Class Of Interconnected Nonlinear Systems Research Articles

Design of distributed event‐triggered states and unknown disturbances observers for time‐varying delay interconnected systems

SummaryThis article considers the problem of designing distributed event‐triggered states and unknown disturbances observers for a class of nonlinear interconnected systems where the local state vectors are affected by unknown delays and the nonlinear function satisfying the Lipschitz condition. Distributed observers are designed based on the local input vector and both the local and remote output vectors. Different from previously distributed observers for interconnected systems where the local and remote output vectors are updated continuously, the one in this article uses only information on the local and remote output vectors updating at triggering instants of proposed event‐triggered mechanisms. This indicates that the proposed method in this article is better than the existing ones in saving communication resources while still keeping an acceptable estimation performance. Sufficient conditions for the existence of the proposed distributed observers are established and are formed in a convex optimization problem which can be easily solved by using the MATLAB LMI Control Toolbox. Finally, a numerical example is given to confirm the effectiveness and advantages of the proposed method.

An estimation method for sensor faults based on observer in interconnected systems.

In this research, a class of nonlinear interconnected systems with sensor faults were investigated and an estimation method was proposed for system sensor faults based on the theory of system state reconstruction. Considering sensor fault vectors in nonlinear interconnected systems, this method constructed a generalized nonlinear interconnected system, whose state was designed by augmenting the original system state and fault vectors, which provides a foundation for fault estimation of nonlinear interconnected systems. An augmented observer was developed by equivalent transformation of generalized interconnected system, so as to realize robust estimations of sensor faults in interconnected systems. This estimation method took into account the effect of external disturbance of the system on fault estimation and estimated the convergence speed of error system; the developed method also considered the convenience of solving the gain matrix of the augmented observer, which was beneficial to the realization of sensor fault estimation in interconnected system. The sensor estimation method proposed in the paper has the advantages of robustness in fault estimation,rapidity in error convergence, and convenience in solving the gain matrix. Finally, the state and sensor fault estimation errors of two interconnected systems can both approach 0 within 10 seconds, thus achieving the purpose of fault estimation. Two simulation experiments verified the effectiveness of the proposed fault estimation method and provided a reference for the fault estimation method of nonlinear interconnected systems with disturbance.

Attack-resilient fault detection for interconnected systems under DoS attack

In light of the expanding cyber-space applications, the imperative consideration of cyber-attack ramifications on system security is evident. This paper presents a resilient dynamic event-triggered fault detection scheme for a class of nonlinear interconnected systems subjected to denial of service (DoS) attacks. To counteract multifaceted threats, the co-design challenge involving switched-type fault detection filters and a resilient dynamic event-triggered transmission mechanism is addressed. In the design phase of the filters, the frequency information of the signal is considered comprehensively and linear solvable conditions ensuring desired augment system performance are delineated. Through a series of comparative simulation experiments, the findings support the conclusion that the proposed attack-tolerant fault detection mechanism not only conserves network resources but also demonstrates superior detection capabilities for specific frequency fault signals.

Decentralised controller design for robust stabilisation and L 2 gain of nonlinear interconnected systems

In this paper, a decentralised controller is extended for robust stabilisation and L 2 gain analysis of a class of nonlinear interconnected systems via dynamic output feedback control within the LMI framework. This large-scale system is composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. An LMI approach is sufficiently proposed as a feasibility problem of a BMI with respect to controller gains via dynamic output feedback structure. An example of inverted pendulums is used to illustrate the applicability of extended approach.

Actuator fault detection and isolation in a class of nonlinear interconnected systems

In this paper, the problem of actuator fault detection and isolation is investigated for a class of nonlinear interconnected large-scale systems with modelling uncertainty and measurement noise, where each subsystem can have multiple inputs and multiple outputs (MIMO). The main contribution of this work is the derivation of a scheme that is able to diagnose single or multiple actuator faults in one or multiple subsystems. Each subsystem is monitored by a local diagnosis agent which contains the actuator fault detection module and the isolation module. The detection threshold in the fault detection module is generated through the use of a novel filtering technique, while the fault isolation module is realised by applying a reasoning-based decision logic based on a fault signature matrix. Fault propagation among subsystems is investigated and the results obtained allow for the identification of the subsystems that contain the faulty actuators. Finally, the effectiveness of the proposed actuator fault diagnosis method is demonstrated through a simulation example.

Observer‐based event‐triggered distributed model predictive control for a class of nonlinear interconnected systems

AbstractIn this paper, an observer‐based event‐triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event‐triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event‐triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed‐loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.

Event-Triggered Learning-Based Fault Accommodation for a Class of Nonlinear Interconnected Systems.

In this article, a distributed learning-based fault accommodation scheme is proposed for a class of nonlinear interconnected systems under event-triggered communication of control and measurement signals. Process faults occurring in the local dynamics and/or propagated from interconnected neighboring subsystems are considered. An event-triggered nominal control law is used for each subsystem before detecting any fault occurrence in its dynamics. After fault detection, the corresponding event-triggered fault accommodation law is utilized to reconfigure the nominal control law with a neural-network-based adaptive learning scheme employed to estimate an ideal fault-tolerant control function online. Under the asynchronous controller reconfiguration mechanism for each subsystem, the closed-loop stability of the interconnected systems in different operating modes with the proposed event-triggered learning-based fault accommodation scheme is rigorously analyzed with the explicit stabilization condition and state upper bound derived in terms of event-triggering parameters, and the Zeno behavior is shown to be excluded. An interconnected inverted pendulum system is used to illustrate the proposed fault accommodation scheme.

