Event-Based Adaptive Neural Tracking Control for Discrete-Time Stochastic Nonlinear Systems: A Triggering Threshold Compensation Strategy

Real time adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural network proportional-integral-derivative controller for nonlinear systems

This paper presents an adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural PID controller for handling the problems of uncertainties in nonlinear systems. The proposed controller combines probabilistic processing with a Takagi-Sugeno-Kang fuzzy neural system to proficiently address stochastic uncertainties in controlled systems. The stability of the controlled system is ensured through the utilization of Lyapunov function to adjust the controller parameters. By tuning the probability parameters of the controller design, an additional level of control is achieved, leading to enhance the controller performance. Furthermore, it can operate without relying on the system's mathematical model. The proposed control approach is employed in nonlinear dynamical plants and compared to other existing controllers to validate its applicability in engineering domains. Simulation and experimental investigations demonstrate that the proposed controller surpasses alternative controllers in effectively managing external disturbances, random noise, and a broad spectrum of system uncertainties.

Codesign of FDI Attacks Detection, Isolation, and Mitigation for Complex Microgrid Systems: An HBF-NN-Based Approach

The primary purpose of this article is to design an intelligent false data injection (FDI) attacks detection, isolation, and mitigation scheme for a class of complex microgrid systems with electric vehicles (EVs). First, a networked microgrid with an EV model is well established, which takes load disturbance, wind generation fluctuation, and FDI attacks into account so as to truly reflect the operation process of the complex system. Then, an intelligent hyper basis function neural network (HBF-NN) observer is designed to accurately estimate the state of the microgrids, learn, and reconstruct the possible attack signal online. Subsequently, a novel HBF-NN-based H∞ controller is skillfully designed to mitigate the negative impact of FDI attacks online, so as to ensure the normal operation of the complex systems in an unreliable network environment. Finally, a two-stage integrated intelligent detection and maintenance algorithm is summarized and one simulation is presented to provide tangible evidence of the feasibility and superiority of the proposed FDI attacks detection, isolation, and mitigation methodology.

Adaptive NN Fixed-Time Fault-Tolerant Control for Uncertain Stochastic System With Deferred Output Constraint via Self-Triggered Mechanism

For a class of nonstrict-feedback stochastic nonlinear systems with the injection and deception attacks, this article explores the problem of adaptive neural network (NN) fixed-time control ground on the self-triggered mechanism in a pioneering way. After developing the self-triggered mechanism and the delay-error-dependence function, a neural adaptive delay-constrained fault-tolerant controller is proposed by employing the backstepping technique. The self-triggered mechanism does not require an additional observer to determine the time of the data transmission, which reduces the consumption of the system resources more efficiently. In addition, the whole Lyapunov function with the delay-error-dependence term is developed to solve the deferred output constraint problem. Under the proposed controller, it can be proven that all the signals within the closed-loop system are semiglobally uniformly bounded in probability, while the convergence time is independent of the initial state and the deferred output constraint control performance is achieved. The feasibility and the superiority of the proposed control strategy are shown by some simulations.

Adaptive Neural State Estimation of Markov Jump Systems Under Scheduling Protocols and Probabilistic Deception Attacks

The neural-network (NN)-based state estimation issue of Markov jump systems (MJSs) subject to communication protocols and deception attacks is addressed in this article. For relieving communication burden and preventing possible data collisions, two types of scheduling protocols, namely: 1) the Round-Robin (RR) protocol and 2) weighted try-once-discard (WTOD) protocol, are applied, respectively, to coordinate the transmission sequence. In addition, considering that the communication channel may suffer from mode-dependent probabilistic deception attacks, a hidden Markov-like model is proposed to characterize the relationship between the malicious signal and system mode. Then, a novel adaptive neural state estimator is presented to reconstruct the system states. By taking the influence of deception attacks into performance analysis, sufficient conditions under two different scheduling protocols are derived, respectively, so as to ensure the ultimately boundedness of the estimate error. In the end, simulation results testify the correctness of the adaptive neural estimator design method proposed in this article.

