This paper proposes a fault tolerant control strategy for unmanned marine vehicles (UMVs) suffering from unknown actuator bias faults to avoid the structural complexity of conventional T-S fuzzy model. A fault observer is introduced to estimate actuator fault through online learning for real-time control input compensation. Further, to conserve network resources, an adaptive frequency event-triggered mechanism (AFETM) is applied. Unlike conventional event-triggered control methods that use fixed thresholds, AFETM dynamically adjusts the triggering condition based on historical transmission frequency and error, effectively reducing unnecessary data transmission. Moreover, instead of the traditional dual-network adaptive dynamic programming structure, a single critic network is employed to solve the Hamilton-Jacobi-Isaacs equation, significantly reducing computational burden and parameter complexity. Additionally, the stability of the UMV system is analyzed using the Lyapunov stability theorem, which demonstrates that the system states are uniformly ultimately bounded (UUB) under the proposed method. Simulation results demonstrate that the proposed AFETM reduces communication load by 99.6% and 25.4% compared with time-triggered mechanisms static and event-triggered methods, while ensuring UUB stability of the system states under actuator faults and disturbances.

Conventional Model Predictive Control (MPC) often loses recursive feasibility when tasked with tracking aggressive or discontinuous dynamic reference trajectories. While existing Feasibility Governor (FG) frameworks effectively address this issue for steady-state setpoint regulation, they are often ill-suited for tracking continuously time-varying references, leading to conservative performance or tracking lag. To address this gap, this paper proposes a novel Dual-type Reference Governor (DRG) framework that seamlessly integrates with Tube-based MPC (TMPC). Unlike traditional governors, the DRG features a dual-mode architecture designed specifically for dynamic tracking: an Initial RG (IRG) handles large reference jumps to recover feasibility, while a Terminal RG (TRG) manages local trajectory refinement. Furthermore, to tackle the computational burden associated with robust control, a DRG-driven adaptive prediction horizon mechanism is introduced. This mechanism dynamically shortens the horizon during smooth tracking and extends it only when necessary for feasibility recovery. Theoretical analysis establishes the recursive feasibility and closed-loop stability of the proposed framework. Simulation studies and hardware experiments on a vehicle robot platform demonstrate that the DRG+TMPC significantly outperforms standard TMPC and conventional FG approaches in terms of tracking accuracy for dynamic targets and computational efficiency.

This study investigates the mean-square reachable set (RS) consensus of nonlinear Markov-switched multiagent systems (MASs) with time-varying delays, in which a multirate sampled-data consensus (MRSDC) control scheme is designed for the first time under general uncertain semi-Markov transition (GUST) switched topologies. First, the nonlinear Markov-switched MAS is transformed into quasilinear subsystems by applying the Takagi-Sugeno (T-S) fuzzy modeling technique, where the GUST-based Markov model characterizes both the operation mode and abrupt variations in the communication network topologies among all agents. Second, an aperiodic MRSDC control strategy is developed to reduce the sampling frequency of certain sensors below the single-rate threshold by adaptively adjusting their sampling rates, thereby enhancing flexibility and improving consensus performance. Furthermore, a new free-weighting integral inequality is introduced to handle the integral quadratic term involving time-varying delay bounds. Subsequently, an appropriate looped-side Lyapunov functional is designed, leveraging aperiodic multirate sampling and time-varying delay characteristics. Next, by combining the constructed Lyapunov functional with the proposed integral inequality and an improved reciprocally convex combination inequality, sufficient conditions are derived in the form of linear matrix inequalities (LMIs). These conditions not only ensure the mean-square leaderless consensus of the resulting MASs but also guarantee that all reachable states remain confined within ellipsoidal attracting-like regions under the MRSDC scheme. Finally, numerical validations are conducted to demonstrate the effectiveness of the proposed MRSDC control strategies using interconnected single-link robot arm systems (SLRASs), while a comparative numerical example further illustrates the superiority of the proposed method.

