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This paper concerns the stabilization problem of stochastic uncertain complex-valued delayed networks (SUCVDNs) via aperiodically intermittent nonlinear control. It is worth noting that the intermittent control is aperiodic and nonlinear. As a special case, when each control width tends to zero, intermittent control becomes impulsive control. Hence, the stabilization problem of SUCVDNs via impulsive control is also studied. The main method is the combination of the Lyapunov method and Kirchhoff’s matrix tree theorem in graph theory, which does not require us to solve any linear matrix inequalities. Different from previous results on complex-valued system, we consider the complex-valued system on complex space directly by using complex version Itô’s formula and (conjugate) ${\mathbb {R}}$ derivative. Then we give some sufficient criteria, which have a close relationship with the control interval and the topological structure of the considered network. The main results are applied to a class of stochastic complex-valued coupled oscillators, and numerical examples are also presented to show the effectiveness of the control strategies. [ABSTRACT FROM AUTHOR]

This paper deals with a state-feedback control scheme for nonlinear stochastic systems with Markovian switching. First, we present the results on the practically $ {p}$ -moment exponential stability with respect to an additional disturbance and the practically $ {p}$ -moment asymptotic stability relying on a specific event. However, elements in this event are hard to be observed directly. The main aim of this paper is to develop a self-triggered sampling rule to overcome this difficulty. By applying the improved monotone growth condition, Itô’s formula, Fubini’s theorem, Gronwall inequality, and comparison lemma, we establish a novel lemma to estimate the lower bound and upper bound of second-moment for state and error, respectively. Moreover, we also establish the practically asymptotic stability in mean square with the help of Jensen’s inequality technique, properties of $ {\mathcal {K}}$ -function and result on $ {p}$ -moment input-to-state stability. Furthermore, from Lipschitz continuity and monotonicity of functions, we obtain the value of the maximum triggering interval based on lasted-observed state. Finally, we give some remarks and discussions to show the significance of our results by comparing with those in the previous literature. [ABSTRACT FROM AUTHOR]

Dissipativity of stochastic nonlinear systems with state-dependent switching is investigated in this brief. Switching instants are introduced reasonably, based on the evolution of the state trajectory, which are proved to be stopping times. They are the key to apply Itô’s formula and Dynkin’s formula in stochastic systems. Based on these stopping times, some sufficient conditions on dissipativity of switched stochastic systems are provided. Furthermore, the criteria on global asymptotic stability and input-to-state stability in probability are presented by using a common Lyapunov function technique and multiple Lyapunov functions techniques, respectively. Finally, a numerical example is given to illustrate the validity of our results. [ABSTRACT FROM PUBLISHER]

Stability is an important indicator for evaluating complex dynamic systems’ performance. Many problems in practice are abstracted into the stability of networks. This study examines stochastic fuzzy Cohen-Grossberg neural networks(CGNNs) with delayed $p$ th moment exponential stability and almost sure exponential stability. It is an improvement and supplement to existing work. Our method is based on integral inequality, differential inequality, stochastic analysis theory and Itô’s formula, which discusses the system’s stability, we have obtained sufficient conditions for system stability, which avoided the construction of complex Lyapunov functions. Moreover, our method does not require that the activation function be bounded, differentiable and monotone, and provides sufficient con $\cdot $ editions decreased conservative. At the same time, it is verified that fuzzy and stochastic terms have positive effects on system stability. Finally, the effectiveness of the results is verified by a simulation example.

Given a probability measure $\mu $ over $\mathbb {R}^{n}$ , it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan used a stochastic localization argument to prove a general decomposition result of this type. In Eldan’s theorem, the ‘number of components’ is characterized by the entropy of the mixture, and ‘closeness to product’ is characterized by the covariance matrix of each component. We present an elementary proof of Eldan’s theorem which makes use of an information theory (or estimation theory) interpretation. The proof is analogous to the one of an earlier decomposition result known as the ‘pinning lemma.’ [ABSTRACT FROM AUTHOR]

The event-triggered impulsive control (ETIC) problem is studied for stochastic networked control systems (NCSs) under random cyber attacks. The random cyber-attacks model is proposed to integrate denial-of-service (DoS) attacks and deception attacks into a unified framework by means of two independent Bernoulli random sequences. In ETIC systems, the impulsive control time sequence is generated by the event-triggered mechanism (ETM). Both continuous ETM and periodic ETM are developed by continuous measuring and periodic sampling, respectively. In order to exclude the Zeno behavior, an easy and effective method is provided to choose the waiting time of continuous ETM and the sampling period of periodic ETM. According to the proposed ETMs, sufficient conditions of the mean-square exponential stability are derived for stochastic NCSs. An example of Chua’s circuits is given to explain our ETIC schemes. [ABSTRACT FROM AUTHOR]