Leader-Follower Formation Learning Control of Discrete-Time Nonlinear Multiagent Systems

This article investigates the leader-follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader-follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader-follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed i_n -step predictors, the leader's future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific "learning rules," the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader-follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

Adaptive Multigradient Recursive Reinforcement Learning Event-Triggered Tracking Control for Multiagent Systems

This article proposes a fault-tolerant adaptive multigradient recursive reinforcement learning (RL) event-triggered tracking control scheme for strict-feedback discrete-time multiagent systems. The multigradient recursive RL algorithm is used to avoid the local optimal problem that may exist in the gradient descent scheme. Different from the existing event-triggered control results, a new lemma about the relative threshold event-triggered control strategy is proposed to handle the compensation error, which can improve the utilization of communication resources and weaken the negative impact on tracking accuracy and closed-loop system stability. To overcome the difficulty caused by sensor fault, a distributed control method is introduced by adopting the adaptive compensation technique, which can effectively decrease the number of online estimation parameters. Furthermore, by using the multigradient recursive RL algorithm with less learning parameters, the online estimation time can be effectively reduced. The stability of closed-loop multiagent systems is proved by using the Lyapunov stability theorem, and it is verified that all signals are semiglobally uniformly ultimately bounded. Finally, two simulation examples are given to show the availability of the presented control scheme.

Event-Triggered Adaptive NN Tracking Control for MIMO Nonlinear Discrete-Time Systems

This article concentrates on the design of a novel event-based adaptive neural network (NN) control algorithm for a class of multiple-input-multiple-output (MIMO) nonlinear discrete-time systems. A controller is designed through a novel recursive design procedure, under which the dependence on virtual controls is avoided and only system states are needed. The numbers of the event-triggered conditions and parameters updated online in each subsystem reduce to only one, which largely reduces the computation burden and simplifies the algorithm realization. In this case, radial basis function NNs (RBFNNs) are employed to approximate the control input. The semiglobal uniformly ultimate boundedness (SGUUB) of all the signals in the closed-loop system is guaranteed by the Lyapunov difference approach. The effectiveness of the proposed algorithm is validated by a simulation example.

Dynamic event-triggered resilient state estimation for time-varying complex networks with Markovian switching topologies

This paper addresses a resilient state estimation problem for an array of nonlinear complex networks with switching topologies under the dynamic event-triggered mechanism (ETM). To reduce the unnecessary data delivery, the dynamic ETM is introduced to schedule the data delivery from sensors to estimators. The model of the switched complex networks is established by adopting a Markov chain which is better to reflect the characteristics of practical complex networks. A set of novel estimators is obtained by using the properties of Kronecker product combining with the Lyapunov-Krasovskii method, and some easy-to-check conditions are derived such that the dynamics of state estimation error satisfies the prescribed H_∞ performance index. In addition, the parameters of the designed resilient state estimators can be acquired by solving a series of convex optimization problems. In the end, a simulation example is given to demonstrate the validity of the proposed theoretical results in this paper.

Dynamic Learning From Adaptive Neural Control for Discrete-Time Strict-Feedback Systems

This article first investigates the issue on dynamic learning from adaptive neural network (NN) control of discrete-time strict-feedback nonlinear systems. To verify the exponential convergence of estimated NN weights, an extended stability result is presented for a class of discrete-time linear time-varying systems with time delays. Subsequently, by combining the n -step-ahead predictor technology and backstepping, an adaptive NN controller is constructed, which integrates the novel weight updating laws with time delays and without the σ modification. After ensuring the convergence of system output to a recurrent reference signal, the radial basis function (RBF) NN is verified to satisfy the partial persistent excitation condition. By the combination of the extended stability result, the estimated NN weights can be verified to exponentially converge to their ideal values. The convergent weight sequences are comprehensively represented and stored by constructing some elegant learning rules with some novel sequences and the mod function. The stored knowledge is used again to develop a neural learning control scheme. Compared with the traditional adaptive NN control, the proposed scheme can not only accomplish the same or similar tracking tasks but also greatly improve the transient control performance and alleviate the online computation. Finally, the validity of the presented scheme is illustrated by numerical and practical examples.

