Stabilization of Neural-Network-Based Control Systems via Event-Triggered Control With Nonperiodic Sampled Data

Novel criteria of sampled-data synchronization controller design for gated recurrent unit neural networks under mismatched parameters

Synchronization between neural networks (NNs) has been intensively investigated to analyze stability, convergence properties, neuronal behaviors and response to various inputs. However, synchronization techniques of NNs with gated recurrent units (GRUs) have not been provided until now due to their complicated nonlinearity. In this paper, we address the sampled-data synchronization problems of GRUs for the first time, and propose controller design methods using discretely sampled control inputs to synchronize master and slave GRUs. The master and slave GRUs are mathematically modeled as a linear parameter varying (LPV) system in which the parameter of the slave GRUs is constructed independently of the master GRUs. This distinctive modeling feature provides flexibility to extend the existing master and slave NNs into a more general structure. Indeed, the sampled-data synchronization can be achieved by formulating the design condition in terms of linear matrix inequalities (LMIs). The novel sampled-data synchronization criteria are devised by combining the H∞ controller design with the looped-functional approach. The synthesized synchronization controllers guarantee not only asymptotic stability of the synchronization error system with aperiodic sampling, but also provides a satisfactory H∞ control performance. Moreover, the communication efficiency is improved by using the proposed method in which the sampled-data synchronization controller is combined with the event-triggered mechanism. Finally, the numerical example validates the proposed theoretical contributions via simulation results.

Sampled-Data-Based Dissipative Stabilization of IT-2 TSFSs Via Fuzzy Adaptive Event-Triggered Protocol

In this research, the fuzzy adaptive event-triggered control (FAETC) issue is addressed for uncertain nonlinear networked control systems with network-induced delays (NIDs) and external disturbance. In order to effectively capture parameter uncertainties, the interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy model is utilized to represent such a system. Considering the fact that the controller is fuzzy and the threshold can promptly update its state according to the current and latest sampled signals (SSs), it becomes quite challenging to solve the dissipative stabilization problem (DSP) with the existing schemes. Then, a novel FAETC protocol is put forward to reduce the utilization of communication resources while maintaining the desired control performance. By employing the fuzzy-logic technique and the looped Lyapunov functional (LLF) approach, sufficient conditions related to the relationship between the stabilization and desired dissipative performance for the resulting system are formulated. A numerical example is used to validate the feasibility of our attained results.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Zonotopic Fault Detection for 2-D Systems Under Event-Triggered Mechanism

This article studies the problem of event-triggered fault detection (FD) for 2-D systems subjected to amplitude-bounded exogenous disturbance and measurement noise via a zonotopic residual evaluation mechanism. An event-triggered mechanism is introduced into the FD framework to save limited communication resources. A finite-frequency (FF) mixed l_∞/h_∞ index is derived to ensure the residual signal is sensitive to a fault signal while robust to disturbance and noise, based on which an optimal mixed l_∞/h_∞ FD filter design criterion is provided. Instead of constant thresholds, novel zonotope-based dynamic thresholds are utilized for residual evaluation. Finally, simulation results are presented to illustrate the effectiveness of the developed mechanism.

Leader-Following Event-Triggered Adaptive Practical Consensus of Multiple Rigid Spacecraft Systems Over Jointly Connected Networks

In this article, we study the leader-following practical attitude consensus problem of a group of multiple uncertain rigid spacecraft systems over jointly connected networks by a distributed event-triggered control law. We first establish a lemma that allows the problem to be converted to a distributed practical stabilization problem of a well-defined uncertain dynamical system. Then, we combine the adaptive distributed observer technique and the adaptive control technique to design an event-triggered adaptive control law and an event-triggered mechanism to solve our problem. The effectiveness of our design is illustrated by a numerical example.

Exponential passivity of discrete-time switched neural networks with transmission delays via an event-triggered sliding mode control

This paper investigates the exponential passivity of discrete-time switched neural networks (DSNNs) with transmission delays via an event-triggered sliding mode control (SMC). Firstly, a novel discrete-time switched SMC scheme is constructed on the basis of sliding mode control method and event-triggered mechanism. Next, a state observer with transmission delays is designed to estimate the system state. Moreover, some new weighted summation inequalities are further proposed to effectively evaluate the exponential passivity criteria for the closed-loop system. Finally, the effectiveness of theoretical results is showed through a simulative analysis on a multi-area power system.

