Problem Of Linear Systems Research Articles

Fully distributed and attack-immune protocols for linear multiagent systems by linear time-varying feedback

This paper addresses the leader-following consensus problem for general linear multiagent systems under general directed topology, with a focus on the scenarios where only relative output information is available. To solve such problem, most existing observer-based protocols rely on relative observer information among neighboring agents, which is obtained through the communication network and can be susceptible to network attacks. To overcome this limitation, this paper proposes a novel class of distributed observer-based linear time-varying protocols, in which the feedback gain is designed with two time-varying terms, one of which tends towards infinity as time increases, while the other tends towards zero. Compared to existing protocols, the proposed protocols offer significant advantages. Notably, they do not require information exchange through the communication network, making them immune to network attacks. Furthermore, the protocols operate in a fully distributed manner, which makes them resilient to changes in the topology graph. Simulation results demonstrate the effectiveness of the proposed approach.

Integrated fault estimation and control for unknown discrete-time systems: a data-based multivariable-coordinated optimisation method

This paper addresses the integrated fault estimation and robust control problem for unknown linear discrete-time systems. The considered problem is formulated as a multivariable multiobjective optimisation one. A data-based coordinated design strategy that co-designs an output feedback H ∞ / H ∞ controller and a residual generator is proposed to optimise both H ∞ fault estimation and robust control performances. Based on the input and output data, the design parameters of the controller and the residual generator are determined by using Q-learning technique and introducing a new matrix block identification Q-learning method, respectively. Compared with the existing single-variable multiobjective optimisation methods, the proposed strategy can achieve better fault estimation performance, remove the restriction condition of using input and output data, and extend the traditional Q-learning technique to the case of designing a residual generator with a low-rank condition. Finally, simulation results illustrate the effectiveness of the proposed method.

Unknown input filtering under full accessibility attacks

This study initially addresses the state estimation problem for discrete-time linear time-invariant systems under the influence of both exogenous attacks and random noises. As the filtering side, we make no prior assumptions or have any prior knowledge about the nature of attacks. We employ a specific unknown input filtering approach, which has been examined in prior research, to simultaneously estimate both the system states and attacks. Differing from existing works, our emphasis on full accessibility attacks, a particular class of unknown inputs, reveals that the dynamic estimation gains of the adopted filtering reduce directly to static ones. The second contribution of this study is to mitigate the influence of attacks by utilizing the estimated attack signals. Under this strategy, the deviation between nominal states and attacked states is characterized by evaluating the upper bound of the covariance matrix of the errors.

Resilient consensus for multi-agent systems under distributed denial-of-service attacks: a graph-based approach

This paper considers the leader-following consensus problem of general linear multi-agent systems (MASs) under high-intensity distributed denial-of-service (DDoS) attacks, which are full-coverage on the communication network from the perspective of the whole system. Motivated by a simulation example of double-integrator MASs, a distributed leader-following consensus scheme based on directed acyclic graph (DAG) is proposed to improve the system robustness against DDoS attacks. Through Lyapunov stability analysis, it is proved that the consensus of the MASs with DAG can be achieved under DDoS attacks of nearly arbitrary intensity, as long as there is no channel completely blocked by the attacks. The proposed consensus scheme only needs simple requirement for the directed acyclic topology graph of the MASs, making it easy to implement in practice. Finally, a numerical simulation of multi-robot systems under DDoS attacks is carried out to illustrate the effectiveness and superiority of the proposed DAG-based consensus scheme.

Distributed System Identification for Linear Stochastic Systems Under an Adaptive Event‐Triggered Scheme

ABSTRACTThis article considers a distributed identification problem for linear stochastic systems whose input and output observations are scheduled by an adaptive event‐triggered scheme. An event detector with time‐varying thresholds is designed to control the transmission of measurements from the sensors to the estimators, which leads to that only a subset of input and output data is available for identification. The estimators exchange information over a network and cooperatively identify the unknown parameters. A distributed recursive identification algorithm under the event‐triggered scheme is proposed based on the distributed stochastic approximation algorithm with expanding truncations (DSAAWET). Under mild assumptions, the strong consistency of the algorithm is proved, that is, the estimates generated from each estimator achieve consensus and converge to the true parameters with probability one. Finally, two numerical examples are provided to validate the theoretical results of the algorithm.

