A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs

Nonfragile Near-Optimal Control of Stochastic Time-Varying Multiagent Systems With Control- and State-Dependent Noises

In this paper, the near-optimal nonfragile consensus control design problem is investigated for a class of discrete time-varying multiagent systems (MASs) with control- and state-dependent noises. A decentralized observer-based control protocol is proposed by using the relative output measurements. The gain perturbations/variations of the controller as well as the state- and control-dependent noises are simultaneously taken into consideration, which could better reflect the complexities in reality. The corresponding time-varying observer-based nonfragile near-optimal consensus protocol is designed for the underlying MASs over a finite horizon. To be specific, a certain upper bound is first derived for the associate cost function for the MASs. Then, such an upper bound is minimized by using the completing-the-square technique and Moore-Penrose pseudo inverse. The parameters of the time-varying observer/controller are obtained in terms of the solutions to the Riccati-like recursion. In virtue of the matrix partitioning technique, the explicit expressions of the control/observer parameters are presented. Finally, based on the derived consensus protocol, an upper bound of the associate cost function is provided as time goes to infinity. Some numerical simulations are conducted to demonstrate the validity of the proposed methodology.

Nonfragile Dissipative Synchronization for Markovian Memristive Neural Networks: A Gain-Scheduled Control Scheme

In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov-Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available.

A Threshold-Parameter-Dependent Approach to Designing Distributed Event-Triggered H∞ Consensus Filters Over Sensor Networks

This paper is concerned with distributed event-triggered H_∞ consensus filtering for a discrete-time linear system over a sensor network. Different from some existing event-triggered communication schemes (ETCSs), a new distributed ETCS is first developed to reduce the communication frequency of neighboring sensors, where the threshold parameter in an event triggering condition is time-varying with attainable upper and lower bounds. Then a threshold-parameter-dependent approach is proposed to derive criteria for designing the desired H_∞ consensus filters and the ETCS such that the resultant filtering error system is asymptotically stable with the prescribed H_∞ performance while maintaining satisfactory resource efficiency. Furthermore, a polytope-like transformation with regard to time-varying threshold parameters is performed and a recursive algorithm is presented to determine the threshold-parameter-dependent filter matrix sequences and event triggering weighting matrix sequence. Two illustrative examples are employed to show the effectiveness of the developed approach.

Event-Triggered Containment Control of Multi-Agent Systems With High-Order Dynamics and Input Delay

This paper studies the problem of distributed containment control for multi-agent systems with high-order dynamics and input delays. Two event-triggered control algorithms are proposed for multi-agent systems without and with input delay, respectively. The communication instants between two linked followers are determined by the event-triggering condition, and every follower can detect the event based on its own control input. For the followers, edge-based estimators are adopted to predict state differences to neighbors. Control inputs of the followers are calculated based on the predicted values of the state differences. To deal with the input delay, a delay comprehension approach is developed. It is proved that for arbitrarily large but bounded input delays, the followers can move into the convex hull spanned by the leaders asymptotically. Simulation results show the effectiveness of the proposed algorithms.

Stability Analysis of Linear Systems under Time-Varying Samplings by a Non-Standard Discretization Method

This paper is concerned with the stability of linear systems under time-varying sampling. First, the closed-loop sampled-data system under study is represented by a discrete-time system using a non-standard discretization method. Second, by introducing a new sampled-date-based integral inequality, the sufficient condition on stability is formulated by using a simple Lyapunov function. The stability criterion has lower computational complexity, while having less conservatism compared with those obtained by a classical input delay approach. Third, when the system is subject to parameter uncertainties, a robust stability criterion is derived for uncertain systems under time-varying sampling. Finally, three examples are given to show the effectiveness of the proposed method.

