Byzantine-Resilient Second-Order Consensus in Networked Systems.

This article studies the second-order consensus problem in networked systems containing the so-called Byzantine misbehaving nodes when only an upper bound on either the local or the total number of misbehaving nodes is known. The existing results on this subject are limited to malicious/faulty model of misbehavior. Moreover, existing results consider consensus among normal nodes in only one of the two states, with the other state converging to either zero or a predefined value. In this article, a distributed control algorithm capable of withstanding both locally bounded and totally bounded Byzantine misbehavior is proposed. When employing the proposed algorithm, the normal nodes use a combination of the two relative state values obtained from their neighboring nodes to decide which neighbors should be ignored. By introducing an underlying virtual network, conditions on the robustness of the communication network topology for consensus on both states are established. Numerical simulation results are presented to illustrate the effectiveness of the proposed control algorithm.

Robust Collision-Avoidance Formation Navigation of Velocity and Input-Constrained Multirobot Systems.

In this work, we consider the safe deployment problem of multiple robots in an obstacle-rich complex environment. When a team of velocity and input-constrained robots is required to move from one area to another, a robust collision-avoidance formation navigation method is needed to achieve safe transferring. The constrained dynamics and the external disturbances make the safe formation navigation a challenging problem. A novel robust control barrier function-based method is proposed which enables collision avoidance under globally bounded control input. First, a nominal velocity and input-constrained formation navigation controller is designed which uses only the relative position information based on a predefined-time convergent observer. Then, new robust safety barrier conditions are derived for collision avoidance. Finally, a local quadratic optimization problem-based safe formation navigation controller is proposed for each robot. Simulation examples and comparison with existing results are provided to demonstrate the effectiveness of the proposed controller.

The Future of Process Industry: A Cyber-Physical-Social System Perspective.

The process industry is an industrial field of interdisciplinary nature involving electrical engineering, energy, petroleum, chemical, and metallurgy, which play a key role in the sustainable development. As a main source of CO 2 emissions, the process industry will undertake a large part of the emission reduction task. In order to incorporate the impact of social factors, such as environment, society, and human to support the future process industry, the cyber-physical-social system (CPSS) framework should be considered as a promising way to enhance the transformation of the process industry. The development of CPSS technologies will fundamentally change the infrastructure of conventional industrial systems, offering a great opportunity for the greenization, high-value, and digitalization in the process industry. This article first presents the current status of the process industry. Through a CPSS framework, the current developments of the process industry as well as the main challenges and opportunities are discussed. A vision for the future process industry based on CPSS is described by focusing on three aspects, namely, the greenization and low carbon, high-value and high-end, digitalization, and intellectualization in process manufacturing. Finally, the advanced technologies and approaches in CPSS driven by artificial intelligence and industrial digitalization, which are important in achieving the sustainable development of the process industry, are outlined. The development of the comprehensive digital technologies, such as virtual reality, digital twin, blockchain, and big data, will stimulate the implementation of a ground-breaking concept formed in the CPSS framework called industrial metaverse.

Fixed-Time Cooperative Tracking Control for Double-Integrator Multiagent Systems: A Time-Based Generator Approach.

In this article, both the fixed-time distributed consensus tracking and the fixed-time distributed average tracking problems for double-integrator-type multiagent systems with bounded input disturbances are studied. First, a new practical robust fixed-time sliding-mode control method based on the time-based generator is proposed. Second, two fixed-time distributed consensus tracking observers for double-integrator-type multiagent systems are designed to estimate the state disagreement between the leader and the followers under undirected and directed communication, respectively. Third, a fixed-time distributed average tracking observer for double-integrator-type multiagent systems is designed to measure the average value of multiple reference signals under undirected communication. Note that all the proposed observers are constructed with time-based generators and can be trivially extended to that for high-order integrator-type multiagent systems. Furthermore, by combining the proposed fixed-time sliding-mode control method with the information provided by the fixed-time observers, the fixed-time controllers are designed to solve the fixed-time distributed consensus tracking and the distributed average tracking problems. Finally, a few numerical simulations are shown to verify the results.

Control and Optimisation of Power Grids Using Smart Meter Data: A Review.