On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method

On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method

Leader-Following Sampled-Data Consensus of Multiagent Systems With Successive Packet Losses and Stochastic Sampling.

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that cause the sampling interval to deviate from the expected value and fluctuate according to a certain probability distribution. This probability distribution can be determined in advance through statistical analysis. Taking into account this stochastic sampling interval, this article focuses on addressing the leader-following sampled-data consensus problem for linear multiagent systems (MASs) with successive packet losses. First, the relationship of the equivalent sampling interval between two successive update instants is established, taking into account the double randomness introduced by both SPLs and stochastic sampling. Then, the equivalent discrete-time MAS is obtained, and the overall leader-following consensus problem is formulated as a stochastic stability problem of the equivalent system by incorporating the sampled-data consensus protocol and properties of the Laplacian matrix. Based on the equivalent the discrete-time system, a consensus criterion is derived under a directed graph by using the Lyapunov theory and leveraging a vectorization technique. By the introduction of a matrix reconstruction approach, the mathematical expectation of a product of three matrices, including the system matrix and its transpose, can be determined. Then, the consensus protocol gain is designed. Finally, an example is provided to validate our theoretical results.

Data-Based Tampered-Data Recovery Strategy With Encoding Against Stealthy Attack for Unknown Discrete-Time Systems.

This study addresses a tampered-data recovery problem for linear discrete-time systems with completely unknown system dynamics under stealthy attacks. The basic idea is to identify the stealthy attack, that lies in any of attack-stealthy subspaces, and compensate for it. Different from the existing sparse recovery methods which are applicable to nonstealthy sparse attacks, a novel encoding scheme, where a set of subdecoding matrices is designed specifically for each 1-D attack-stealthy subspace, is developed so that the parameters of the stealthy attack can be identified via a subspace projection technique. A necessary and sufficient condition of determining the targeted subspace by using n parallel attack identification filters is established for this encoding scheme. Especially, a composite encoding matrix characterizes the lower and upper boundaries of the recovery error covariance's trace. A simulation example of a flight vehicle illustrates the efficiency of the proposed approach.

Distributed State Estimation for Linear Systems in Networks With Antagonistic Interactions.

This article deals with the distributed state estimation problem for linear systems in networks with cooperative interactions and antagonistic interactions, where the cooperative interactions and the antagonistic interactions are characterized by the positive weights and the negative weights, respectively. Due to the coexistence of the cooperative interactions and the antagonistic interactions, the existing methods based on the non-negatively weighted graph become not applicable. First, a partition method of the nodes and a decomposition form of the system matrices are introduced. Then a new form of distributed observers is proposed in the network with cooperative interactions and antagonistic interactions. Necessary and sufficient conditions, which guarantee the existence of proposed distributed observers, are presented. In particular, when the communication network is cooperative, the proposed method is suitable for two cases, that is, the nodes in each independent strongly connected component are jointly detectable, or each node is jointly detectable with its neighbors. Finally, three examples are simulated to illustrate the effectiveness of the proposed methods.

A dynamic event-triggered approach for observer-based formation control of multi-agent systems with designable inter-event time

This paper addresses the leader-following formation control problems for generic linear multi-agent systems under directed topology with designable inter-event time. A synthesis approach combining controller and observer design is developed under a dynamic event-triggered communication and control scheme. The proposed feedback control, state estimation, and event-triggered rules are distributed, and only local information is required for each agent to implement these algorithms. The proposed dynamic event-triggered protocol incorporates model-based estimation and clock-like auxiliary dynamic variables to prolong the inter-event time and economize the network resources. Furthermore, the inter-event time is designable, which allows more flexible tuning of communication frequency with only minor performance degradation. Sufficient conditions for formation control are established by linear matrix inequalities. The proposed method exhibits significant improvement over the dynamic event-triggered control methods described in the existing literature. Compared to the existing static event-triggered strategy, the proposed approach significantly reduces the utilization of communication resources while preserving asymptotic convergence to the desired formation. Comparative simulations demonstrate the validity and effectiveness of the proposed theoretical results.

