Stochastic Switching Topologies Research Articles

Distributed consensus and formation control of multi-AUV systems under actuator faults and switching topology

This note presents the distributed consensus and formation control for a group of AUVs, comprising one leader and three followers arranged in a diamond formation. The study addresses significant control challenges, including external disturbances, noise, model uncertainties, actuator faults, stochastic switching topologies, time-varying communication delays, and positional information between agents. Stochastic switching topologies are assumed to follow a Markov chain. To effectively address these challenges and ensuring satisfactory performance levels, two control architectures have been formulated to facilitate the imposition of desired trajectories upon the system states. The initial architecture amalgamates sliding mode control methodology with adaptive algorithms, designed explicitly for tracking missions in the presence of fully functional actuators. In response to potential actuator failures, the second control architecture integrates passive fault-tolerant techniques, significantly enhancing system reliability under such circumstances as well as switching topology. The proposed framework demonstrates its effectiveness in managing the high nonlinearity and coupled dynamics of AUVs. Simulation results validate the efficacy of the developed strategy. It successfully establishes a desired consensus and formation among agents, reduces chattering phenomena, accurately tracks reference trajectories, handles disturbances and uncertainties within an unknown domain, and achieves finite-time convergence.

Synchronization of stochastic switching complex networks with a target of nonzero inputs

SummaryIn this article, we study the mean square synchronization problems for complex networks with a target of nonzero inputs under stochastic switching topology that is driven by an ergodic continuous‐time Markov process. First, we design an adaptive continuous controller based on relative full states that is consist of a synchronization term and an uncertainty elimination term, where the latter term can completely eliminate the effects of target's nonzero inputs and is continuous by adding an exponential decay function with positive initial values into the denominator. By developing a stochastic Lyapunov function, we show that zero error synchronization in the mean square sense can be achieved if the union of switching graphs contains a directed spanning tree with the target being the root. Second, we design an adaptive continuous controller based on relative outputs. Finally, we give two simulation examples to validate the theoretical results.

Distributed consensus tracking of nonlinear MASs under stochastic switching topologies via aperiodically intermittent control

SummaryIn this article, we investigate the mean‐square consensus tracking problem of nonlinear MASs subjected to external disturbances under stochastic switching topologies. An aperiodically intermittent control strategy is proposed to guarantee consensus tracking in the mean‐square sense, which depends only on the local state information of the neighbors and the leader. The stochastic switching signal of the interaction topologies is modeled as a continuous‐time Markov process, and the aperiodically intermittent control method is driven by a discrete‐time series of stochastic samples, that are independent of each other. Moreover, several sufficient conditions are established to ensure the feasibility of the control strategy. The proofs are given by employing matrix inequality theory and Lyapunov stability theory. Finally, numerical simulations are provided to verify the feasibility of the proposed theoretical results.

Adaptive mean‐square consensus of heterogeneous multiagent systems with stochastic switching topologies

AbstractThe leader–following consensus of linear heterogeneous multiagent systems is investigated in this paper. To comply with the most practical scenario, the communicating topologies among agents are assumed to switch stochastically and driven by a continuous‐time discrete‐state Markov process, whose state space corresponds to all the possible topologies. A novel distributed adaptive compensator is designed for the followers to reconstruct the exogenous signals without knowing the Laplacian matrix who is regarded as a global information, and sufficient conditions are given to ensure the compensator converges to the dynamic of the leader asymptotically in the mean square sense. Then, based on the compensator, we solved the consensus problem both by distributed state and measurement output feedback control schemes under output regulation framework, which allow followers to have nonidentical state dimensions. Finally, the theoretical results are demonstrated by a numerical example.

