Output-Feedback-Based Adaptive Leaderless Consensus for Heterogenous Nonlinear Multiagent Systems With Switching Topologies.

This article investigates the leaderless output consensus control problem for a class of nonlinear multiagent systems with heterogenous system orders and unmatched unknown parameters via output-feedback control. The interaction topology among the agents is undirected and jointly connected. Due to the heterogenous system orders and switching topology among the agents, the classical distributed adaptive backstepping-based control technique cannot be applied to solve the problem considered in this article. To solve this issue, a novel distributed reference system is first proposed for each agent, by using only relative outputs of the neighboring agents. Subsequently, a fully distributed reference system-based adaptive leaderless output consensus control scheme is designed via output-feedback control. A remarkable merit of the proposed control scheme lies in that precisely known nonlinear dynamics, system states, distributed parameter estimates, and the states of virtual reference system are no longer needed to be shared with neighbors. This implies that the communication burden can be effectively alleviated, and even the communication network can be replaced by some perception sensors. Finally, two illustrative examples are provided to verify the effectiveness of the proposed control scheme.

Decentralized Adaptive Secure Control of Uncertain Nonlinear Time-Varying Interconnected Systems Against Sensor and Actuator Attacks.

In this article, the decentralized adaptive secure control problem for cyber-physical systems (CPSs) against deception attacks is investigated. The CPSs are formed as a type of nonlinear interconnected strict-feedback systems with uncertain time-varying parameters. The attack affects the information transmission between sensor and actuator in a multiplicative manner. A novel decentralized adaptive backstepping secure control strategy is established by exploiting a particular kind of Nussbaum functions and a flat-zone Lyapunov function analysis approach. It is shown that all of closed-loop signals remain globally bounded, and each output signal eventually converges into a small neighborhood of the origin. Simulation results on an illustrative example are provided to display the effectiveness of the proposed control scheme.

Adaptive Anti-Disturbance Control for a Class of Uncertain Nonlinear Systems With Composite Disturbances.

High-precision and safety control in face of disturbances and uncertainties is a challenging issue of both theoretical and practical importance. In this article, new adaptive anti-disturbance control schemes are proposed for a class of uncertain nonlinear systems with composite disturbances, including additive disturbances, multiplicative actuator faults, and implicit disturbances deeply coupled with system states. Both the cases with known and unknown control/fault directions are investigated. By properly fusing the techniques of disturbance observers and adaptive compensation, it is shown that all closed-loop signals are globally uniformly bounded and the tracking error converges to zero asymptotically, no matter the control/fault directions are known or not. In the case of known directions, the proposed control scheme, for the first time, guarantees asymptotic tracking and L ∞ tracking performance simultaneously in face of disturbances and actuator faults. Moreover, novel Nussbaum functions and a contradiction argument are introduced, which allow the system to have multiple unknown nonidentical control directions and unknown time-varying fault direction. Simulation results illustrate the effectiveness of the proposed control schemes.

Asymptotic Tracking Control With Bounded Performance Index for MIMO Systems: A Neuroadaptive Fault-Tolerant Proportional-Integral Solution.

It is technically challenging to maintain stable tracking for multiple-input-multiple-output (MIMO) nonlinear systems with modeling uncertainties and actuation faults. The underlying problem becomes even more difficult if zero tracking error with guaranteed performance is pursued. In this work, by integrating filtered variables into the design process, we develop a neuroadaptive proportional-integral (PI) control with the following salient features: 1) the resultant control scheme is of the simple PI structure with analytical algorithms for auto-tuning its PI gains; 2) under a less conservative controllability condition, the proposed control is able to achieve asymptotic tracking with adjustable rate of convergence and bounded performance index collectively; 3) with simple modification, the strategy is applicable to square or nonsquare affine and nonaffine MIMO systems in the presence of unknown and time-varying control gain matrix; and 4) the proposed control is robust against nonvanishing uncertainties/disturbances, adaptive to unknown parameters and tolerant to actuation faults, with only one online updating parameter. The benefits and feasibility of the proposed control method are also confirmed by simulations.

