This paper addresses the consensus-based distributed dispatch problem for multiple generators by incorporating a backup system for dealing with denial-of-service (DoS) attacks. A novel backup system-based approach has been proposed, motivated by digital twins, by considering generator information and incorporating predictive neural networks (NNs) under the occurrence of DoS attacks on a smart grid. This approach integrates the machine learning predictive feature of XGBoost with consensus protocol to mitigate the multi-channel DoS attacks. The convergence and stability analysis has been provided for the distributed optimization by the application of multiple Lyapunov functions, Lyapunov redesign, and consideration of the absence or occurrence of attacks. The predictive capability of the proposed method allows the dispatch framework to intelligently forecast, adjust, and allocate energy based on dynamic inputs, such as demand fluctuations or DoS-induced disruptions. Compared with conventional methods addressing DoS attacks, this approach is superior: (i) in dealing with DoS attacks due to consideration of an offline trained dynamic backup system, and (ii) can handle multi-channel DoS attacks due to a digital twin-oriented backup system for predicting the generator behavior. Finally, an extensive simulation study is presented to model the NNs, analyze different predictive NNs, and deploy NNs for DoS mitigation.

This paper deals with a multifaceted output feedback consensus control approach for multi-agent systems (MASs) under stochastic denial-of-service (DoS) cyber-attacks. First, a fully-distributed resilient cooperative state estimation approach to estimate the leader’s state by followers over a sensor network has been devised. The proposed estimation approach ensures robust state estimation, exponential convergence, and stability of the adaptive mechanism against perturbations. Then, a new multi-objective fully-distributed secure output-feedback consensus control approach under DoS-attacks is proposed for achieving the leader-following consensus among MASs over a directed network. Several objectives like fully-distributed consensus, reliance on both leader’s and followers’ outputs, robustness against disturbances, exponential convergence of estimation, and consensus errors have been considered in the proposed resilient consensus methodology. In contrast to existing methods, the proposed secure consensus approach does not require the global information of network connectivity, is applicable to directed communication topologies, is robust against perturbations, and employs outputs of both leader and followers for feedback. An illustrative simulation study is presented for F-18 aircraft systems to demonstrate the effectiveness of the proposed methodologies for secure cooperative state estimation and resilient consensus control.

This article investigates the leader-following cluster consensus for generic linear heterogeneous multiagent systems (MASs). Unlike the existing research, a novel event-triggered (ET) control mechanism is designed and developed on the transmission side of the agents, over directed communication topologies, to reduce communication load. For this purpose, a variable threshold function as the fully distributed ET condition (ETC) is suggested, which provides a smooth transition and considers both maximum and minimum threshold levels for triggering. A relative-state feedback-based cluster consensus control protocol is designed by considering the cooperative and competitive interaction behavior of agents. Then, the convergence analysis is performed by utilizing the Lyapunov method. This work is then further extended for the ET observer-based output feedback cluster consensus problem. The proposed ETC naturally eliminates the Zeno behavior for each agent. In contrast to existing methods, a variable threshold-based ET scheme, a cooperation-competition network, and an elimination of Zeno behavior for both state-based and output-based methods have been considered for the leader-following cluster consensus. Finally, illustrative examples are used to validate the theoretical results.

This paper is concerned with the resilient leader-following consensus control (LFCC) of multi-agent systems (MASs) subjected to denial-of-service (DoS) attacks. Unlike most existing studies, the considered DoS attacks can independently jeopardize different communication links and are modeled using the Markovian switching phenomenon. First, a cooperative fully-distributed estimator is introduced that enables the follower agents to estimate the leader’s state. The proposed cooperative estimator relaxes the requirement for knowledge about the exact leader state during the occurrence of DoS attacks. The cooperative estimator is then used to solve the resilient LFCC of MASs under two different control protocols. The dynamic state feedback (DSF)-based consensus protocol is first used to solve the fully-distributed resilient LFCC problem with cooperative estimation of the leader state. Then, to overcome the limitation of the follower’s state unavailability, a novel dynamic output feedback (DOF)-based control protocol is introduced to solve the resilient consensus problem. The design conditions for the proposed estimators and controllers are derived using the Lyapunov theory. Unlike existing studies, the proposed strategy 1) employs estimated states for feedback, 2) is fully-distributed, and 3) is independent of bounds on attack frequency or duration. Finally, the applicability of the presented strategies is validated through a simulation example involving the F-18 aircraft model.Note to Practitioners—The purpose of the present work is to provide an output feedback approach for the LFCC of MASs by incorporating cyber attacks. The cyber attacks in the form of DoS while communicating over a network have been considered. The state estimation problem over a network under DoS attacks on communication links has been solved by using the cooperative estimator equation. Then, the adaptive and smoothing coupling weights are updated by applying the local estimation error. The proposed approach employs an adaptive mechanism for handling DoS attacks over the communication topology to deal with unknown connections. This mechanism does not require knowledge of the topology between agents and, consequently, does not require the central unit for implementation. Then, two approaches are used to solve the problem of resilient cooperative control: 1) by employing the estimation of the leader’s state only; 2) by employing both estimates of the leader’s and followers’ states. The proposed approach can be applied practically by solving cooperative and conventional observers along with adaptation weights, recursively, in addition to an algebraic equation for estimated state feedback. Moreover, the presented method can deal with independent attacks on different communication channels, which is a practical scenario. The proposed approach can be applied to consensus and formation control applications under cyber attacks, like the formation of aircrafts, consensus in robots, and synchronization in power systems. The presented approach has been applied to attain consensus in F-18 aircrafts, and simulation results are shown.