Minimum‐variance recursive state estimation for complex networks with stochastic switching topologies and random quantization under try‐once‐discard protocol

SummaryThis article is concerned with the issue of minimum‐variance recursive state estimation (MVRSE) for a class of nonlinear dynamical complex networks (NDCNs) with stochastic switching topologies and random quantization under the try‐once‐discard (TOD) protocol. Two sequences of Bernoulli distributed random variables with given occurrence probabilities are utilized to characterize the stochastic switching manners of network topologies and the randomly occurring quantized output measurements, where the quantization effects are portrayed by the uniform quantizer. Moreover, the TOD protocol is adopted to arrange the order of the information transmission of network nodes so as to alleviate the communication burden and mitigate the network congestions. The focus of the MVRSE issue is to develop a novel state estimation algorithm such that, for all stochastic switching topologies, random quantization effects and TOD protocol, an optimized upper bound of the estimation error covariance is guaranteed by properly designing the estimator gain. In addition, the theoretical proof is derived, which illustrates that the state estimation error is exponentially mean‐square bounded under certain conditions. Meanwhile, we also present the related theoretical analysis, which discusses the impact caused by random quantization. Finally, a numerical experiment is utilized to show the validity of the novel MVRSE approach.

Secure Synchronization of Coupled Systems via Double Event-Triggering Mechanisms With Actuator Fault

This paper studies the global exponential synchronization almost surely (GES a.s.) for coupled systems (CSs) with stochastic switching topology by using event-based output feedback control. It is assumed that the sensor-controller channel is subject to stochastic deception attacks and the actuator faults may occur to some modes. Novel double mode-dependent adaptive event-triggering mechanisms (ETMs) are introduced based on sampled data technique. Not only the Zeno phenomenon is naturally excluded, but also the asynchronous phenomenon is skillfully avoided. Based on the Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) technology, some sufficient conditions are presented to guarantee GES a.s. of the concerned system. Moreover, the event-based output feedback controller and the double ETMs can be designed by solving LMIs. In addition, an event-based pinning control is considered and some sufficient conditions are presented. As a theoretic application, our proposed results can be applied to secure synchronization problem for CSs subject to stochastic mixed attacks consisting of denial-of-service (DoS) attacks and deception attacks. Finally, two numerical examples are presented to demonstrate the effectiveness and the merits of the theoretical analysis.

Distributed robust filtering for cyber-physical systems under periodic denial-of-service jamming attacks

This article focuses on a class of distributed security estimation for cyber-physical systems against denial-of-service attacks. First, an energy-constrained periodic denial-of-service jamming attack model and a Markov stochastic process-based switching topology model are developed. Then, Bernoulli random variables are applied to indicate whether measurement and estimation between nodes are successfully transmitted, where the data loss phenomenon is subject to denial-of-service attacks and inherent network properties. With the help of Lyapunov functions and linear matrix inequalities, sufficient conditions are established to guarantee that the error system satisfies exponentially mean-square stability and robust [Formula: see text] performance. Finally, two numerical simulation examples prove the effectiveness of the proposed distributed filtering method.

Consensus of nonlinear multiagent systems with uncertain disturbance under stochastic switching topologies

In this paper, we investigate the mean square consensus problem of leader‐following nonlinear multiagent systems which suffer from white noise disturbance under randomly switching interaction topologies. The control protocol of each agent is designed based on its local information from its neighbors and the leader. Using matrix inequality theory and stochastic stability theory, a sufficient condition is presented to guarantee the mean square consensus. Moreover, two special cases: balanced topologies switching randomly and random connection failures are considered. Finally, two corresponding numerical simulations are provided to demonstrate the theoretical results.

Bounded consensus of double-integrator stochastic multi-agent systems

<p style='text-indent:20px;'>In the framework of fixed topology and stochastic switching topologies, we study the mean-square bounded consensus(MSBC) of double-integrator stochastic multi-agent systems(SMASs) including additive system noises and communication noises. Combining algebra, graph theory and random analysis, we obtain several equivalent conditions for double-integrator SMASs to reach MSBC. In addition, the simulation examples also verify the correctness of the theoretical results.</p>

Reliable asynchronous control for delayed multi-agent systems with stochastic faults and switching topologies

The issue of exponential consensus for delayed multi-agent systems (MASs) with stochastic faults and switching topologies is addressed in this work. In contrast with the existing relative works on MASs with a fixed communication topology, the topological graph is governed by an uncertain Markov chain, where the restrictions on transition rates (TRs) of Markov switching topologies are loose, which may be partially known or completely unknown. Moreover, a reliable asynchronous control protocol with the stochastic failure behaviour of the actuator on account of the relative information of neighbouring agents is devised. Relaxation of criterions with respect to the consensus of delayed MASs based on the Lyapunov methodology, Wirtinger's inequality and an improved reciprocally convex combination strategy are derived. An unmanned aerial vehicle (UAV) is presented to demonstrate the superiority and applicability of the proposed method.