In this brief, the almost sure exponential consensus of multi-agent systems is investigated. A consensus protocol is designed with aperiodically intermittent communication noise rather than common continuous communication noise. Based on the consensus protocol, some sufficient conditions are given. Moreover, theoretical results show that the larger the noise control gain is, the larger the convergence rate of exponential convergency becomes in an almost sure sense. Besides, when the consensus protocol with aperiodically intermittent communication noise degenerates into one with periodically intermittent communication noise or one with common continuous communication noise, two corollaries are presented respectively. Then, the main results are used to consider almost sure exponential consensus of oscillator systems, and some simulations are provided. [ABSTRACT FROM AUTHOR]

In this article, we apply the active disturbance rejection control (ADRC) to the output tracking of a class of lower triangular nonlinear systems subject to mismatched bounded stochastic disturbances of unknown statistic characteristics and nonvanishing at the origin. A major obstacle is that the paths of the stochastic disturbances are nowhere differentiable almost surely which causes that the stochastic disturbances cannot be refined into the control input channel by the usual way of state transformation. To overcome this obstacle, a set of second-order extended state observers is first designed to estimate, in real time, the disturbance in each channel, and then a backstepping ADRC based on feedforward compensation and a constructive backstepping procedure is developed, guaranteeing that the closed-loop output tracks a time-varying reference signal in practically mean square and the closed-loop states are practically bounded in probability first defined in this article. Finally, some numerical simulations are presented to validate the effectiveness of the proposed backstepping ADRC approach. [ABSTRACT FROM AUTHOR]

We consider the discrete-time distributed bipartite-consensus problem for multiagent systems subject to measurement noises and time-varying random networks, where the information exchange among the agents can be antagonistic and disturbed by both multiplicative and additive noises. The antagonistic information is characterized by a signed random graph. The main challenge is that the coexistence of multiplicative noise and antagonistic information does not allow the multiplicative noise term to be converted into an error equation. Based on the semi-decomposition method and Lyapunov-based technique, we derive sufficient conditions for stochastic approximation step size to assure the mean square bipartite consensus. Moreover, the convergence rate of the consensus error is explicitly formulated, which is tightly linked to the step size and the eigenvalues of the Laplacian matrix. Finally, we verify the main results via a numerical example. [ABSTRACT FROM AUTHOR]

A new consensus protocol with aperiodically intermittent discrete-time state observation noise (AIDSON) is introduced. With the help of the proposed AIDSON, the almost sure exponential consensus (ASEC) of multiagent systems is investigated. Through the Lyapunov method and stochastic comparison principle, some sufficient conditions can be obtained. Moreover, the upper bounds of the rest rate of intermittent communication noise and the duration between two consecutive observations are estimated. Additionally, the larger the noise intensity is, the faster multiagent systems reach the ASEC. Furthermore, the established results are applied to the consensus analysis of single-link robot arms and oscillators and some simulations are presented. [ABSTRACT FROM AUTHOR]

This article addresses the problem of finite-time stabilization for a class of high-order nonlinear stochastic systems with asymmetric output constraints. A novel barrier Lyapunov function (BLF) is first presented to handle such asymmetric constraints. Further, based on the proposed BLF and the adding a power integrator technique, a controller design approach is developed by the backstepping method. It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated. Another novelty of this approach is that it is a unified tool owing to its simultaneous application to the systems without output constraints. Finally, the validity of the proposed scheme can be verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this article, we propose a decentralized approach to formation control in groups of stochastic mobile robots. Different from existing work, we explicitly model the presence of stochastic perturbations affecting the dynamics and model the multivehicle system through stochastic differential equations. We design a decentralized formation control strategy where only a subset of informed agents is aware of the desired target locations and derive sufficient conditions for almost sure convergence to the desired formation pattern. Specifically, we illustrate how the achievement of the control goal is related to the intensity of the noise and to the topology of the communication graph among the robots. The proposed formation control strategy is tested through extensive numerical analyses and validated experimentally on ground robots. [ABSTRACT FROM AUTHOR]