Performance analysis method for NCSs with coding and quantization constraints

This paper studied the performance of networked control systems (NCSs) with coding and quantization constraints. In the forward channel of NCSs, the effects of noise and coding-decoding under a two-degree of freedom controller (2DOF) are considered, while in the feedback channel, the effects of quantization and bandwidth are taken into account. The performance expression is achieved by the spectral factorization. From the results, it can be concluded that the performance is determined by the given plant construction (non minimum phase (NMP) zeros, unstable poles), characteristics of the channel parameters. At the same time, the additive white Gaussian noise (AWGN), coding-decoding, quantization, bandwidth and other factors in the communication path also affect the performance of the network communication path. Finally, the effectiveness and merits of the proposed control scheme are verified by simulations.

Model-Based Event-Triggered Tracking Control of Underactuated Surface Vessels With Minimum Learning Parameters

This article studies the model-based event-triggered control (ETC) for the tracking activity of the underactuated surface vessel (USV). Following this ideology, the continuous acquisition of states is no longer needed, and the communication traffic is reduced in the channel of sensor to controller. The control laws are fabricated in the frame of an adaptive model, which is renewed with the states of the original system whenever the triggering condition is violated. In the scheme, both internal and external uncertainties are approximated by the neural networks (NNs). To decrease the computing complexity, the minimum learning parameters (MLPs) are involved both in the adaptive model and the derived controller. The adaptive laws of only two MLPs are devised, and their updating only happens at triggering instants. Using the MLPs, an adaptive triggering condition is further derived. To avoid the "Zeno" phenomenon in small tracking errors, a dead-zone operator is designed for the triggering condition. Furthermore, we incorporate the dynamic surface control (DSC) into the controller design, such that the jumping of virtual control laws at triggering instants is smoothed and the problem of "complexity explosion" is circumvented. Through the techniques of the impulsive dynamic system and the direct Lyapunov function, the parameter setting for the DSC is derived to guarantee the semiglobal uniformly ultimate boundedness (SGUUB) of all the error signals in the closed-loop system. Finally, the effectiveness of the proposed scheme is validated through the simulation.

Tracking Performance Limitations of MIMO Networked Control Systems With Multiple Communication Constraints

In this paper, the tracking performance limitation of networked control systems (NCSs) is studied. The NCSs are considered as continuous-time linear multi-input multioutput (MIMO) systems with random reference noises. The controlled plants include unstable poles and nonminimum phase (NMP) zeros. The output feedback path is affected by multiple communication constraints. We focus on some basic communication constraints, including additive white noise (AWN), quantization noise, bandwidth, as well as encoder-decoder. The system performance is evaluated with the tracking error energy, and used a two-degree-of-freedom (2DOF) controller. The explicit representation of the tracking performance is given in this paper. The results indicate the tracking performance limitations rely to internal characteristics of the plant (unstable poles and NMP zeros), reference noises [the reference noise power distribution (RNPD) and its directions], and the characteristics of communication constraints. The characteristics of communication constraints include communication noise power distribution (CNPD); quantization noise power distribution (QNPD), and their distribution directions; transform bandwidth allocation (TBA); transform encoder-decoder allocation (TEA), and their allocation directions; and NMP zeros and MP part of bandwidth. Moreover, the tracking performance limitations are also affected by the angles between the each transform NMP zero direction and RNPD direction, and these angles between each transform unstable poles direction and the direction of communication constraint distribution/allocation. In addition, for MIMO NCSs, bandwidth (there are not identical two channels) can always affect the direction of unstable poles, and the channel allocation of bandwidth and encode-decode may be used for a feasible method for the performance allocation of each channel. Finally, an instance is given for verifying the effectiveness of the theoretical outcomes.

Torus-Event-Based Fault Diagnosis for Stochastic Multirate Time-Varying Systems With Constrained Fault

In this paper, the torus-event-based fault detection and isolation (FDI) problem is investigated for a class of time-varying multirate systems. An ellipsoidal constraint is first adopted to describe the fault in a more practical pattern, and a novel torus-event-triggering scheme is proposed to improve the unilateral triggering mechanism. The aim is to design the torus-event-based fault detection filter and fault isolation estimators such that both the prescribed variance constraint on the estimation error and the desired H_∞ performance on the disturbance are guaranteed over the finite horizon. Especially, the residual evaluation function is employed to detect the fault, and the residual matching function is developed to isolate the fault. Furthermore, three optimization problems are provided to seek separately the minimal parameters on the H_∞ performance level, the upper bound of the estimation error variance, and the triggering torus. Finally, two simulation examples are utilized to show the effectiveness of the FDI scheme proposed in this paper.