Silent packet loss (SPL) poses a significant challenge for state estimation, due to the lack of information regarding the packet loss status (PLS). This issue is particularly prominent in event-based systems, where the interplay between event-triggered feedback mechanisms and SPL complicates the estimation process. Existing approaches often employ detectors, but achieving 100% detection accuracy remains nearly impossible, and false detections further complicate the probability distribution of system states. In this article, we propose a silent message-passing mechanism (SMPM) to address the SPL of measurements, which may be coupled with an event-based scheduler, as the feedback channel is also affected by the SPL. Besides, a dynamic Chi-square ( $d$ - $\mathcal {X}^{2}$ ) detector is proposed, whose detection accuracy is proven to converge to 100% with time. Subsequently, an estimator based on the $d$ - $\mathcal {X}^{2}$ detector under the SMPM is designed for unstable systems with the SPL of measurements. More importantly, a stability condition is established, revealing the relationship between the SPL rate and estimation performance. Both simulations and experiments validate the effectiveness of the theoretical findings presented in this article.

The main objective of this study is to develop a fault-tolerant fuzzy time-constrained memory-sampled-data control (TCMSDC) mechanism for analyzing the consensus performance of nonlinear multiagent systems (MASs) affected by stochastic actuator faults and external disturbances. To achieve this, the nonlinear MASs are first converted into quasi-linear subsystems using the Takagi–Sugeno (T-S) fuzzy model. In contrast to existing memory-sampled-data consensus methods, the constructed TCMSDC signals vary over time within each sampling period, thereby enhancing consensus performance. Thereafter, a Markov variable process is applied to model multiple stochastic actuator faults in the considered MASs. Furthermore, an aperiodic-sampling-dependent asymmetric dual-looped functional (ASADLF) is constructed, which incorporates different sets of matrices designed for each sampling instance. Subsequently, a new nonorthogonal polynomial integral inequality (NOPII) is introduced to approximate the integral quadratic terms. By leveraging this ASADLF along with the proposed NOPII technique, less conservative consensus criteria are derived in the form of linear matrix inequalities (LMIs), and the TCMSDC gain parameters are obtained to guarantee mean-square asymptotic consensus with$H_{\infty }$performance for the considered MASs. Finally, the effectiveness and advantages of the proposed TCMSDC approach in enhancing fault tolerance and achieving reliable consensus under stochastic actuator faults are validated through numerical simulations on multi-ship steering autonomous surface vehicles (SSASVs) and mass–spring systems.

In this work, a novel dual-type reference governor (DRG) is proposed to handle the unreachable reference within the prediction horizon for the model predictive control (MPC). The proposed method, featuring two types of reference governor (RG) designs, ensures efficient reference tracking and MPC feasibility throughout the entire process. The first type, the initial RG, is specifically designed to adjust references when the controller receives a new target reference. This addresses a gap in existing research on command/feasibility governors (FGs), which overlooks this scenario. The second type, named terminal RG, ensures the convergence of auxiliary references to the current target reference. By introducing control variables, it expands the feasible set of auxiliary references compared to existing methods, thereby further accelerating the convergence speed. The recursive feasibility, finite-time convergence, and asymptotic stability of the combined DRG+MPC closed-loop system with the proposed algorithm are demonstrated in the article. To validate the effectiveness of the proposed algorithm, numerical simulations were conducted in two vehicle application scenarios: adaptive cruise control (ACC) and lane changing control (LCC), using their respective vehicle models. The results indicate that, compared to existing methods such as classical MPC, tracking MPC (TMPC), and FG+MPC, the proposed approach guarantees both reference tracking performance and low computational burden.