Multiloop Decentralized H∞ Fuzzy PID-Like Control for Discrete Time-Delayed Fuzzy Systems Under Dynamical Event-Triggered Schemes

This article is concerned with the multiloop decentralized H_∞ fuzzy proportional-integral-derivative-like (PID-like) control problem for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays under dynamical event-triggered mechanisms (ETMs). The sensors of the plant are grouped into several nodes according to their physical distribution. For resource-saving purposes, the signal transmission between each sensor node and the controller is implemented based on the dynamical ETM. Taking the node-based idea into account, a general multiloop decentralized fuzzy PID-like controller is designed with fixed integral windows to reduce the potential accumulation error. The overall decentralized fuzzy PID-like control scheme involves multiple single-loop controllers, each of which is designed to generate the local control law based on the measurements of the corresponding sensor node. These kinds of local controllers are convenient to apply in practice. Sufficient conditions are obtained under which the controlled system is exponentially stable with the prescribed H_∞ performance index. The desired controller gains are then characterized by solving an iterative optimization problem. Finally, a simulation example is presented to demonstrate the correctness and effectiveness of the proposed design procedure.

Joint state and actuator fault estimation for networked systems under improved accumulation-based event-triggered mechanism

The joint state and actuator fault estimation problem is investigated in this paper for a type of networked systems subject to loss of the actuator effectiveness (LAE). A so-called improved accumulation-based event-triggered mechanism (ETM) is used to regulate the transmission of signals between the sensors and the estimator for the purpose of communication resource saving. Compared with the traditional ETM schemes, such accumulation-based ETM is robust against the "undesired" abrupt changes of signals (which would occur due to certain big noises). Different from the integral-based ETM for continuous-time systems, the improved accumulation-based ETM proposed in this paper is a "weighted" ETM, where a given weight coefficient is employed to "balance" the weights of output measurements in different time instants. The multiplicative LAE is described by an unknown diagonal matrix. The object of this paper is to design a remote estimator such that both the fault signals and system states can be simultaneously estimated in the sense of minimizing an upper bound of the corresponding estimation error covariance at each sampling instant. First, the upper bound of the estimation error covariance is given by means of the induction method. Then, the desired estimator gain is calculated recursively by solving two sets of coupled matrix equations. Finally, two simulation examples are given to verify the usefulness of the strategy we proposed subject to the LAE under the improved accumulation-based ETM.

Event-Based Design of Finite-Time Adaptive Control of Uncertain Nonlinear Systems

The problem of finite-time adaptive tracking control against event-trigger error is investigated in this article for a type of uncertain nonlinear systems. By fusing the techniques of command filter backstepping technical and event-triggered control (ETC), an adaptive event-triggered design method is proposed to construct the controller, under which the effect of event-triggered error can be compensated completely. Moreover, the proposed controller can increase robustness against uncertainties and event error in the backstepping design framework. In particular, we establish the finite-time convergence condition under which the tracking error asymptotically converges to zero in finite time with the aid of a scaling function. Detailed and rigorous stability proofs are given by making use of the improved finite time stability criterion. Two simulation examples are provided to exhibit the validity of the designed adaptive ETC approach.

Disturbance Observer-Based Minimum Entropy Control for a Class of Disturbed Non-Gaussian Stochastic Systems

In this article, a novel control algorithm is developed for a class of nonlinear stochastic systems subject to multiple disturbances, including exogenous dynamic disturbance and general non-Gaussian noise. An observer is designed to estimate the exogenous disturbance, and then the disturbance compensation is incorporated into a feedback control strategy for the non-Gaussian system. Considering the ability of entropy in randomness quantification, a performance index is established based on the generalized entropy optimization principle. Furthermore, it is adjusted to be available for the controller solution, which also solves the coupling between two kinds of disturbances. On this basis, the optimal controller is provided in a recursive way, with which the closed-loop stability and good antidisturbance ability can be guaranteed simultaneously. Compared with the existing studies on the non-Gaussian stochastic systems, the proposed control algorithm has merits in multiple disturbances decoupling and enhanced antidisturbance performance. Finally, a simulation example is given to demonstrate the effectiveness of theoretical results.

Adaptive model-based dynamic event-triggered output feedback control of a robotic manipulator with disturbance

This paper focuses on the stable tracking control of the manipulator with constrained communication, unmeasurable velocity, and nonlinear uncertainties. An NN observer-depended output feedback scheme in the discrete-time domain is developed by virtue of the model-based dynamic event-triggered backstepping technique in the channel of sensor to controller. For generalizing the zero-order-holder (ZOH) implementation, a plant model is built to approximate the triggered states in the time flow, and according to which, the control law is fabricated. Based on model-based error events, we construct a dead-zone triggered condition with a dynamically adjustable threshold, making the threshold evolve with the system performance, to achieve flexible communication scheduling and avoid the accumulation of triggers in small tracking errors. The internal and external nonlinear uncertainties are online compensated by the neural network, and the aperiodic adaptive law is derived in the sense of control stability to save the computation. Finally, the conditions for semi-global ultimate uniform bounded (SGUUB) of all variables are given via impulse Lyapunov analysis, and a positive lower bound in the time interval between consecutive executions to guarantee the Zeno free behavior is obtained. Simulations are conducted on a three-link manipulator to illustrate the effectiveness of our method.

