findings is verified through several numerical examples.

Finite-Time-Prescribed Performance-Based Adaptive Fuzzy Control for Strict-Feedback Nonlinear Systems With Dynamic Uncertainty and Actuator Faults

In this article, finite-time-prescribed performance-based adaptive fuzzy control is considered for a class of strict-feedback systems in the presence of actuator faults and dynamic disturbances. To deal with the difficulties associated with the actuator faults and external disturbance, an adaptive fuzzy fault-tolerant control strategy is introduced. Different from the existing controller design methods, a modified performance function, which is called the finite-time performance function (FTPF), is presented. It is proved that the presented controller can ensure all the signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in finite time. The effectiveness of the presented control scheme is verified through the simulation results.

Lag-Bipartite Formation Tracking of Networked Robotic Systems Over Directed Matrix-Weighted Signed Graphs

This article studies the lag-bipartite formation tracking (LBFT) problem of the networked robotic systems (NRSs) with directed matrix-weighted signed graphs. Unlike the traditional formation tracking problems with only cooperative interactions, solving the LBFT problem implies that: 1) the robots of the NRS are divided into two complementary subgroups according to the signed graph, describing the coexistence of cooperative and antagonistic interactions; 2) the states of each subgroup form a desired geometric pattern asymptotically in the local coordinate; and 3) the geometric center of each subgroup is forced to track the same leader trajectory with different plus-minus signs and a time lag. A new hierarchical control algorithm is designed to address this challenging problem. Based on the Lyapunov stability argument and the property of the matrix-weighted Laplacian, some sufficient criteria are derived for solving the LBFT problem. Finally, simulation examples are proposed to validate the effectiveness of the main results.

Seeking Tracking Consensus for General Linear Multiagent Systems With Fixed and Switching Signed Networks

The existing studies for tracking consensus of multiagent systems (MASs) are all restricted to networks with only cooperative relationships among agents. Tracking consensus, however, requires beyond these traditional models due to the ubiquitous competition in many real-world MASs, such as biological systems and social systems. Taking into account this fact, this article aims to extend the dynamics of tracking consensus to signed networks containing both cooperative and competitive relationships among agents. A group of agents with general linear dynamics is considered. The cases of the fixed network as well as switching networks are analyzed, respectively. In the end, some algebraic conditions related to the network structure and the positive/negative edge weight are established to ensure the implementation of tracking consensus. Moreover, the single decoupling system is allowed to be strictly unstable in theory, and the upper bound of the eigenvalue modulus of the system matrix related to the system instability is given.

Predictor-Based Neural Dynamic Surface Control for Bipartite Tracking of a Class of Nonlinear Multiagent Systems

This article is concerned with bipartite tracking for a class of nonlinear multiagent systems under a signed directed graph, where the followers are with unknown virtual control gains. In the predictor-based neural dynamic surface control (NDSC) framework, a bipartite tracking control strategy is proposed by the introduction of predictors and the minimal number of learning parameters (MNLPs) technology along with the graph theory. Different from the traditional NDSC, the predictor-based NDSC utilizes prediction errors to update the neural network for improving system transient performance. The MNLPs technology is employed to avoid the problem of "explosion of learning parameters". It is proved that all closed-loop signals steered by the proposed control strategy are bounded, and the system achieves bipartite consensus. Simulation results verify the efficiency and effectiveness of the strategy.

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.

Distributed Control of Time-Varying Signed Networks: Theories and Applications

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent's self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks.

Further Results for Edge Convergence of Directed Signed Networks

The edge convergence problems have been explored for directed signed networks recently in 2019 by Du, Ma, and Meng, of which the analysis results, however, depend heavily on the strong connectivity of the network topologies. The question asked in this article is: whether and how can the edge convergence be achieved when the strong connectivity is not satisfied? The answer for the case of spanning tree is given. It is shown that if a signed network is either structurally balanced or r-structurally unbalanced, then the edge state can be ensured to converge to a constant vector. In contrast, if a signed network is both structurally unbalanced and r-structurally balanced, then its edge state does not converge to a constant vector any longer, but to a time-varying vector trajectory with a constant speed. Further, the dynamic behavior results of edges can be derived to address the node convergence problems of signed networks. The simulation examples are provided to illustrate the validity of the established edge convergence results.

Bipartite Tracking Consensus of Generic Linear Agents With Discrete-Time Dynamics Over Cooperation-Competition Networks

This article addresses the bipartite tracking consensus for a set of mobile autonomous agents over directed cooperation-competition networks. Here, cooperative and competitive interactions among the agents are described by positive and negative edges of the directed network topology, respectively. Both fixed and switching network topologies are considered. For the case with fixed network topology, the matrix product technique is utilized to derive the convergence result. For the case with switching network topologies, some key results related to the composition of binary relations are the main technical tools of analyzing the error system. In addition, the upper bound for the spectral radius of the system matrix is given to ensure the convergence of the system even if the single uncoupled system is strictly unstable. The applicability of the derived results is verified through two simulation experiments.

Adaptive Neural Control for a Class of Nonlinear Multiagent Systems

This article studies the adaptive neural controller design for a class of uncertain multiagent systems described by ordinary differential equations (ODEs) and beams. Three kinds of agent models are considered in this study, i.e., beams, nonlinear ODEs, and coupled ODE and beams. Both beams and ODEs contain completely unknown nonlinearities. Moreover, the control signals are assumed to suffer from a class of generalized backlash nonlinearities. First, neural networks (NNs) are adopted to approximate the completely unknown nonlinearities. New barrier Lyapunov functions are constructed to guarantee the compact set conditions of the NNs. Second, new adaptive neural proportional integral (PI)-type controllers are proposed for the networked ODEs and beams. The parameters of the PI controllers are adaptively tuned by NNs, which can make the system output remain in a prescribed time-varying constraint. Two illustrative examples are presented to demonstrate the advantages of the obtained results.

Edge Convergence Problems on Signed Networks

This paper focuses on characterizing edge dynamics of signed networks subject to both cooperative and antagonistic interactions and copes with the state convergence problems of the resulting edge systems. To represent the two competitive classes of interactions that emerge in signed networks, signed digraphs are adopted and the relevant edge Laplacian matrices are introduced, with which an edge-based distributed protocol is presented. The relation between the edge Laplacian matrix and the structural balance (or unbalance) of a signed digraph is disclosed by taking advantage of properties of undirected cycles. Further, it is shown that for a signed network, the state of its edge system converges to a constant vector, regardless of whether its associated signed digraph is structurally balanced or unbalanced. This result does not need to impose the assumption upon the digon sign-symmetry of the signed digraph that is generally required by the node-based distributed protocols. In particular, the state convergence results of edges can be exploited to handle traditional bipartite consensus problems for the nodes of signed networks. Simulation examples are given to illustrate the effectiveness of the edge-based analysis method proposed for signed networks.