This paper addresses the consensus control problem of heterogeneous multi-UAV systems against Byzantine attacks. A drone compromised by Byzantine attacks transmits erroneous values to its neighbors while applying wrong input signals for itself, which is aggressive and challenging to defend. Inspired by the concept of digital twin technology, we introduce a new hierarchical protocol equipped with a virtual twin layer (TL), which decouples the challenges into two defense schemes: one against Byzantine edge attacks on the TL and the other against Byzantine node attacks on the cyber-physical layer (CPL). In the TL, we provide a topology reconfiguration strategy that enhances the resilience of the communication network by judiciously adding a minimal number of key edges. We rigorously demonstrate that the control strategy attains asymptotic consensus within a finite timeframe, given that the topology on the TL adheres to a strongly$(2f+1)$-robustness criterion. Within the CPL, decentralized chattering-free controllers are proposed to ensure the resilient output consensus for the heterogeneous multi-UAV systems against Byzantine node attacks. Furthermore, the derived consensus controller exhibits an exponential convergence characteristic. The effectiveness and practicality of the obtained theoretical results are verified by a UAV swarm flight experiment. Note to Practitioners—Cooperative control of UAVs presents significant prospects for application and development, becoming a focal point of automatic control. By modeling UAV swarms as multi-agent systems, various complex distributed control methods have been conveniently proposed and implemented economically in practical systems. However, when certain agents are compromised and interfere with their neighbors, the whole network may become highly susceptible to failure. This paper specifically studies the resilient consensus control against the significant active internal threats, Byzantine attacks. The published results have primarily focused on cases where the leader UAV has no input signals. In practical applications, however, the leader often has a pre-established trajectory sent by the host and the followers are unaware of this input information. This significantly complicates the task of identifying Byzantine attackers. In this work, we introduce a new hierarchical protocol inspired by the concept of digital twin technology, which decouples the challenges into defense against Byzantine edge attacks on the TL and the defense against Byzantine node attacks on the cyber-physical layer. The experiment shows the feasibility and security of our control scheme, which provides valuable guidance for the practical applications of drones.

This paper addresses the problem of distributed estimation and motion control (DEMC) in multi-agent systems (MASs) with both linear and Lipschitz nonlinear dynamics. Unlike conventional DEMC methods designed for MASs under ideal conditions, this work investigates scenarios where all agents are vulnerable to various forms of attacks. The considered attacks comprise false-data injection (FDI) attacks and denial of service (DoS) attacks that affect the communication channels among agents to destabilize the MAS. Also, the unbounded actuator attacks which exist in practical environments to intentionally degrade the MAS performance is considered. To cope with these kinds of attacks, two novel resilient approaches are established aimed at estimating and following a mobile target under attacks. The proposed distributed attack-resilient control strategies are designed based on a dual-layer structure, guaranteeing effective DEMC with an ultimately bounded error. The results from two simulation examples are provided to validate the presented algorithms. Note to Practitioners—The motivation of this work is to deal with the DEMC problem for MASs under multiple attacks. In most of the existing DEMC schemes for MASs, having a healthy network and dynamics is a requirement. However, in practical environments, MASs as an important subclass of cyber-physical systems are subject to different types of attacks that affect the network and dynamics of MASs and may seriously jeopardize the performance of the DEMC algorithm, or even worse, lead to instability. Therefore, a resilient hierarchical DEMC algorithm is proposed for MASs which allows agents to estimate and follow a mobile target under multiple attacks. The proposed scheme is resilient to most existing cyber-attacks and is designed for MASs with both linear and nonlinear dynamics. It can be applied to various practical engineering systems such as autonomous vehicles, mobile robots, and intelligent transportation systems. The stability and convergence of the proposed algorithms are analyzed mathematically, and it is shown that the agents not only track the estimated target but also can cope with multiple attacks through simulation experiments.