Recently, a connection between the age of information and remote estimation error was found in a sampling problem of Wiener processes: If the sampler has no knowledge of the signal being sampled, the optimal sampling strategy is to minimize the age of information; however, by exploiting causal knowledge of the signal values, it is possible to achieve a smaller estimation error. In this paper, we generalize the previous study by investigating a problem of sampling a stationary Gauss-Markov process named the Ornstein-Uhlenbeck (OU) process, where we aim to find useful insights for solving the problems of sampling more general signals. The optimal sampling problem is formulated as a constrained continuous-time Markov decision process (MDP) with an uncountable state space. We provide an exact solution to this MDP: The optimal sampling policy is a threshold policy on instantaneous estimation error and the threshold is found. Further, if the sampler has no knowledge of the OU process, the optimal sampling problem reduces to an MDP for minimizing a nonlinear age of information metric. The age-optimal sampling policy is a threshold policy on expected estimation error and the threshold is found. In both problems, the optimal sampling policies can be computed by low-complexity algorithms (e.g., bisection search and Newton’s method), and the curse of dimensionality is circumvented. These results hold for (i) general service time distributions of the queueing server and (ii) sampling problems both with and without a sampling rate constraint. Numerical results are provided to compare different sampling policies. [ABSTRACT FROM AUTHOR]

Genetic Regulatory Networks (GRNs) play an important role for the development and evolution of biological systems. On the basis of the development for DNA microarray technologies, a profound study for GRNs becomes possible at genome scale. In this article, the global dissipativity and corresponding attractive set for the GRNs with stochastic disturbances and time-delays are investigated based on Lyapunov theory. Stochastic disturbances are considered into both the feedback regulation process and the translation process for reflecting the inherent noise perturbations on a foundation of factual knowledge. Through the resort to the several appropriate Lyapunov-Krasovskii Functionals (LKFs) combining with Itô's formula and different inequality techniques, some corresponding sufficient conditions and the attractive set are obtained for the GRNs in linear matrix inequality form, which are easy to verify by the numerical software. Finally, one three-node GRN is proposed and analyzed to illustrate the validity of the proposed results by using the Field-Programmable Gate Array (FPGA) hardware simulation tool.

This article addresses an adaptive fuzzy finite-time control for a class of uncertain strict-feedback nonlinear systems with backlashlike hysteresis and stochastic disturbances. At first, a novel criterion of semiglobally finite-time stability in probability (SGFSP) is established based on Lyapunov function method. Under the proposed stability criterion, an adaptive fuzzy finite-time control scheme is designed. In the design process of the controller, command filter technique is introduced to overcome the problems of “explosion of complexity” and “singularity” inhered in the traditional adaptive finite-time control based on the backstepping method. Meanwhile, via constructing the corresponding error compensating systems, the effect of errors generated by the command filters is reduced, such that the original systems have more better tracking performance. To cope with the influence of backlashlike hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. It is shown that the tracking error can converge to a small neighborhood of original in finite time, and the closed-loop system is SGFSP under the constructed controller. Finally, the effectiveness of the proposed control strategy is further verified by two simulation examples. [ABSTRACT FROM AUTHOR]

A model-free distributed control scheme that implements active voltage control in low voltage distribution network (LVDN) is proposed. By solving an individual Hamilton-Jacobi-Bellman-Flemming function with public information, users can compute a good approximation to their optimal control trajectory and take uncertainties into account in a distributed manner. A detailed mathematical framework is given, accompanied by a discussion on the different entries of uncertainties. The proposed control scheme uses a broadcast signal to indicate the probability distribution in mean field theory, and to streamline the demand on Fokker-Planck-Kolmogorov PDE or Mc-Kean Vlasov SDE, which relieves the computational burden. A realistic semiurban distribution network is modified as the study case, with a benchmark of centralized ACOPF to study the performance of the proposed approach. Moreover, two special cases including communication latency and packet loss are given as well, in order to test the robustness of the proposed approach. The results prove that the proposed approach is able to deliver good approximation to the optimal control with uncertainty in a model-free and distributed manner. [ABSTRACT FROM AUTHOR]