Data-Driven Practical Cooperative Output Regulation Under Actuator Faults and DoS Attacks.

This article addresses the resilient practical cooperative output regulation problem (RPCORP) for multiagent systems subjected to both denial-of-service (DoS) attacks and actuator faults. Fundamentally different from the existing solutions to RPCORPs, the system parameters considered in this article are unknown to each agent, and a novel data-driven control approach is introduced to handle such an issue. The solution starts with developing resilient distributed observers for each follower in the presence of DoS attacks. Then, a resilient communication mechanism and a time-varying sampling period are introduced to, respectively, ensure the neighbor state is available as soon as attacks disappear and to avoid targeted attacks launched by intelligent attackers. Furthermore, a model-based fault-tolerant and resilient controller is designed based on the Lyapunov approach and the output regulation theory. In order to remove the reliance on system parameters, we leverage a new data-driven algorithm to learn controller parameters via the collected data. Rigorous analysis shows that the closed-loop system can resiliently achieve practical cooperative output regulation. Finally, a simulation example is given to illustrate the effectiveness of the achieved results.

Event-Triggered Practical Prescribed Time Output Feedback Neuroadaptive Tracking Control Under Saturated Actuation.

This work focuses on the issue of event-triggered practical prescribed time tracking control for a type of uncertain nonlinear systems subject to actuator saturation and unmeasurable states as well as time-varying unknown control coefficients. First, a state observer with simple structure is constructed by means of neural network technology to estimate the unmeasurable system states under time-varying control coefficients. Then, with the help of one-to-one nonlinear mapping of the tracking error, an event-triggered output feedback control scheme is developed to steer the tracking error into a residual set of predefined accuracy within a preassigned settling time. Unlike existing related control methods, there is no need to involve finite-time state observer or fractional power feedback of system states, and thus, the control solution presented here is less complex and more acceptable. The key technique in control design lies in the establishment of an alternative first-order auxiliary system for dealing with the impact arisen from the input saturation. In our proposed approach, a new bounded function related to auxiliary variable and new dynamics of the auxiliary system are skillfully utilized such that the upper bound of the difference between actual input and designed input signal is not involved in implementation of the controller.

Adaptive Event-Triggered Fast Finite-Time Stabilization of High-Order Uncertain Nonlinear Systems and Its Application in Maglev Systems.

This article is concerned with the global fast finite-time adaptive stabilization for a class of high-order uncertain nonlinear systems in the presence of serious nonlinearities and constraint communications. By renovating the technique of continuous feedback domination to the construction of a serial of integral functions with nested sign functions, this article first proposes a new event-triggered strategy consisting of a sharp triggered rule and a time-varying threshold. The strategy guarantees the existence of the solutions of the closed-loop systems and the fast finite-time convergence of original system states while reaching a compromise between the magnitude of the control and the trigger interval. Quite different from traditional methods, a simple logic is presented to avoid searching all the possible lower bounds of trigger intervals. An example of the maglev system and a numerical example are provided to demonstrate the effectiveness and superiority of the proposed strategy.

Optimal Control of Temporal Networks With Variable Input and Node-Source Connection.

Many networked systems built upon real-life physical or social interactions have time-varying connections among individual units, where the temporal changes in connectivity and/or interaction strength lead to complicated dynamics. The temporal network model was proposed in the form of controlled linear dynamical systems acting in an ordered sequence of time intervals. One of the core challenges in network science is the control of networks and the optimization of the control strategy. However, most canonical frameworks for solving optimal control problems were established for static networks featuring constant topology. New theories and techniques are yet to be developed for the temporal networks, with an important case being that the input and the source-node connection are both variables. In this work, by formulating a quadratic energy cost without solving the Riccati differential equation, we show that the control effort can be reduced substantially by improving either the system trajectories or the input matrices. The two approaches are further combined in a coordinate descent framework, integrating linearly constrained quadratic programming, and a projected gradient descent method. Taken together, the results underline the potential of temporal networks as energy-efficient control systems and present strategies to improve the control input. Moreover, the proposed algorithms can serve as a starting point for future engineering of real-world temporal networks.