Interval observer-based consensus tracking for multi-agent systems under Markovian switching topologies with stealthy attack

This article investigates the bounded consensus tracking problem for uncertain linear multi-agent systems (MASs) under Markovian switching topologies in the presence of unknown but bounded disturbances and stealthy attacks. First, a class of interval observers (IOs) is designed to estimate confidence bounds of agents states and stealthy attack signals. The stealthy attack is considered as that the output information is modified by the malicious attacker. Second, distributed control protocols under Markovian switching topologies are proposed for the MASs based on the designed IOs to achieve bounded consensus. The mean-square error bounds depend on the error bounds of disturbances. After rigorous mathematical proofs, some sufficient conditions are acquired for achieving control goals. Simulations are provided to validate the effectiveness of the proposed IOs and control protocols.

Fully distributed time-varying formation tracking control for linear multi-agent systems with unknown external disturbances

This work investigates the time-varying formation tracking (TVFT) problem for linear multi-agent systems with a leader of unknown input in the presence of unknown external disturbances on directed graphs. Each agent is subjected to different external disturbances generated by unknown exosystems. To eliminate the unknown external disturbances of each follower, an adaptive disturbance observer and a state observer are constructed first. Then, utilizing the estimated information, a fully distributed TVFT protocol is designed with adaptive coupling parameters such that the global information of the communication topology is not required. By the developed distributed controller, the multi-agent system on a communication topology containing a directed spanning tree can asymptotically track the leader with a desired time-varying formation and simultaneously reject external disturbances in spite of their unknown exosystems. Furthermore, the proposed controller is modified to a continuous one to eliminate the chattering problem. Finally, a simulation example is provided to illustrate the effectiveness of theoretical results.

On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method

On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method

Stability Analysis of Matrices and Single-Parameter Matrix Families on Special Regions

This paper proposes an efficient method for determining the D-stability of matrices using Kelley’s cutting-plane method. The study examines the D-stability of matrices in symmetric regions of the complex plane, defined by quadratic matrix inequalities (QMI) and polynomial functions. Using Kelley’s cutting-plane method, we present an iterative algorithm for determining the D-stability of a given matrix. Further, the robustness of single-parameter matrix families is analyzed, and a method is proposed for considering their D-stability. Through examples, we indicate the possible applicability of the proposed approach in addressing stability problems in linear systems.

Weak dangling block reordering and multi-step block compression for efficiently computing and updating PageRank solutions

The PageRank model is a powerful tool for network analysis, utilized across various disciplines such as web information retrieval, bioinformatics, community detection, and graph neural network. Computing this model requires solving a large-dimensional linear system or eigenvector problem due to the ever-increasing scale of networks. Conventional preconditioners and iterative methods for general linear systems or eigenvector problems often exhibit unsatisfactory performance for such problems, particularly as the damping factor parameter approaches 1, necessitating the development of specialized methods that exploit the specific properties of the PageRank coefficient matrix. Additionally, in practical applications, the optimal settings of the hyperparameters are generally unknown in advance, and networks often evolve over time. Consequently, recomputation of the problem is necessary following minor modifications. In this scenario, highly efficient preconditioners that significantly accelerate the iterative solution at a low memory cost are desirable. In this paper, we present two techniques that leverage the sparsity structures and numerical properties of the PageRank system, as well as a preconditioner based on the computed matrix structure. Experiments demonstrate the positive performance of the proposed methods on realistic PageRank computations.