This paper investigates the bipartite event-triggered output consensus problem in heterogeneous linear multi-agent systems (MASs) with a leader operating under signed jointly connected digraphs. The research addresses both cooperative and adversarial communication among agents by introducing a novel edge-based bipartite event-triggering mechanism (ETM), as well as a dynamic ETM for communication between the leader and followers. Subsequently, a distributed bipartite compensator utilizing the composite ETMs is proposed to estimate the states of the leader, and serves as a reference for the states of followers. Moreover, a significant feature of the compensator is that it reduces the frequency of communication between the leader and followers. Besides, it is proven that the system with the compensator can exclude Zeno behavior. Furthermore, observers designed to estimate the states of followers, as well as a new distributed control protocol, are proposed to address the output tracking problem of heterogeneous linear MASs. The results demonstrate that, through the proposed protocol, the output tracking error of the closed-loop control system converges to zero exponentially. Finally, the theoretical findings of this study are validated through a numerical example and an application example.

We consider a scenario in which a group of robots tracks a group of targets in an open space. In particular, the robots are heterogeneous, and the targets are adversarial, capable of attacking the robots and severing the links between the robots and their corresponding sensors. Additionally, each robot is required to estimate the state of the targets individually on the basis of the communication graph. We propose a framework that adaptively balances accuracy and safety while automatically repairing the communication graph. Our framework follows a two-stage strategy: In the first stage, we assess the entire team to determine if repair is necessary. If necessary, by quantifying the team’s observability using the trace of the Grammian matrix, we propose a computationally efficient repair strategy. In the second stage, safety and accuracy are quantified, with the sensing margin serving as the dynamic weight to guide robot coordination. To validate the effectiveness of our work, we simulated a monitoring and tracking task and compared our network reconfiguration strategy with greedy and One-Hop-Grammian-based methods. The simulation results demonstrate the effectiveness and efficiency of our approach.

This work studies the problem of finding optimal distributed resource allocation policies on wireless networks in the existence of an unknown malicious adding-edge attacker, depicted as the games of games (GoG) model. Specifically, two subnetwork policymakers constitute a Nash game, while a Stackelberg game captures the confrontation between each subnetwork policymaker and the malicious attacker. We first demonstrate that by utilizing the Foschini-Miljanic algorithm, the communication resource allocation of cellular networks can be converted into a geometric program (GP) that can be efficiently solved by convex optimization. Then, the upper limit of attack magnitude that the network can withstand is calculated. It is shown that the proposed GP framework is solvable within the attack bound and a Gestalt Nash equilibrium (GNE) exists for the GoG. Moreover, a heuristic algorithm that iteratively employs GP is developed to obtain the optimal policy profiles of subnetworks, which can converge asymptotically. Correspondingly, a greedy heuristic adding-edge strategy is proposed to identify the set of the most vulnerable edges for the attacker. Finally, simulation examples show that the obtained algorithm is resilient to malicious attacks and can attain the GNE. Despite the presence of malicious attacks, all channels’ transmission and interference gains can be well-adjusted within a limited budget.

This paper investigates the bipartite consensus problem for heterogeneous multi-agent systems subjected to Byzantine attacks. Byzantine agents send erroneous signals to their neighbors while utilizing incorrect input signals themselves, posing significant challenges for defense. To defend against Byzantine attacks, we propose a resilient heterogeneous impulsive bipartite consensus algorithm for multi-agent systems. This approach ensures that information transmission occurs exclusively at sampling points, significantly reducing control costs, minimizing communication redundancy, and enhancing system robustness. During each sampling event, agents eliminate the most extreme values from their neighbors and utilize the remaining information to generate the control input. By employing this resilient scheme and leveraging the properties of Sarymsakov matrices, we demonstrate that the proposed impulsive control method effectively limits the impact of Byzantine attacks. We also determine the maximum allowable number of Byzantine agents and the corresponding network robustness required to ensure the agents achieve bipartite consensus. Finally, simulations and experiments validate the effectiveness of the proposed approach.