This paper addresses a fully-distributed consensus control scheme for multi-agent systems (MASs) with state and input nonlinearities under denial-of-service (DoS) attacks. When agents interact with their neighbors, an adversary with malicious intent randomly launches DoS attacks on specific communication channels in the network, resulting in Markovian switching communication topology. Under stochastic DoS attacks, a fully-distributed secure consensus algorithm is proposed using Lyapunov function analysis that is based solely on immediate partial information per node rather than global information. In addition, the developed approach does not require any specific probability or topology pattern under DoS attack. Furthermore, a novel treatment of the input nonlinearity has been established. For this purpose, the input nonlinearity has been transformed, and a condition in terms of a cumulative nonlinearity bound has been formulated via graph characteristics and algebraic properties. Resilient consensus control design conditions have been established by taking into account the input and state nonlinearities. The developed methods only require a spanning tree between MASs for a union of graph topologies under malicious attacks. Moreover, the resultant consensus protocol is fully-distributed by means of an adaptation mechanism, which has been specifically developed for the directed topologies. The efficiency of the consensus approach has been demonstrated using a simulation of robotic systems along with comparison with a closely-related existing work. Note to Practitioners—The purpose of the present study is to provide a control approach for the consensus of nonlinear MASs under DoS cyber-attacks. Nonlinearities in the state equation and control input are considered, which arise owing to the modeling process of physical systems and actuator’s nonlinear characteristics, respectively. A property for dealing with input nonlinearities in MASs has been provided from the consensus control perspective. DoS attacks can be launched by malicious attackers in cyber-physical systems by blocking the communication channels for information flow. A control scheme has been provided by application of time-varying and adaptive parameters to deal with the resilient consensus control of nonlinear MASs under DoS attacks. In addition, a simple design method is established for practitioners to determine the controller gains using numerical routines. The developed distributed consensus method does not require the knowledge of communication topology to find the parameters of the control systems, and such a method is referred to as a fully-distributed consensus approach. The resultant scheme considers the directed graph topologies which do not require bidirectional communication between any two systems. The study has been tested for the consensus of robotic agents under DoS attacks, and the results are compared with the methods available in the literature.

This article addresses the distributed cooperative protocol for nonlinear agents with the aim of attaining the optimal leader-following consensus. The main challenges encountered when deriving the cooperative optimal protocol are caused due to the conservatism of Lipschitz nonlinear dynamics, uncertainties, disturbances, and coupling of agents. Until now, the consensus optimal protocols for Lipschitz nonlinear agents are provided in the existing literature, which is conservative and has limited applications. To tackle these issues, a cooperative protocol is provided for intelligent nonlinear systems that are optimal for the performance index and robust against uncertainties and disturbances. The performance index of the optimal protocol depends on the Lipschitz nonlinearities is converted into linear parameter-varying (LPV) form. The LPV approach reduces the conservatism of the existing methods for Lipschitz nonlinearities that improves the scope of the design approach and is applicable to practical applications of nonlinear multiagents. The optimal solution is obtained by solving the algebraic Riccati equation. The proposed optimal scheme increases the region of the feasibility of the Lipschitz constant by extracting precise information about nonlinearities. Moreover, a robust cooperative optimal protocol is designed that has ensured optimal consensus for the nonlinear agents and eliminated the negative effects of parameter uncertainties and disturbances. Finally, the results are verified through a simulation example of multiple nonlinear robotic manipulators.

In this article, the group consensus problem is addressed for a network of multiagent systems (MASs). Unlike in existing literature, where a relative-state feedback-based distributed control input is used to achieve group consensus, this work aims at designing a relative-output-based distributed control law to achieve the same goal. To that effect, the Lyapunov stability theory is used to formulate the sufficient and necessary conditions for the existence of such a feedback controller and then separate conditions have been included for its design. In addition to that, a new linear matrix inequality is explored to choose the intracluster coupling strengths to ensure group consensus. In this article, the relative-output-based control approach is investigated for both the leaderless and the leader-following frameworks of the group consensus problem, and the theoretical findings presented are validated using numerical examples and simulation results.

In active noise control systems, the performance of the most celebrated filtered-x-least mean square (FxLMS) adaptive algorithm is degraded in the presence of non-linearity in the secondary path. In this article, we propose a novel approach to improve the performance of FxLMS algorithm in the presence of saturation type non-linearity in the secondary path. In the proposed method, the weights of the controller are adapted by minimizing a cost function consisting of two terms. The first term is the squared instantaneous residual error while the second term is the weighted square of the difference between input and output of (estimated) saturation non-linearity. Consequently, in case the saturation has occurred, the resultant adaptive algorithm minimizes the residual error while keeping the controller output close to its saturation limit. This avoids unnecessary fluctuation of the (controller) weights due to large variation (or windup) of the controller output after the saturation has occurred. Numerical simulations are provided to verify the superiority of the reported approach as compared to existing methods under different conditions.