This article investigates a fuzzy boundary control problem of a class of stochastic nonlinear systems modeled by the Itô-type parabolic stochastic partial differential equation (SPDE). Initially, a Takagi–Sugeno fuzzy SPDE model is proposed to accurately represent the nonlinear SPDE system. Then, on the basis of the infinite-dimensional infinitesimal operator, a fuzzy boundary static output feedback controller is developed in terms of a set of linear matrix inequalities to locally exponentially stabilize the resulting system in the mean square sense. By using an approximation argument and constructing a Lyapunov function for the mild solution, the local mean square exponential stability of the closed-loop system is proved. Meanwhile, the closed-loop well-posedness analysis is also given by virtue of the semigroup theory. Finally, a simulation study on a Belousov–Zhabotinsky reaction–diffusion system with random parameter variation is presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, based on the exponential synchronization of double-layered networks composed of multiple subnets, we bring forward a chaotic secure communication scheme, which is robust to different network sizes, time-varying delays, and stochastic noise. Cluster analysis is used to process the nodes with different dynamics, such that the subnets in the transmitter and receiver are one-to-one correspondence and constitute subnet pairs, while the node size of each subnet can be inconsistent. Each subnet pair is only accountable for encrypting/decrypting a part of information. There are many encryption/decryption units and they are operating in parallel, which can not only indicate the complex characteristic of different nodes but also speed up the information encryption/decryption. The proposed scheme applies the chaotic signals yielded by many chaotic systems as key sequences, such that the key space can grow with node sizes in the transmitter. This scheme is not subject to the constraint on the amplitude of the original message and chaotic signal, the influence of time-delay and stochastic noise, and it shows that only the nodes with large degrees need to apply controllers in restoring the original information. Both theoretical analysis and numerical simulation manifest the feasibility and validity of the given scheme. [ABSTRACT FROM AUTHOR]

This paper establishes the stability criteria for genetic regulatory networks with random disturbances. We assume the nonlinear feedback regulation function to satisfy the sector-like condition and the random perturbation to have a finite second-order moment. First, under the globally Lipschitz condition, the existence and uniqueness of solution to random genetic regulatory networks are considered by exploiting an iterative approximation method. Then, by feat of the random analysis method and matrix technique, sufficient conditions are given to guarantee the noise-to-state stability in mean and globally asymptotic stability in probability, respectively. At last, two simulation examples are exploited in order to verify the validity of the proposed theory. [ABSTRACT FROM AUTHOR]

This paper established the vector Razumikhin-type theorem on exponential stability for stochastic functional differential systems by the stochastic analysis techniques and the property of M -Matrix. Several novel stability criteria with vector \mathscr L -operator differential inequalities for stochastic delay differential systems, especially some of which includes the cross-item, were obtained by means of the vector Razumikhin theorem. By applying these new results, the robustness of global exponential stability of delay recurrent neural networks to random disturbed has been analyzed. [ABSTRACT FROM AUTHOR]

This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Itô diffusions) can be defined and studied on manifolds. No knowledge is assumed of either differential geometry or continuous-time processes. The arguably dry approach is avoided of first introducing differential geometry and only then introducing stochastic processes; both areas are motivated and developed jointly. [ABSTRACT FROM PUBLISHER]

A new stochastic dynamic model for the generation of rain attenuation time series for fixed satellite and Line-of-sight (LOS) terrestrial links operating above 10 GHz is presented. The model's concept originate from the classic Maseng-Bakken (M-B) approach apart that it generates Gamma distributed rain attenuation time-series and not lognormal as in M-B approach. Gamma-distributed links are typical at heavy rain climatic regions where the new model is expected to perform better than the M-B. The comparison with experimental results in terms of exceedance probability is very encouraging. [ABSTRACT FROM PUBLISHER]

This article investigates the distributed dynamic output-feedback bipartite consensus for a class of stochastic nonlinear multiagent systems (MASs) with time delays and actuators faults under directed switching graphs. First, a distributed extended state compensator is constructed for each agent to compensate for the consensus errors and actuators’ faults only using the output information of neighbors. Then, based on the compensator, a linear memoryless output-feedback controller is designed. Using a technical lemma and the stochastic Lyapunov stability theory, it is proved that combined with the given constraint conditions on graphs switching the 2nd-moment asymptotic bipartite consensus for the MASs can be achieved. Different from existing results, the proposed compensator can not only save the network bandwidth but also compensate for the actuators’ faults. The proposed scheme also significantly relaxes the conditions on the communication network to directed switching graphs and even allows the graph to be disconnected over some time intervals. The common design parameters under any graphs can avoid the detection of graph switching, which will need global topology information. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]