Resilient Cooperative Control for Networked Lagrangian Systems Against DoS Attacks.

In this article, we study the distributed resilient cooperative control problem for directed networked Lagrangian systems under denial-of-service (DoS) attacks. The DoS attacks will block the communication channels between the agents. Compared with the existing methods for the linear networked systems, the considered nonlinear networked Lagrangian systems with asymmetric channels under DoS attacks are more challenging and still not well explored. In order to solve this problem, a novel resilient cooperative control scheme is proposed by using the sampling control approach. Sufficient conditions are first derived in the absence of DoS attacks according to a multidimensional small-gain scheme. Then, in the presence of DoS attacks, the proposed resilient scheme works in a switching manner. Inspired by multidimensional small-gain techniques, the Lyapunov approach is used to analyze the closed-loop system, which enables us to establish sufficient stability conditions for the control gains in terms of the duration and frequency of the DoS attacks.

Training Deep Neural Network for Optimal Power Allocation in Islanded Microgrid Systems: A Distributed Learning-Based Approach.

Currently, numerical optimization methods are used to solve distributed optimal power allocation (OPA) problems for islanded microgrid (MG) systems. Most of them are developed based on rigorous mathematical derivation. However, the complexity of such optimization algorithms inevitably creates a gap between theoretical analysis and real-time implementation. In order to bridge such a gap, in this article we provide a new distributed learning-based framework to solve the real-time OPA problem. Specifically, inspired by the human-thinking scheme, distributed deep neural networks (DNNs) together with a dynamic average consensus algorithm are first employed to obtain an approximate OPA solution in a distributed manner. Then a distributed balance generation and demand algorithm is designed to fine-tune it to obtain the final optimal feasible solution. In addition, it is theoretically proved that the proposed DNN can well approximate one existing OPA algorithm (Guo et al. 2018), where quantitative numbers of at most how many hidden layers and neurons are provided. Several experimental case studies show that our proposed distributed learning framework can achieve similar optimal results to those obtained by using typical existing distributed numerical optimization methods while it is superior in terms of simplicity and real-time capability.

A Distributed Lyapunov-Based Redesign Approach for Heterogeneous Uncertain Agents With Cooperation-Competition Interactions.

A swarming behavior problem is investigated in this article for heterogeneous uncertain agents with cooperation-competition interactions. In such a problem, the agents are described by second-order continuous systems with different intrinsic nonlinear terms, which satisfies the "linearity-in-parameters" condition, and the agents' models are coupled together through a distributed protocol containing the information of competitive neighbors. Then, for four different types of cooperation-competition networks, a distributed Lyapunov-based redesign approach is proposed for the heterogeneous uncertain agents, where the distributed controller and the estimation laws of unknown parameters are obtained. Under their joint actions, the heterogeneous uncertain multiagent system can achieve distributed stabilization for structurally unbalanced networks and output bipartite consensus for structurally balanced networks. In particular, the concept of coherent networks is proposed for structurally unbalanced directed networks, which is beneficial to the design of distributed controllers. Finally, four illustrative examples are given to show the effectiveness of the designed distributed controller.

Adaptive Resilient Secondary Control for Microgrids With Communication Faults.

In this article, we consider the resilience problem in the presence of communication faults encountered in distributed secondary voltage and frequency control of an islanded alternating current microgrid. Such faults include the partial failure of communication links and some classes of data manipulation attacks. This practical and important yet challenging issue has been taken into limited consideration by existing approaches, which commonly assume that the measurement or communication between the distributed generations (DGs) is ideal or satisfies some restrictive assumptions. To achieve communication resilience, a novel adaptive observer is first proposed for each individual DG to estimate the desired reference voltage and frequency under unknown communication faults. Then, to guarantee the stability of the closed-loop system, voltage and frequency restoration, and accurate power sharing regardless of unknown communication faults, sufficient conditions are derived. Some simulation results are presented to verify the effectiveness of the proposed secondary control approach.