Event-Triggered and Memory-Based Sliding Mode Variable Structure Control for Memristive Systems

This paper is concerned with a novel event-triggered sliding mode variable structure control (ESMC) scheme to achieve robust stabilization of memristive systems (MSs). First, a memory-based sliding surface, including the past and the current information of the system states, is introduced. Two switching gain matrices of such kinds of switching surfaces, which satisfy the guaranteed cost performance of the sliding reduced order dynamics, are achieved by employing linear matrix inequality techniques. Second, a sliding mode controller using an event-triggered mechanism is constructed to ensure that the trajectories of the uncertain MS slide towards the proposed memory-based switching hyperplane, and thus, the stabilization of entire MSs is reached. Finally, the effectiveness of the proposed results is demonstrated through simulations.

A Novel Finite-Sum Inequality-Based Method for Robust $H_\infty$ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays

This paper is concerned with the problem of robust ${H}_{\infty}$ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust ${H}_{\infty}$ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding-Decoding-Based Approach

The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding-decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding-decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.

Hierarchical Type Stability Criteria for Delayed Neural Networks via Canonical Bessel-Legendre Inequalities

This paper is concerned with global asymptotic stability of delayed neural networks. Notice that a Bessel-Legendre inequality plays a key role in deriving less conservative stability criteria for delayed neural networks. However, this inequality is in the form of Legendre polynomials and the integral interval is fixed on . As a result, the application scope of the Bessel-Legendre inequality is limited. This paper aims to develop the Bessel-Legendre inequality method so that less conservative stability criteria are expected. First, by introducing a canonical orthogonal polynomial sequel, a canonical Bessel-Legendre inequality and its affine version are established, which are not explicitly in the form of Legendre polynomials. Moreover, the integral interval is shifted to a general one . Second, by introducing a proper augmented Lyapunov-Krasovskii functional, which is tailored for the canonical Bessel-Legendre inequality, some sufficient conditions on global asymptotic stability are formulated for neural networks with constant delays and neural networks with time-varying delays, respectively. These conditions are proven to have a hierarchical feature: the higher level of hierarchy, the less conservatism of the stability criterion. Finally, three numerical examples are given to illustrate the efficiency of the proposed stability criteria.

Collective Behaviors of Mobile Robots Beyond the Nearest Neighbor Rules With Switching Topology

This paper is concerned with the collective behaviors of robots beyond the nearest neighbor rules, i.e., dispersion and flocking, when robots interact with others by applying an acute angle test (AAT)-based interaction rule. Different from a conventional nearest neighbor rule or its variations, the AAT-based interaction rule allows interactions with some far-neighbors and excludes unnecessary nearest neighbors. The resulting dispersion and flocking hold the advantages of scalability, connectivity, robustness, and effective area coverage. For the dispersion, a spring-like controller is proposed to achieve collision-free coordination. With switching topology, a new fixed-time consensus-based energy function is developed to guarantee the system stability. An upper bound of settling time for energy consensus is obtained, and a uniform time interval is accordingly set so that energy distribution is conducted in a fair manner. For the flocking, based on a class of generalized potential functions taking nonsmooth switching into account, a new controller is proposed to ensure that the same velocity for all robots is eventually reached. A co-optimizing problem is further investigated to accomplish additional tasks, such as enhancing communication performance, while maintaining the collective behaviors of mobile robots. Simulation results are presented to show the effectiveness of the theoretical results.

Cooperative Control of Mobile Sensor Networks for Environmental Monitoring: An Event-Triggered Finite-Time Control Scheme

This paper deals with the problem of environmental monitoring by developing an event-triggered finite-time control scheme for mobile sensor networks. The proposed control scheme can be executed by each sensor node independently and consists of two parts: one part is a finite-time consensus algorithm while the other part is an event-triggered rule. The consensus algorithm is employed to enable the positions and velocities of sensor nodes to quickly track the position and velocity of a virtual leader in finite time. The event-triggered rule is used to reduce the updating frequency of controllers in order to save the computational resources of sensor nodes. Some stability conditions are derived for mobile sensor networks with the proposed control scheme under both a fixed communication topology and a switching communication topology. Finally, simulation results illustrate the effectiveness of the proposed control scheme for the problem of environmental monitoring.