This paper provides a comprehensive review of the applications of smart meters in the control and optimisation of power grids to support a smooth energy transition towards the renewable energy future. The smart grids become more complicated due to the presence of small-scale low inertia generators and the implementation of electric vehicles (EVs), which are mainly based on intermittent and variable renewable energy resources. Optimal and reliable operation of this environment using conventional model-based approaches is very difficult. Advancements in measurement and communication technologies have brought the opportunity of collecting temporal or real-time data from prosumers through Advanced Metering Infrastructure (AMI). Smart metering brings the potential of applying data-driven algorithms for different power system operations and planning services, such as infrastructure sizing and upgrade and generation forecasting. It can also be used for demand-side management, especially in the presence of new technologies such as EVs, 5G/6G networks and cloud computing. These algorithms face privacy-preserving and cybersecurity challenges that need to be well addressed. This article surveys the state-of-the-art of each of these topics, reviewing applications, challenges and opportunities of using smart meters to address them. It also stipulates the challenges that smart grids present to smart meters and the benefits that smart meters can bring to smart grids. Furthermore, the paper is concluded with some expected future directions and potential research questions for smart meters, smart grids and their interplay.

Batch-Based Learning Consensus of Multiagent Systems With Faded Neighborhood Information.

This article addresses the batch-based learning consensus for linear and nonlinear multiagent systems (MASs) with faded neighborhood information. The motivation comes from the observation that agents exchange information via wireless networks, which inevitably introduces random fading effect and channel additive noise to the transmitted signals. It is therefore of great significance to investigate how to ensure the precise consensus tracking to a given reference leader using heavily contaminated information. To this end, a novel distributed learning consensus scheme is proposed, which consists of a classic distributed control structure, a preliminary correction mechanism, and a separated design of learning gain and regulation matrix. The influence of biased and unbiased randomness is discussed in detail according to the convergence rate and consensus performance. The iterationwise asymptotic consensus tracking is strictly established for linear MAS first to demonstrate the inherent principles for the effectiveness of the proposed scheme. Then, the results are extended to nonlinear systems with nonidentical initialization condition and diverse gain design. The obtained results show that the distributed learning consensus scheme can achieve high-precision tracking performance for an MAS under unreliable communications. The theoretical results are verified by two illustrative simulations.

Finite-Time Convergent Primal-Dual Gradient Dynamics With Applications to Distributed Optimization.

This article studies the finite-time (FT) convergence of a fast primal-dual gradient dynamics (PDGD), called FT-PDGD, for solving constrained optimization with general constraints and cost functions. Based on the nonsmooth analysis and augmented Lagrangian function, sufficient conditions are established for FT-PDGD to enable the realization of primal-dual optimization in FT. A specific class of nonsmooth sign-preserving functions is defined and analyzed for ensuring FT stability. Particularly, the matrix of linear equations is not required to have a full-row rank and the cost function is not necessary to be strictly convex. By introducing auxiliary variables for general linear inequality constraints, reduced sufficient conditions are further derived for the optimization with linear equality and inequality constraints after transformation. In addition, by the nonsmooth analysis, the switching dynamics evolved in both primal and dual variables are carefully investigated and the upper bound on the convergence time is explicitly provided. Moreover, as applications of FT-PDGD, several FT convergent distributed algorithms are designed to solve distributed optimization with separated and coupled linear equations, respectively. Finally, two case studies are conducted to show the performance of the proposed algorithms.

A Generalized Supertwisting Algorithm.

The work proposes a generalized supertwisting algorithm (GSTA) and its constructive design strategy. In contrast with the conventional STA, the most remarkable characteristic of the proposed method is that the discontinuous term in the conventional STA is replaced with a fractional power term, which can fundamentally improve the performance of the conventional STA. It is shown that if the fractional power in the nonsmooth term becomes -1/2, the GSTA will reduce to the conventional STA. Under the GSTA, it will be rigorously verified by taking advantage of strict Lyapunov analysis that the sliding variables can finite-time converge to an arbitrarily small region in a neighborhood of the origin by tuning the gains and the fractional power. Finally, simulation studies are provided to demonstrate the superiority of the theoretically obtained results.

A Novel Adaptive Gain Strategy for Stochastic Learning Control.

This article studies the conflicting goals of high-precision tracking and quick convergence speed, which is a longstanding problem in the learning control of stochastic systems. In such systems, a decreasing gain sequence is necessary to ensure the asymptotic convergence of the generated input sequence to a fixed limit. However, the convergence speed is adversely affected by gain sequences of this nature. In this article, we propose a novel multistage learning control strategy to resolve this conflict, where each stage consists of several iterations. The learning gain remains constant in each stage but is reduced at the transition from a given stage to the subsequent stage. The switching iteration between two stages is determined by the tracking performance index of the contracted input error and the accumulated noise drift. Furthermore, an improved mechanism is proposed to optimize the lengths of the different stages. The asymptotic convergence of the input sequence generated by the newly proposed strategy is strictly established by thoroughly analyzing the properties of the proposed gain sequence. Numerical simulations are presented to verify the theoretical results.