This work investigates the time-varying formation-tracking problem of multiagent systems under hybrid attacks, including denial-of-service (DoS) attacks and actuation attacks. State estimators are designed for each node of the swarm leveraging relative information from neighboring estimators to generate the desired positional states for formation tracking. The direct use of corrupted consensus control inputs is avoided, thereby defending against actuation attacks targeted at node input signals. Furthermore, we propose an event-triggered protocol with a sampling mechanism to enhance resilience against DoS attacks on communication with neighboring estimators equipped with a topology recovery policy. This resilient protocol against DoS attacks is fully distributed and does not require prior knowledge of network topology, making it scalable to large networks. Finally, an adaptive attack-resilient control scheme is introduced to counteract potential unbounded actuation attacks via output feedback, enabling each follower to track the positional states provided by the distributed estimators. The tracking error is proven to be uniformly ultimately bounded. The proposed event-triggered hierarchical control scheme is validated through its application to spacecraft formation.

This article focuses on the issues of security sampled-data-based$H_{\infty }$control design for interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems against false-data injection (FDI) attacks and external disturbances using a supervision of machine learning (SML) algorithm. To improve the bounds of sampled data period, an SML algorithm is proposed to optimize the allocation of network resources and ensure the effective utilization of bandwidth. Besides, two improved integral inequalities are introduced to estimate the integral quadratic terms that account for signal transmission delays and sampling information. Meanwhile, an appropriate asymmetric looped Lyapunov-Krasovskii functional (ALLKF) is constructed incorporating information on the fuzzy membership function (FMF), aperiodic sampling pattern, and transmission delays to facilitate model conservativeness. Next, based on the constructed fuzzy ALLKF along with the proposed inequalities, a set of necessary conditions for achieving asymptotic stability with$H_{\infty }$performance is derived through linear matrix inequalities (LMIs), and then control parameters can be obtained to guarantee the less conservative stabilization results of considered closed-loop systems. Finally, to verify the superiority and feasibility of the proposed theoretical observations, the hacked permanent magnet synchronous generator (PMSG)-based wind energy system (WES) is numerically validated. Additionally, comparative examples are presented to demonstrate the improved conservativeness of the proposed technique.

This study aims to solve the mean-square asymptotic synchronization problem of additive time-varying delayed Markovian jumping neural networks (ATVMJNNs) under the framework of multiple stochastic samplings and its direct application in secure image encryption (SIE). To do this, first, we assume the existence of multiple sampled data periods that satisfy a Bernoulli distribution and introduce random variables to represent the positions of input delays and sampling periods. Then, based on these assumptions, we develop a mode-dependent discontinuous Lyapunov-Krasovskii functional (DLKF) to reduce model conservatism. Next, we introduce a new auxiliary slack-matrix-based integral inequality (ASMBII) to approximate the integral quadratic terms arising from the derivative of the DLKFs. Furthermore, we develop a multiple stochastic sampling framework to achieve asymptotic synchronization between the primary and secondary systems, and less conservative criteria for asymptotic stability in the mean square sense of the error model are derived by solving a set of linear matrix inequalities (LMIs). Finally, we present the numerical validations and corresponding experimental results in a pragmatic application of image processing to demonstrate the benefits of the proposed algorithms and techniques. From both numerical and practical results, the proposed algorithms and techniques can yield superior performance compared to existing studies.

Discovering and tracking wildlife targets are essential for gaining insights into the behavioral patterns and habits of animals within their natural habitats. With low cost and high maneuverability, mini autonomous aerial vehicles (AAVs) can achieve robust and rapid locating and tracking of multiple targets through collaboration. This work proposes a method for multitarget task allocation and path planning for AAV swarms, addressing the challenges of locating and tracking multiple wildlife with very high frequency (VHF) radio tags while avoiding potential disturbances to the wildlife. Our approach proposes a layered framework for the multi-AAV multitarget wildlife tracking problem: 1) the state estimation layer performs fast receiver signal strength indicator (RSSI) signal acquisition and employs the particle filtering algorithm to localize targets’ positions; 2) the task assignment layer uses a quadratic allocation method for AAVs’ real-time target allocation, starting with reasonable initial target sets via mixed-integer programming and efficiently readjusting targets based on real-time environment; and 3) the motion planning layer introduces an optimization-based approach to generate smooth and executable trajectories that can simultaneously ensure desired safe distances from objects of interest. Simulation experiments validate the effectiveness of the obtained AAV swarm tracking scheme.