Neuronal State Estimation for Neural Networks With Two Additive Time-Varying Delay Components

This paper is concerned with the state estimation for neural networks with two additive time-varying delay components. Three cases of these two time-varying delays are fully considered: 1) both delays are differentiable uniformly bounded with delay-derivative bounded by some constants; 2) one delay is continuous uniformly bounded while the other is differentiable uniformly bounded with delay-derivative bounded by certain constants; and 3) both delays are continuous uniformly bounded. First, an extended reciprocally convex inequality is introduced to bound reciprocally convex combinations appearing in the derivative of some Lyapunov-Krasovskii functional. Second, sufficient conditions are derived based on the extended inequality for three cases of time-varying delays, respectively. Third, a linear-matrix-inequality-based approach with two tuning parameters is proposed to design desired Luenberger estimators such that the error system is globally asymptotically stable. This approach is then applied to state estimation on neural networks with a single interval time-varying delay. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

Reliable Output Feedback Control for T-S Fuzzy Systems With Decentralized Event Triggering Communication and Actuator Failures

Due to the unavailability of full state variables in many control systems, this paper is concerned with the design of reliable observer-based output feedback controller for a class of network-based Takagi-Sugeno fuzzy systems with actuator failures. In order to better allocate network resources under the case that the sensor nodes are physically distributed, the decentralized event triggering communication scheme is adopted such that each sensor node is capable to determine the transmission of its local measurement information independently. Considering that the implementation of the controller may not be synchronized with the plant trajectories due to asynchronous premise variables with such communication mechanism, a novel piecewise fuzzy observer-based output feedback controller is developed. By applying a piecewise Lyapunov function and some techniques on matrix convexification, an approach to the design of observer and controller gain is derived for the augmented closed-loop system to be asymptotically stable with a guaranteed H_∞ performance and reduced transmission frequency. Finally, two examples are given to show the effectiveness of the developed method.

Finite-Horizon ${\mathcal H}_{\infty }$ Consensus Control of Time-Varying Multiagent Systems With Stochastic Communication Protocol

This paper is concerned with the distributed ℋ∞ consensus control problem for a discrete time-varying multiagent system with the stochastic communication protocol (SCP). A directed graph is used to characterize the communication topology of the multiagent network. The data transmission between each agent and the neighboring ones is implemented via a constrained communication channel where only one neighboring agent is allowed to transmit data at each time instant. The SCP is applied to schedule the signal transmission of the multiagent system. A sequence of random variables is utilized to capture the scheduling behavior of the SCP. By using the mapping technology combined with the Hadamard product, the closed-loop multiagent system is modeled as a time-varying system with a stochastic parameter matrix. The purpose of the addressed problem is to design a cooperative controller for each agent such that, for all probabilistic scheduling behaviors, the ℋ∞ consensus performance is achieved over a given finite horizon for the closed-loop multiagent system. A necessary and sufficient condition is derived to ensure the ℋ∞ consensus performance based on the completing squares approach and the stochastic analysis technique. Then, the controller parameters are obtained by solving two coupled backward recursive Riccati difference equations. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.

Cooperative Output Regulation of Heterogeneous Linear Multi-Agent Systems by Event-Triggered Control

In this paper, we consider the cooperative output regulation problem of heterogeneous linear multi-agent systems (MASs) by event-triggered control. We first develop an event-triggering mechanism for leader-following consensus of homogeneous MASs. Then by proposing an internal reference model for each agent, a novel distributed event-triggered control scheme is developed to solve the cooperative output regulation problem of heterogeneous MASs. Furthermore, a novel self-triggered control scheme is also proposed, such that continuous monitoring of measurement errors can be avoided. The feasibility of both proposed control schemes is studied by excluding Zeno behavior for each agent. An example is finally provided to demonstrate the effectiveness of the control schemes.