Distributed Robust Filtering for Wireless Sensor Networks with Markov Switching Topologies and Deception Attacks.

This paper is concerned with the distributed full- and reduced-order - state estimation issue for a class of discrete time-invariant systems subjected to both randomly occurring switching topologies and deception attacks over wireless sensor networks. Firstly, a switching topology model is proposed which uses homogeneous Markov chain to reflect the change of filtering networks communication modes. Then, the sector-bound deception attacks among the communication channels are taken into consideration, which could better characterize the filtering network communication security. Additionally, a random variable obeying the Bernoulli distribution is used to describe the phenomenon of the randomly occurring deception attacks. Furthermore, through an adjustable parameter E, we can obtain full- and reduced-order - state estimator over sensor networks, respectively. Sufficient conditions are established for the solvability of the addressed switching topology-dependent distributed filtering design in terms of certain convex optimization problem. The purpose of solving the problem is to design a distributed full- and reduced-order filter such that, in the presence of deception attacks, stochastic external interference and switching topologies, the resulting filtering dynamic system is exponentially mean-square stable with prescribed - performance index. Finally, a simulation example is provided to show the effectiveness and flexibility of the designed approach.

Robust formation control of thrust-propelled vehicles under deterministic and stochastic topology

ABSTRACT Formation control of multiple thrust-propelled vehicles (TPVs) under deterministic and stochastic switching topologies and communication delay is addressed. Introducing a new version of variable structure control and based upon sliding mode technique, adaptive control and projection operator, we effectively handle the impact of uncertainties on the mass and inertia matrix and a set of time-varying disturbances affecting the translational and rotational dynamics. Global stability of the whole closed-loop system is guaranteed through Lyapunov stability theory. For the deterministic topology, sufficient condition in terms of LMIs is derived to achieve formation in the presence of jointly connected switching topology. In the case of stochastic topology, based on the concept of super-martingales, it is shown that if the probability of existing a connected topology is not zero, under some conditions, formation is almost surely solved in the network. Finally, numerical simulations verify the effectiveness of the proposed control framework.

Distributed filtering for nonlinear time‐delay systems over sensor networks subject to multiplicative link noises and switching topology

SummaryThis paper is concerned with the distributed filtering problem for a class of nonlinear time‐delay system over sensor networks subject to multiplicative link noises and switching topology. Both discrete and distributed time delays are included in the system model. Each sensor estimates the system state by means of the measurements not only from itself but also from its neighboring nodes according to an interactive topology. The multiplicative stochastic link noises are taken into consideration to reflect the random perturbations during the information exchanges between sensor nodes. The considered communication topology is switching according to certain predetermined rules. The purpose of the addressed problem is to develop a distributed filtering strategy such that, in the presence of multiplicative stochastic link noises and switching topology, the resulting filtering error dynamics is exponentially stable in the mean square sense and also satisfies the prespecified weighted disturbance attenuation level. In light of the average dwell time technique in combination with stochastic analysis, sufficient conditions are derived for the solvability of the addressed distributed filtering problem, and the desired filtering gains are then obtained through solving certain convex optimization problems. An illustrative simulation example is presented to demonstrate the correctness and applicability of the obtained theoretical results.

Distributed state estimation for stochastic discrete-time sensor networks with redundant channels

This paper investigates the distributed state estimation problem for a class of sensor networks described by discrete-time stochastic systems with stochastic switching topologies. In the sensor network, the redundant channel and the randomly varying nonlinearities are considered. The stochastic Brownian motions affect both the dynamical plant and the sensor measurement outputs. Through available output measurements from each individual sensor, the distributed state estimators are designed to approximate the states of the networked dynamic system. Sufficient conditions are established to guarantee the convergence of the estimation error systems for all admissible stochastic disturbances and randomly varying nonlinearities. Then, the distributed state estimator gain matrices are derived using the linear matrix inequality method. Moreover, a numerical example is given to verify the effectiveness of the theoretical results.