This article copes with the distributed control and target tracking (DCTT) problem in general linear and Lipschitz multiagent systems (MASs). In comparison to the traditional DCTT algorithms that were developed for MASs in ideal conditions, two schemes based upon a resilient protocol are proposed for linear and nonlinear MASs to estimate and track a mobile target where all agents are subject to composite attacks, including camouflage attacks, DoS attacks, sensor attacks, and actuator attacks. Based on the digital twin approach, a twin layer (TL) with high privacy and security is introduced to separate the problem of DCTT into two tasks: 1) handling DoS attacks on the TL and defending against sensor and 2) actuator attacks on the cyber-physical layer (CPL). First, two distributed estimation algorithms are established to reconstruct the agents and target dynamics for every agent on the TL in the presence of DoS attacks. Second, using the reconstructed agents and target dynamics on the TL, a resilient distributed control protocol is designed to resist sensor and actuator attacks on the CPL. The current scheme guarantees the achievement of control and target tracking such that the DCTT error of the proposed design is ultimately bounded in terms of linear matrix inequality. By applying two simulation examples, the presented algorithms are also validated.

This paper presents MFCalib, an innovative extrinsic calibration technique for LiDAR and RGB camera that operates automatically in targetless environments with a single data capture. At the heart of this method is using a rich set of edge information, significantly enhancing calibration accuracy and robustness. Specifically, we extract both depth-continuous and depth-discontinuous edges, along with intensity-discontinuous edges on planes. This comprehensive edge extraction strategy ensures our ability to achieve accurate calibration with just one round of data collection, even in complex and varied settings. Addressing the uncertainty of depth-discontinuous edges, we delve into the physical measurement principles of LiDAR and develop a beam model, effectively mitigating the issue of edge inflation caused by the LiDAR beam. Extensive experiment results demonstrate that MFCalib outperforms the state-of-the-art targetless calibration methods across various scenes, achieving and often surpassing the precision of multi-scene calibrations in a single-shot collection. To support community development, we make our code available open-source on GitHub.

This article delves into the distributed resilient output containment control of heterogeneous multiagent systems against composite attacks, including Denial-of-Service (DoS) attacks, false-data injection (FDI) attacks, camouflage attacks, and actuation attacks. Inspired by digital twin technology, a twin layer (TL) with higher security and privacy is employed to decouple the above problem into two tasks: 1) defense protocols against DoS attacks on TL and 2) defense protocols against actuation attacks on the cyber-physical layer (CPL). Initially, considering modeling errors of leader dynamics, distributed observers are introduced to reconstruct the leader dynamics for each follower on TL under DoS attacks. Subsequently, distributed estimators are utilized to estimate follower states based on the reconstructed leader dynamics on the TL. Then, decentralized solvers are designed to calculate the output regulator equations on CPL by using the reconstructed leader dynamics. Simultaneously, decentralized adaptive attack-resilient control schemes are proposed to resist unbounded actuation attacks on the CPL. Furthermore, the aforementioned control protocols are applied to demonstrate that the followers can achieve uniformly ultimately bounded (UUB) convergence, with the upper bound of the UUB convergence being explicitly determined. Finally, we present a simulation example and an experiment to show the effectiveness of the proposed control scheme.

This article studies the resilient formation tracking control problem for spacecraft swarm while considering actuation attacks and input saturation. A distributed Lyapunov-based model predictive controller (DLMPC) framework is designed for spacecraft swarm to track the target trajectory in a preset formation shape and achieve attitude consensus. To ensure formation safety, a collision avoidance term is introduced into the DLMPC framework. To guarantee the feasibility and stability of the DLMPC, we first construct the Lyapunov-based adaptive auxiliary controller and then use its stability to construct the stability constraint. The DLMPC inherits the characteristic of the Lyapunov-based adaptive auxiliary controller and employs online optimization to guarantee better formation tracking performance. As a novel framework for spacecraft formation control, the proposed DLMPC has the advantage of improving the formation tracking performance through persistently online optimization, especially, in adversarial dynamic environments. The simulation results validate the superiority and resilience of the DLMPC, and the proposed DLMPC framework shows improvement in formation tracking performance.