A Hierarchical Security Control Framework of Nonlinear CPSs Against DoS Attacks With Application to Power Sharing of AC Microgrids.

In this article, we investigate the distributed resilient observers-based decentralized adaptive control problem for cyber-physical systems (CPSs) with time-varying reference trajectory under denial-of-service (DoS) attacks. The considered CPSs are modeled as a class of nonlinear multi-input uncertain multiagent systems, which can be used to model an AC microgrid system consisting of distributed generators. When the communication to a subsystem from one of its neighbors is attacked by a DoS attack, the transmitted information is unavailable and the existing distributed adaptive methods used to estimate the bound of the n th-order derivative of the reference trajectory become nonapplicable. To overcome this difficulty, we first design a new distributed estimator for each subsystem to ensure that the magnitude of the state of the estimator is larger than the bound of the n th-order derivative of the reference trajectory after a finite time. By employing the estimator state, a distributed observer with a switching mechanism is proposed. Then, a new block backstepping-based decentralized adaptive controller is developed. Based on the DoS communication duration property, convex design conditions of observer parameters are derived with the Lebesgue integral theory and the average dwell time method. It is proved that the output tracking errors will approach a compact set with the developed method. Finally, the design method is successfully applied to show the effectiveness of the proposed method to solve the power sharing problem for AC microgrids.

Adaptive Consensus Control for Nonlinear Multiagent Systems With Unknown Control Directions Using Event-Triggered Communication.

In this article, under directed graphs, an adaptive consensus tracking control scheme is proposed for a class of nonlinear multiagent systems with completely unknown control coefficients. Unlike the existing results, here, each agent is allowed to have multiple unknown nonidentical control directions, and continuous communication between neighboring agents is not needed. For each agent, we design a group of novel Nussbaum functions and construct a monotonously increasing sequence in which the effects of our Nussbaum functions reinforce rather than counteract each other. With these efforts, the obstacle caused by the unknown control directions is successfully circumvented. Moreover, an event-triggering mechanism is introduced to determine the time instants for communication, which considerably reduces the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors can converge to an arbitrarily small residual set. Simulation results illustrate the effectiveness of the proposed scheme.

Adaptive Bearing-Only Formation Tracking Control for Nonholonomic Multiagent Systems.

In this article, we consider the formation tracking problem of nonholonomic multiagent systems only using relative bearing measurements between the agents. Such a practical and important yet challenging issue has been taken into limited consideration by existing approaches, which usually requires additional measurements such as relative positions. The contributions of this article are two-fold. First, a fully distributed reference velocity estimator is proposed. Under the proposed adaptive estimator, each agent can estimate the time-varying reference velocity asymptotically. Second, an input-to-state stable controller is designed according to the bearing rigid theory. Under the proposed controller, the formation with bearing-only constraints can be achieved. Finally, the proposed scheme is demonstrated and its effectiveness is verified by presenting some simulation and experimental tests.

Key Nodes Selection in Controlling Complex Networks via Convex Optimization.

Key nodes are the nodes connected with a given number of external source controllers that result in minimal control cost. Finding such a subset of nodes is a challenging task since it impossible to list and evaluate all possible solutions unless the network is small. In this paper, we approximately solve this problem by proposing three algorithms step by step. By relaxing the Boolean constraints in the original optimization model, a convex problem is obtained. Then inexact alternating direction method of multipliers (IADMMs) is proposed and convergence property is theoretically established. Based on the degree distribution, an extension method named degree-based IADMM (D-IADMM) is proposed such that key nodes are pinpointed. In addition, with the technique of local optimization employed on the results of D-IADMM, we also develop LD-IADMM and the performance is greatly improved. The effectiveness of the proposed algorithms is validated on different networks ranging from Erdos-Rényi networks and scale-free networks to some real-life networks.

A Unified Event-Triggered Control Approach for Uncertain Pure-Feedback Systems With or Without State Constraints.