Event-triggered H∞ filtering control for a class of distributed parameter systems with Markovian switching topology

The H∞ filtering problem for distributed parameter systems with stochastic switching topology is investigated in this paper based on event-triggered control scheme. The switching topology which subjects to a Markovian chain is considered in filter design because of the communication uncertainty of practical networks. An event-triggered mechanism as a sampling scheme is developed aiming at the benefit of reducing the computation load or saving the limited network resources. Based on some novel integral inequalities, the improved delayed method is proposed for the H∞ filtering control problem with event-triggered scheme. Moreover, by employing stochastic stability theory, filters with Markovian jump parameters are designed to guarantee that the stochastically mean square stability and H∞ performance of the underlying error system. Finally, in order to illustrate the applicability of the obtained results, numerical examples are presented.

Energy-to-peak consensus for multi-agent systems with stochastic disturbances and Markovian switching topologies

This paper is concerned with the problem of energy-to-peak consensus for a class of multi-agent systems with both stochastic disturbances and Markovian switching topologies. The objective is to design a control protocol in the form of dynamic output feedback, such that the multi-agent system reaches mean square consensus and has a prescribed energy-to-peak disturbance attenuation level. By using linear transformations, the problem is transformed into a standard energy-to-peak control problem. Then a new bounded real lemma is established. On the basis of this, an approach for the design of the control protocol is developed, by which the desired gain can be obtained via solving a number of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

The Consensus for Discrete-Time Heterogeneous Networked Systems Consisting of Second-Order Agents and Third-Order Agents

This paper studies the consensus problem for the heterogeneous multiagent systems. The systems considered are assumed to consist of second-order agents and third-order agents. Both the fixed topology and the stochastic switching topology are considered. We first convert the heterogeneous multiagent systems into the equivalent error systems. Then, we analyze the consensus problem of the multiagent systems by analyzing the stability problem of the error systems. A sufficient condition for consensus of heterogeneous multiagent systems is obtained based on algebraic graph theory and linear system theory for the case of fixed topology. A necessary and sufficient condition for mean-square consensus of multiagent systems is obtained for the case of switching topology. Simulation examples are given to show the effectiveness of the obtained results.

Event-triggered based distributed H∞ consensus filtering for discrete-time delayed systems over lossy sensor network

This paper investigates the issue of event-triggered distributed H∞ consensus filtering for discrete time-varying delay systems over lossy sensor networks with stochastic switching topologies. For each sensor node, the event-triggering mechanism is given by an event detector, which determines whether to transmit the output measurement or not. The communication links between the event detector and the distributed filter are assumed to be over a lossy network, and the missing probability is governed by a set of random variables. Through available output measurements from not only the individual sensor but also its neighbouring sensors, according to the interconnection topology to estimate the system states, a sufficient condition is established for the desired distributed filter to ensure that the overall filtering dynamics are stochastically stable and achieve a prescribed distributed H∞ average performance. Meanwhile, the corresponding solvability conditions for the desired distributed filter gains are characterized in terms of feasibility linear matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed approaches.

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.

Distributed ${\mathcal{H}}_{\infty}$ Filtering for a Class of Discrete-Time Markov Jump Lur’e Systems With Redundant Channels

This paper investigates the problem of distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for a class of discrete-time Markov jump Lur'e systems over sensor networks with stochastic switching topologies. As a first effort, the redundant channels are considered to use in the data transmission to strive against the fragility of networks commonly configured by a single channel in the communication networks subject to quantization and randomly occurring packet dropouts. By constructing a Lur'e-type Lyapunov function interconnected with a cone-bounded nonlinearity, the filtering performance analysis for the underlying systems is carried out first. Then, a new class of distributed filters, which can be used to reflect the mismatching characteristic of modes jumping between the target plants and the proposed filters, is designed such that the filtering error system is stochastically stable and achieves a prescribed average H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index. A numerical example is provided to show the effectiveness of the proposed filtering scheme.