Controllability and minimum energy control problem of two-dimensional continuous-time fractional linear systems

The effectiveness of this paper lies in a new formulation and solution of the minimum energy control problem for the fractional two-dimensional systems described by the Fornasini–Marchesini first models. The problem of controllability and minimum energy control of a general fractional two-dimensional Fornasini–Marchesini model is newly considered by the authors in this work. Necessary and sufficient controllability conditions are then established using the Gramian matrix. To carry out this study, a new test was described and used in order to give the existence conditions of the solution to the minimum energy control problem and the procedures for calculating an input minimising the given performance index. The usefulness and the precision of the proposed procedure is demonstrated by a numerical examples, Darboux equation and metal rolling process model as a practical application.

Optimal Consensus Control for Continuous-Time Linear Multiagent Systems: A Dynamic Event-Triggered Approach.

This article investigates the optimal consensus problem for general linear multiagent systems (MASs) via a dynamic event-triggered approach. First, a modified interaction-related cost function is proposed. Second, a dynamic event-triggered approach is developed by constructing a new distributed dynamic triggering function and a new distributed event-triggered consensus protocol. Consequently, the modified interaction-related cost function can be minimized by applying the distributed control laws, which overcomes the difficulty in the optimal consensus problem that seeking the interaction-related cost function needs all agents' information. Then, some sufficient conditions are obtained to guarantee optimality. It is shown that the developed optimal consensus gain matrices are only related to the designed triggering parameters and the desirable modified interaction-related cost function, relaxing the constraint that the controller design requires the knowledge of system dynamics, initial states, and network scale. Meanwhile, the tradeoff between optimal consensus performance and event-triggered behavior is also considered. Finally, a simulation example is provided to verify the validity of the designed distributed event-triggered optimal controller.

Resilient Time-Varying Formation Tracking Control for General Linear Multiagent Systems With a Nonautonomous Leader and Adversarial Followers.

This article is concerned with resilient formation tracking problems for general linear multiagent systems, where the leader's control input is unavailable to all the followers and partial followers' behaviors are malicious due to the node attacks. Despite the presence of the nonautonomous leader and the adversarial followers, the remaining benign followers are still expected to track the leader's trajectory with the prescribed time-varying formation. To this end, a resilient scheme comprising an attack detection and isolation strategy and a formation tracking protocol is proposed. The detection strategy enables every benign follower to identify its adversarial neighbors with two-hop communication information, as long as the underlying topology meets given conditions. Then, the detected adversarial agents are directly removed to avoid the spread of their influence, which induces a new problem called node loss. To accommodate possible node loss events, the designed tracking protocol is independent of certain global knowledge, and its convergence is demonstrated by means of the impulsive Lyapunov functions. Finally, the proposed resilient scheme is verified by two simulation examples.

Event-triggered design for optimal output consensus of high-order multi-agent systems

In this paper, we study the optimal output consensus problem for networked linear multi-agent systems. Existing distributed algorithms usually rely on continuous communication among neighbouring agents or continuous update of each agent's local controller. To save communication and computation resources, we apply event-triggered technique to this optimal output consensus problem. We first constructively develop an event-triggered algorithm with a set of applicable parameters relying on event-triggered communication and control and show its effectiveness in solving the problem by rigorous proofs. Then we extend it to the case where the triggering conditions only have to be checked in some sampling time instants. Two simulation examples are given to illustrate the efficacy of our designs.

Fully Distributed Event-Triggered Anti-Windup Consensus of Heterogeneous Systems With Input Saturation and an Active Leader.

This article addresses the event-based fully distributed consensus problem for linear heterogeneous multiagent systems (MASs) subject to input saturation. A leader with unknown but bounded control input is also considered. Based on an adaptive dynamic event-triggered protocol, all the agents can reach output consensus without knowing any global knowledge. Moreover, by applying a multiple-level saturation technique, the input-constrained leader-following consensus control is achieved. The given event-triggered algorithm can be utilized for the directed graph containing a spanning tree with the leader as the root. One distinct feature compared with previous works is that the proposed protocol can achieve saturated control without any a priori condition, instead, the local information is needed. Finally, the numerical simulations are illustrated to verify the performance of the proposed protocol.