Accelerated Learning Control for Point-to-Point Tracking Systems.

In this study, we investigate the accelerated learning control schemes for point-to-point tracking systems (PTSs) with measurement noise. The asymptotic convergence of the generated input sequence has been a long-standing open issue for point-to-point tracking problems because there are infinite possible input candidates that can drive the system dynamics to track the desired reference at specified time instants. An accelerated gradient algorithm and its generalized version with a novel direction regulation matrix are proposed, with the learning gain is adaptively triggered by the practical tracking errors. The learning gain remains constant at the early stage and begins to decrease after a certain number of iterations. The input sequence generated by the proposed scheme converges to a specified limit for any fixed initial input, with the limit being closest to the initial input, in a certain sense. Numerical simulations are provided to verify the theoretical results.

Fully Distributed Adaptive NN-Based Consensus Protocol for Nonlinear MASs: An Attack-Free Approach.

This article works on the consensus problem of nonlinear multiagent systems (MASs) under directed graphs. Based on the local output information of neighboring agents, fully distributed adaptive attack-free protocols are designed, where speaking of attack-free protocol, we mean that the observer information transmission via communication channel is forbidden during the whole course. First, the fixed-time observer is introduced to estimate both the local state and the consensus error based on the local output and the relative output measurement among neighboring agents. Then, an observer-based protocol is generated by the consensus error estimation, where the adaptive gains are designed to estimate the unknown neural network constant weight matrix and the upper bound of the residual error vector. Furthermore, the fully distributed adaptive attack-free consensus protocol is proposed by introducing an extra adaptive gain to estimate the communication connectivity information. The proposed protocols are in essence attack-free since no observer information exchange among agents is undertaken during the whole process. Moreover, such a design structure takes the advantage of releasing communication burden.

Distributed Time-Varying Optimization of Second-Order Multiagent Systems Under Limited Interaction Ranges.

This article investigates the distributed time-varying optimization problem for second-order multiagent systems (MASs) under limited interaction ranges. The goal is to seek the minimum of the sum of local time-varying cost functions (CFs), where each CF is only available to the corresponding agent. Limited communication range refers to the scenario where the agents have limited sensing and communication capabilities, that is, a pair of agents can communicate with each other only if their distance is within a certain range. To handle such a problem, a new continuous connectivity-preserving mechanism is presented to preserve the connectivity of the considered network. Then, two distributed optimization algorithms are presented to solve the optimization problem with time-varying CFs and time-invariant CFs, respectively. Theoretical analysis and two numerical examples are provided to verify the effectiveness of the methods.

Free-Will Arbitrary Time Consensus for Multiagent Systems.

In this article, the free-will arbitrary time consensus is formulated for multiagent systems. This consensus protocol is independent of initial conditions and any other system parameters. With such a protocol, the multiagent system is shown to attain consensus as well as average consensus within the prespecified arbitrary time. Agents rendezvous can also be accomplished with the given protocol. Communication imperfections are easily handled with the designed protocol. Robust free-will arbitrary time consensus protocol is also designed. The stability of such nonlinear nonautonomous protocols is established using suitable Lyapunov functions. Simulation examples confirm the theoretical findings.

Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay.

In this article, we investigate the synchronization of complex networks with general time-varying delay, especially with nondifferentiable delay. In the literature, the time-varying delay is usually assumed to be differentiable. This assumption is strict and not easy to verify in engineering. Until now, the synchronization of networks with nondifferentiable delay through adaptive control remains a challenging problem. By analyzing the boundedness of the adaptive control gain and extending the well-known Halanay inequality, we solve this problem and establish several synchronization criteria for networks under the centralized adaptive control and networks under the decentralized adaptive control. Particularly, the boundedness of the centralized adaptive control gain is theoretically proved. Numerical simulations are provided to verify the theoretical results.

Learning Tracking Over Unknown Fading Channels Based on Iterative Estimation.

With fast developments in communication technologies, a large number of practical systems adopt the networked control structure. For this structure, the fading problem is an emerging issue among other network problems. It has not been extensively investigated how to guarantee superior control performance in the presence of unknown fading channels. This article presents a learning strategy for gradually improving the tracking performance. To this end, an iterative estimation mechanism is first introduced to provide necessary statistical information such that the biased signals after transmission can be corrected before being utilized. Then, learning control algorithms incorporating with a decreasing step-size sequence are designed for both output and input fading cases. The convergence in both mean-square and almost-sure senses of the proposed schemes is strictly proved under mild conditions. Illustrative simulations verify the effectiveness of the entire learning framework.

Designing Event-Triggered Observers for Distributed Tracking Consensus of Higher-Order Multiagent Systems.