This paper considers the leader-following consensus of multiagents with one-sided Lipschitz nonlinear dynamics by considering switching topologies. For the suitable selection of the consensus control gain matrix and coupling weight, a new condition for consensus is achieved for switching communication links with a directed spanning tree in the topology by constraining the dwell time. Employing a communication restoration mechanism allows a method to be obtained for the case in which a topology violates a permanent directed spanning tree. Computationally straightforward consensus controller design conditions that are necessary and sufficient for the former conditions are also developed for both cases. These simpler conditions can be used to obtain consensus protocol gains directly through convex routines. An algorithm is also provided to solve nonlinear constraints using the cone complementary linearization approach by considering a nonlinear objective function optimization problem. A numerical simulation is provided for multiagents that demonstrates the proposed control schemes' efficiency.

This article addresses the robust nonlinear adaptive consensus protocol design approach, for nonlinear multiagent (MA) systems under external perturbations with Lipschitz dynamics. Based on the existing results of the adaptive protocol using relative output information, a modified robust nonlinear adaptive consensus protocol for MAs is proposed. The Lipschitz nonlinearity in the agents’ dynamics and the adaptive protocol are reformulated using a composite linear parameter-varying (LPV) approach. Our composite LPV reformulation is less restrictive because it utilizes all the properties of Lipschitz functions. Consensus protocol design conditions based on the proposed reformulation of Lipschitz nonlinearities, Lyapunov theory, and the modified nonlinear consensus protocol are derived to attain the exponential consensus. The proposed consensus protocol approach is further extended by providing necessary and sufficient conditions for the straightforward evaluation of the robust adaptive protocol gains. The proposed fully distributed consensus protocol is robust to ensure the consensus error and adaptive gains bounded by eliminating the effect of disturbances. The resultant consensus control scheme reduces conservatism and is feasible for large values of Lipschitz constants. Finally, simulation results are presented for verifying the potency of the developed control strategies.

This paper addresses the leaderless consensus control for a network of multiagent systems with the one-sided Lipschitz and quadratic inner-boundedness nonlinear dynamics. A distributed dynamic consensus protocol as a function of relative state feedback of the neighboring agents with edge-based adaptive coupling weights is designed for an undirected communication graph to achieve asymptotic consensus among the nonlinear agents. Further, an extension of the proposed consensus protocol in the presence of external disturbance is devised to ensure the L2stability of the consensus error. This paper is less conservative and more general owing to its application to the systems with large Lipschitz constants and to a broad class of the nonlinear systems. In comparison to the previous consensus control schemes, the proposed approach can be employed to design consensus protocols for the one-sided Lipschitz systems with unknown communication topology. This feature enables the fully distributed consensus control as the communication graph information is not required for the consensus protocol design. Simulation results for a network of six mobile agents are provided to demonstrate the effectiveness of proposed consensus schemes in the absence or presence of an external disturbance.

This article presents a method for contriving the global anti-windup compensator (AWC) gain for nonlinear systems by using the nomenclature of nonlinear parameter varying (NPV) theory. The sufficient conditions for the existence of static AWC for NPV system under actuator saturation while considering the exogenous inputs and actuator constraints guaranteeing the global asymptotic stability of the overall closed-loop system are formulated. Linear matrix inequality (LMI)-based conditions are deducted via Lyapunov theory, NPV theory, global sector condition, minimum and maximum bound on the saturation non-linearity, and parametric variations limits in order to synthesis the AWC which ensure global asymptotic stability of the overall closed-loop system. In order to show the effectiveness of of the suggested AWC methodology the simulation example of the nonlinear induction motor is provided.

This paper addresses the distributed consensus controller design approaches for one-sided Lipschitz nonlinear multiagents by employing relative state feedback. A new treatment for one-sided Lipschitz nonlinearity is rendered from the consensus control point of view. By employing the quadratic inner-boundedness and the one-sided Lipschitz constraints, a sufficient condition for asymptotic consensus of nonlinear systems under strongly connected communication topologies is provided. Further, a robust consensus protocol design scheme for the nonlinear multiagents is derived by ensuring the L2stability of the consensus error system. Furthermore, a novel robust consensus control scheme against amplitude-bounded perturbations is developed that guarantees asymptotic convergence of the consensus error into a compact set. Extensions to the proposed methodologies for the leader-following consensus for a spanning tree communication topology with the leader as the root are addressed. In contrast to the conventional consensus control methodologies, this paper is less conservative and can be applied to a broader class of nonlinear multiagent systems. Moreover, the proposed consensus control approach is less conservative for robustness against disturbances owing to its ability to handle amplitude-bounded disturbances and due to the relaxation of a balanced communication topology. A numerical simulation study is provided for the consensus control of eight mobile agents.