Stubborn State Estimation for Delayed Neural Networks Using Saturating Output Errors

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Distributed Dissipative State Estimation for Markov Jump Genetic Regulatory Networks Subject to Round-Robin Scheduling

The distributed dissipative state estimation issue of Markov jump genetic regulatory networks subject to round-robin scheduling is investigated in this paper. The system parameters randomly change in the light of a Markov chain. Each node in sensor networks communicates with its neighboring nodes in view of the prescribed network topology graph. The round-robin scheduling is employed to arrange the transmission order to lessen the likelihood of the occurrence of data collisions. The main goal of the work is to design a compatible distributed estimator to assure that the distributed error system is strictly (Λ ₁,Λ ₂,Λ ₃) - γ -stochastically dissipative. By applying the Lyapunov stability theory and a modified matrix decoupling way, sufficient conditions are derived by solving some convex optimization problems. An illustrative example is given to verify the validity of the provided method.

Resilient Event-Triggered Controller Synthesis of Networked Control Systems Under Periodic DoS Jamming Attacks

In this paper, the event-based controller synthesis problem for networked control systems under the resilient event-triggering communication scheme (RETCS) and periodic denial-of-service (DoS) jamming attacks is studied. First, a new periodic RETCS is designed under the assumption that the DoS attacks imposed by power-constrained pulsewidth-modulated jammers are partially identified, that is, the period of the jammer and a uniform lower bound on the jammer's sleeping periods are known. Second, a new state error-dependent switched system model is constructed, including the impacts of the RETCS and DoS attacks. According to this new model, the exponential stability criteria are derived by using the piecewise Lyapunov functional. In these criteria, the relationship among DoS parameters, the triggering parameters, the sampling period, and the decay rate is quantitatively characterized. Then, a criterion is also proposed to obtain the explicit expressions of the triggering parameter and event-based state feedback controller gain simultaneously. Finally, the obtained theoretical results are verified by a satellite yaw-angles control system.

Aperiodic adaptive control for neural-network-based nonzero-sum differential games: A novel event-triggering strategy

Owing to the adoption of aperiodic sampling pattern, the event-triggering control mode has been widely investigated in networked systems to save communication and reduce computation. Recently, there has been some preliminary findings to explore applications of this novel mode and to implement it in neural-network-based nonlinear systems by including an event generator. This motivates our investigation. For the first time, this paper designs triggering rules for neural-network-based nonzero-sum differential games characterized by nonlinear dynamics and quadratic cost functions. The main intention of the event-triggering strategy is to reduce communication between controllers and neural networks, thereby mitigating computational loads of controllers. An adaptive critic algorithm is subsequently applied to learn the required Nash equilibrium on line and meantime an alarm sampling period is proposed to ameliorate the learning accuracy. Furthermore, three simulation cases validate the approximate-optimal control performance and appraise virtues of the proposed event-triggering mode.

Event-Triggered Cooperative Global Robust Practical Output Regulation for Second-Order Uncertain Nonlinear Multiagent Systems

In this paper, we study the cooperative global robust practical output regulation problem for a class of second-order uncertain nonlinear multiagent systems via a distributed event-triggered state feedback control strategy. Compared with the existing work, one of the main challenges is that we need to design two distributed internal models to learn both the desired steady-state state and steady-state input for each agent. Moreover, to obtain a directly implementable digital control law, the two distributed internal models of each agent only depend on the sampled states of the neighboring agents and itself. As a result, the resulting augmented system is more complicated, and the control law needs to be recursively designed. To overcome the difficulty, we propose a novel distributed event-triggered control law and a novel distributed event-triggered mechanism to deal with our problem. By adjusting a design parameter in the proposed event-triggered mechanism, we show that the Zeno behavior does not happen and the ultimate bound of the tracking error can be made arbitrarily small. Our design will be illustrated by two examples.