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

Distributed Formation Navigation of Constrained Second-Order Multiagent Systems With Collision Avoidance and Connectivity Maintenance.

In this article, we consider the distributed formation navigation problem of second-order multiagent systems subject to both velocity and input constraints. Both collision avoidance and connectivity maintenance of the network are considered in the controller design. A control barrier function method is employed to achieve multiple control objectives simultaneously while satisfying the velocity and input constraints. First, a nominal distributed leader-following formation controller is proposed which satisfies the velocity and input constraints uniformly and handles switching communication graphs. A nonsmooth analysis is employed to prove the global convergence of the controller. Then, a topology-based connectivity maintenance strategy using a new notion of the formation-guided minimum cost spanning tree is proposed and the corresponding barrier function-based constraints are derived. The barrier function-based collision-avoidance conditions are also developed. All barrier function-based constraints are then combined to formulate a quadratic programming problem which modifies the nominal controller when necessary to achieve both collision avoidance and connectivity maintenance. Simulation results demonstrate the effectiveness of the proposed control strategy.

Resilient Consensus of Multiagent Systems Under Malicious Attacks: Appointed-Time Observer-Based Approach.

This article aims to establish an appointed-time observer-based framework to efficiently address the resilient consensus control problem of linear multiagent systems with malicious attacks. The local appointed-time state observer is skillfully designed for each agent to estimate the agent's actual state value at the appointed time, even in the presence of unknown malicious attacks. Based on the state estimation, a new kind of resilient control strategy is proposed, where a virtual system is constructed for each agent to generate an ideal state value such that the consensus of normal agents can be achieved with the exchange of ideal state values among neighboring agents. To specify the consensus trajectory while achieving resilient consensus, the leader-follower resilient consensus is further studied, where the leader is assumed to be a trusted agent with a bounded control input. Compared with the existing results on the resilient consensus, the proposed distributed resilient controller design reduces the requirement on communication connectivity significantly, where the allowable communication graph is only assumed to contain a directed spanning tree. To verify the theoretical analysis, numerical simulations are finally provided.

Precedence-Constrained Colored Traveling Salesman Problem: An Augmented Variable Neighborhood Search Approach.

A colored traveling salesman problem (CTSP) as a generalization of the well-known multiple traveling salesman problem utilizes colors to distinguish the accessibility of individual cities to salesmen. This work formulates a precedence-constrained CTSP (PCTSP) over hypergraphs with asymmetric city distances. It is capable of modeling the problems with operations or activities constrained to precedence relationships in many applications. Two types of precedence constraints are taken into account, i.e., 1) among individual cities and 2) among city clusters. An augmented variable neighborhood search (VNS) called POPMUSIC-based VNS (PVNS) is proposed as a main framework for solving PCTSP. It harnesses a partial optimization metaheuristic under special intensification conditions to prepare candidate sets. Moreover, a topological sort-based greedy algorithm is developed to obtain a feasible solution at the initialization phase. Next, mutation and multi-insertion of constraint-preserving exchanges are combined to produce different neighborhoods of the current solution. Two kinds of constraint-preserving k -exchange are adopted to serve as a strong local search means. Extensive experiments are conducted on 34 cases. For the sake of comparison, Lin-Kernighan heuristic, two genetic algorithms and three VNS methods are adapted to PCTSP and fine-tuned by using an automatic algorithm configurator-irace package. The experimental results show that PVNS outperforms them in terms of both search ability and convergence rate. In addition, the study of four PVNS variants each lacking an important operator reveals that all operators play significant roles in PVNS.

Iterative Learning Tracking for Multisensor Systems: A Weighted Optimization Approach.

Multisensor systems are widely applied to realize the comprehensive monitoring and control as they feature multiple individual sensors/outputs. In such systems, different sensors can receive different types of operation signals, such as pressure, temperature, and volume. The desired references for different sensors may conflict in that an input signal that can precisely track all references simultaneously does not exist yet. This gap has motivated us to consider the incompatible multiobjective tracking problem for multisensor systems with random process disturbances and measurement noises. Our primary approach is to solve the problem as a weighted optimization problem using iterative learning control (ILC). First, the best achievable trajectory based on multiple references, as well as the weighted optimal tracking index, is carefully defined and then the ILC algorithms with both fixed and decreasing steps are proposed to generate the input sequence. The output driven by the proposed algorithms has been strictly proven to converge to the best achievable trajectory in both the mean square and almost-sure senses. Extensions to a networked implementation, in which the networks between the sensors and the learning controller suffer random data dropouts, are also detailed. Illustrative simulations are provided to verify the theoretical results.