A Partial-Node-Based Approach to State Estimation for Complex Networks With Sensor Saturations Under Random Access Protocol

In this article, the robust finite-horizon state estimation problem is investigated for a class of time-varying complex networks (CNs) under the random access protocol (RAP) through available measurements from only a part of network nodes. The underlying CNs are subject to randomly occurring uncertainties, randomly occurring multiple delays, as well as sensor saturations. Several sequences of random variables are employed to characterize the random occurrences of parameter uncertainties and multiple delays. The RAP is adopted to orchestrate the data transmission at each time step based on a Markov chain. The aim of the addressed problem is to design a series of robust state estimators that make use of the available measurements from partial network nodes to estimate the network states, under the RAP and over a finite horizon, such that the estimation error dynamics achieves the prescribed H_∞ performance requirement. Sufficient conditions are provided for the existence of such time-varying partial-node-based H_∞ state estimators via stochastic analysis and matrix operations. The desired estimators are parameterized by solving certain recursive linear matrix inequalities. The effectiveness of the proposed state estimation algorithm is demonstrated via a simulation example.

Finite-Horizon H∞ State Estimation for Stochastic Coupled Networks With Random Inner Couplings Using Round-Robin Protocol

This article is concerned with the problem of finite-horizon H_∞ state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors' measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon H_∞ state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.

An Event-Triggering Approach to Recursive Filtering for Complex Networks With State Saturations and Random Coupling Strengths

In this article, the recursive filtering problem is investigated for a class of time-varying complex networks with state saturations and random coupling strengths under an event-triggering transmission mechanism. The coupled strengths among nodes are characterized by a set of random variables obeying the uniform distribution. The event-triggering scheme is employed to mitigate the network data transmission burden. The purpose of the problem addressed is to design a recursive filter such that in the presence of the state saturations, event-triggering communication mechanism, and random coupling strengths, certain locally optimized upper bound is guaranteed on the filtering error covariance. By using the stochastic analysis technique, an upper bound on the filtering error covariance is first derived via the solution to a set of matrix difference equations. Next, the obtained upper bound is minimized by properly parameterizing the filter parameters. Subsequently, the boundedness issue of the filtering error covariance is studied. Finally, two numerical simulation examples are provided to illustrate the effectiveness of the proposed algorithm.

A Dynamic Event-Triggered Approach to Recursive Filtering for Complex Networks With Switching Topologies Subject to Random Sensor Failures

This article deals with the recursive filtering issue for a class of nonlinear complex networks (CNs) with switching topologies, random sensor failures and dynamic event-triggered mechanisms. A Markov chain is utilized to characterize the switching behavior of the network topology. The phenomenon of sensor failures occurs in a random way governed by a set of stochastic variables obeying certain probability distributions. In order to save communication cost, a dynamic event-triggered transmission protocol is introduced into the transmission channel from the sensors to the recursive filters. The objective of the addressed problem is to design a set of dynamic event-triggered filters for the underlying CN with a certain guaranteed upper bound (on the filtering error covariance) that is then locally minimized. By employing the induction method, an upper bound is first obtained on the filtering error covariance and subsequently minimized by properly designing the filter parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed filtering scheme.

H∞ and l2-l∞ state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol

In this paper, a protocol-based finite-horizon H_∞ and l₂-l_∞ estimation approach is put forward to solve the state estimation problem for discrete-time memristive neural networks (MNNs) subject to time-varying delays and energy-bounded disturbances. The Round-Robin protocol is utilized to mitigate unnecessary network congestion occurring in the sensor-to-estimator communication channel. For the delayed MNNs, our aim is to devise an estimator that not only ensures a prescribed disturbance attenuation level over a finite time-horizon, but also keeps the peak value of the estimation error within a given range. By resorting to the Lyapunov-Krasovskii functional method, the delay-dependent criteria are formulated that guarantee the existence of the desired estimator. Subsequently, the estimator gains are obtained via figuring out a bank of convex optimization problems. The validity of our estimator is finally shown via a numerical example.