Existing schemes for systems with state constraints require the bounds of the constraints for controller design and may result in conservativeness or even become invalid when they are applied to systems without such constraints. In this paper, we study the problem of event-triggered control for a class of uncertain nonlinear systems by considering the cases with or without state constraints in a unified manner. By introducing a new universal-constrained function and using certain transformation techniques, the original-constrained system is converted into an equivalent totally unconstrained one. Then, an event-triggered adaptive neural-network (NN) controller is designed to stabilize the unconstrained system and compensate for the control sampling errors caused by event-triggered transmission of control signals. Unlike some existing control schemes developed for systems with state constraints, which need to check whether each virtual control meets certain feasibility conditions at every design step, our proposed unified method enables such feasibility conditions to be relaxed. In addition, a suitable event-triggering rule is designed to determine when to transmit control signals. It is theoretically shown that the designed controller can achieve the desired tracking ability and reduce the communication burden from the controller to the actuator at the same time. Simulation verification also confirms the effectiveness of the proposed approach.

Linear Quadratic Optimal Control of Time-Invariant Linear Networks With Selectable Input Matrix.

Optimal control of networks is to minimize the cost function of a network in a dynamical process with an optimal control strategy. For the time-invariant linear systems, · x(t)=A x(t)+B u(t) , and the traditional linear quadratic regulator (LQR), which minimizes a quadratic cost function, has been well established given both the adjacency matrix A and the control input matrix B . However, this conventional approach is not applicable when we have the freedom to design B . In this article, we investigate the situation when the input matrix B is a variable to be designed to reduce the control cost. First, the problem is formulated and we establish an equivalent expression of the quadratic cost function with respect to B , which is difficult to obtain within the traditional theoretical framework as it requires obtaining an explicit solution of a Riccati differential equation (RDE). Next, we derive the gradient of the quadratic cost function with respect to the matrix variable B analytically. Further, we obtain three inequalities of the cost functions, after which several possible design (optimization) problems are discussed, and algorithms based on gradient information are proposed. It is shown that the cost of controlling the LTI systems can be significantly reduced when the input matrix becomes "designable." We find that the nodes connected to input sources can be sparsely identified and they are distributed as evenly as possible in the LTI networks if one wants to control the networks with the lowest cost. Our findings help us better understand how the LTI systems should be controlled through designing the input matrix.

Adaptive Formation Control of Networked Robotic Systems With Bearing-Only Measurements.

In this article, we address the bearing-only formation control problem of 3-D networked robotic systems with parametric uncertainties. The contributions of this article are two-fold: 1) the bearing-rigid theory is extended to solve the nonlinear robotic systems with the Euler-Lagrange-like model and 2) a novel almost global stable distributed bearing-only formation control law is proposed for the nonlinear robotic systems. Specifically, the robotic systems subject to nonholonomic constraints and dynamics are first transformed into a Euler-Lagrange-like model. By exploring the bearing-rigid graph theory, a backstepping approach is used to design the distributed formation controller. Simulations for 3-D robotics are given to demonstrate the effectiveness of the proposed control law. Compared to the distance-rigid formation control approach, the bearing-rigid approach guarantees almost global stability while naturally excluding flip ambiguities.

MAS-Based Distributed Resilient Control for a Class of Cyber-Physical Systems With Communication Delays Under DoS Attacks.

In this article, we investigate the distributed resilient control problem for a class of cyber-physical systems with communication delays under denial-of-service (DoS) attacks. In contrast to the previous DoS attacks results based on multiagent systems (MASs), a new distributed resilient control approach is proposed for more general heterogeneous linear MASs with nonuniform communication delays. Two types of sampled-based observers are, respectively, proposed. Namely, adaptive distributed observers are designed by introducing a buffer mechanism to eliminate the heterogeneous behavior caused by communication delays while adaptive distributed resilient observers are designed by introducing resilient mechanisms to resist the DoS attacks. Furthermore, a time-varying sampling period sequence is provided to prevent the attacker from identifying the sampling period of the system. Based on the developed resilient observers, a controller is developed. It is proved that the considered problem can be solved by the developed method. Finally, a numerical example is given to illustrate the effectiveness of the obtained result.