This work deals with the optimal epidemics policy-seeking problem on networks-of-networks (NoN) in the presence of unknown malicious adding-edge attacks. This problem is investigated in a framework of games-of-games (GoG), in which the conflicts between each network policymaker and the attacker are captured by a series of the Stackelberg games, while all network policymakers together compose a Nash game. First, the tolerable maximum attack magnitude is investigated and given implicitly. Then, we prove the existence of the gestalt Nash equilibrium (GNE) under mild attacks bounded by the above magnitude. A Heuristic algorithm based on iterative geometric programming is proposed to seek the GNE of the above GoG, whose asymptotical convergence is verified. Correspondingly, a greedy Heuristic strategy for the malicious attacker to compromise the NoN topology is developed. The practicability and validity of the above theoretical results and algorithms are illustrated via a simulation example.

This work focuses on the stability analysis of positive Takagi-Sugeno (T-S) fuzzy descriptor systems with time-varying delays. An equivalent augmented system is constructed to investigate the positivity and stability of T-S fuzzy descriptor time-delay systems. By using this transformed system, a necessary and sufficient positivity condition is first derived for systems, which can be verified by linear programming (LP). Then, based on the positivity of T-S fuzzy descriptor systems, a sufficient condition is put forward for the asymptotic stability of systems with bounded and unbounded time-varying delays. Finally, several examples are provided to show the effectiveness of the obtained results.

The analysis and design problems of formation-containment control for high-order linear time-invariant (LTI) multiagent systems (MASs) on directed graphs with observer-based output-feedback protocols are given in this work. To expand the feasibility of state formation configuration, two well-structured compensation signals are introduced for the leaders and followers in the protocols, respectively. Benefitting from the compensation signal of followers, the decoupling between formation control of leaders and containment control of followers is achieved. Thus, a necessary and sufficient condition is first established such that the formation-containment control for high-order LTI MASs can be achieved. Moreover, a heuristic iterative algorithm is developed to compute the controller gains, observer gains, as well as the compensation signals. Finally, two numerical examples are implemented to illustrate the time-varying formation-containment control of high-order MASs, which shows the validity and practicability of the theoretical results and algorithm.

This article addresses the distributed consensus problem for identical continuous-time positive linear systems with state-feedback control. Existing works of such a problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs or strongly connected directed graphs. On the other hand, in this work, the communication topologies of the networked system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Specifically, the problem involves complex eigenvalues, the Hurwitzness of complex matrices, and positivity constraints, which make analysis difficult in the Laplacian matrix. First, a necessary and sufficient condition for the consensus analysis of directed networked systems with positivity constraints is given, by using positive systems theory and graph theory. Unlike the general Riccati design methods that involve solving an algebraic Riccati equation (ARE), a condition represented by an algebraic Riccati inequality (ARI) is obtained for the existence of a solution. Subsequently, an equivalent condition, which corresponds to the consensus design condition, is derived, and a semidefinite programming algorithm is developed. It is shown that, when a protocol is solved by the algorithm for the networked system on a specific communication graph, there exists a set of graphs such that the positive consensus problem can be solved as well.

This paper investigates the problems of reachable set estimation and synthesis for periodic positive systems with two different exogenous disturbances. The lifting method and the pseudoperiodic Lyapunov function method are adopted for the estimation problem. The reachable set bounding conditions are proposed by employing Lyapunov-based inequalities and the S-procedure technique. Two optimization methods are used to minimize the bounding hyper-pyramids of the reachable set. In addition, the state-feedback controller design conditions that make the reachable set of closed-loop systems lie within a given hyper-pyramid are derived. Finally, numerical examples are presented to illustrate the validity of the obtained conditions.