Quantized-output-feedback practical prescribed-time design strategy for decentralized tracking of a class of interconnected nonlinear systems with unknown interaction delays

This paper proposes a decentralized practical prescribed-time (PT) tracking design using quantized output feedback (QOF) for uncertain interconnected lower-triangular systems with unknown time-delay interconnections. The local output signals are assumed to be only measured and quantized for the PT tracker design under a band-limited network. By employing a PT-dependent scaling function, a decentralized memoryless PT observer based on quantized local outputs is developed to estimate local unmeasurable state variables. Owing to output quantization, the available output feedback signals become discontinuous. As a result, the tracking error between the actual (i.e., unquantized) local output and the local desired signal cannot be utilized in the local virtual controller. To address this issue, a novel adaptive compensation mechanism is derived to design the local PT neural network tracking laws using only quantized local outputs and estimated states. The proposed PT tracking controller does not require information on the interconnected nonlinear functions and interaction delays. During the Lyapunov stability analysis, the boundary layer error decomposition approach is employed to address the issue of non-differentiability in the local virtual control laws. The proposed QOF control system achieves practical PT stability. It is shown that the settling time of local tracking errors can be predetermined, regardless of the design parameters and initial conditions. Finally, the proposed QOF decentralization strategy is supported with illustrative examples and a comparison to demonstrate its benefits.

Decentralized Dynamic Event-Triggered Output Feedback Adaptive Fixed-Time Funnel Control for Interconnection Nonlinear systems.

A decentralized dynamic event-triggered output feedback adaptive fixed-time (DDETOFAFxT) funnel controller is described for a class of interconnected nonlinear systems (INSs). A novel dynamic event-triggered mechanism is designed, which includes a triggering control input, fixed threshold, decreasing function of tracking error, and a dynamic variable. To obtain the unknown states, a decentralized linear filter is designed. By introducing a prescribed funnel and using an adding a power integrator technique and a neural network method, a DDETOFAFxT funnel controller is designed to obtain better tracking performance and effectively alleviate the computational burden. Furthermore, it is ensured that the tracking error falls into a preset performance funnel. A simulation example is presented to demonstrate the availability of the designed control scheme.

Decentralized finite-time adaptive neural FTC with unknown powers and input constraints

This paper investigates the finite-time tracking problem of a class of nonlinear interconnected systems, where each subsystem not only is subject to actuator faults but also has unknown system input powers. Based on Lyapunov stability theory and decentralized control method, a novel finite-time adaptive fault-tolerant control (FTC) scheme is proposed such that each tracking error can converge to a small neighborhood of the origin in finite time. Different from the existing works on interconnected systems where the system input powers are assumed to be known and equal to one, the general case where the powers are unknown and larger than one is investigated in this work. Furthermore, input constraints are also applied to avoid actuator damage caused by control signal overshoot and jittering in this work. From theoretical analysis, each tracking error is proven to converge to a small neighborhood of the origin in finite time. Finally, a numerical example is given to demonstrate the validity of proposed control method.

Event‐ driven‐observer‐based adaptive distributed sliding mode fault compensation control for interconnected nonlinear systems

AbstractIn this paper, an event‐driven‐observer‐based distributed adaptive sliding mode fault compensation control method is presented for a class of nonlinear interconnected systems in the occurrence of actuator faults and disturbances. First, a novel event‐based estimator is designed to acquire the state, fault, and lumped disturbance information. Then, by utilizing the observer outputs, an adaptive tracking‐error‐based event condition is established, based on which a distributed sliding mode fault compensation controller is designed. In the proposed control framework, on the one hand, to enhance the robustness and tracking accuracy, two adaptive parameters are constructed; on the other hand, an adaptive event‐based control mechanism is integrated to save the transmission resources. The Zeno phenomenon avoidance performance is analyzed and, finally, the applications to an inverted pendulum system and a machine power system are given to verify the fault tolerance ability of the proposed method.

Design of distributed preview tracking controller for nonlinear interconnected systems with time‐delay

AbstractThe focus of this article is to design a distributed preview tracking controller for a class of nonlinear interconnected systems with time‐delay. By constructing the error systems with the information of previewable reference signal, and defining an performance index, the original preview tracking problem is converted into the control problem of the error system. Based on the relationship between the interconnection matrices and the input matrices, a distributed controller using not only the local state vector information but also the interconnection term information is designed for the error systems. Under this controller, the closed‐loop error system is decoupled. With the help of Lyapunov‐Krasovskii functional, the sufficient conditions, the asymptotic stability of the closed‐loop error system with disturbance attenuation level, are established. The distributed preview tracking controller, which is composed of state feedback, integrator, and preview feedforward, is acquired by integrating the controller of the error system. The proposed preview controller is applied to the chemical reactor recycles system and double‐parallel inverted pendulum system. The simulation verify that this controller is very effective in improving the tracking performance.

Decentralized adaptive fault-tolerant control of interconnected systems with sensor faults

The paper considers a class of interconnected nonlinear systems with unknown sensor faults and uncertain interactions. Each subsystem is subject not only to the local sensor faults but also to the possible effects of faults from other subsystems through uncertain interactions. Both multiplicative and time-varying additive sensor faults are taken into consideration, which are allowed to be unknown. A decentralized adaptive fault-tolerant control (FTC) scheme has been established. To eliminate the effects of faults in the control loop, several auxiliary quantities are constructed wisely and estimated by the designed adaptive mechanism. A smooth function is proposed, by which the uncertain interactions can be compensated even if they are coupled with sensor faults. It is proved that, by using only the corrupted states, all the closed-loop signals are globally uniformly bounded, and the output tracking error converges into an adjustable residual set. Finally, simulation and comparison studies are presented to illustrate the effectiveness of the proposed scheme.

Fast fault detection for nonlinear interconnected systems via deterministic learning

In this paper, a fast fault detection scheme is developed for a class of nonlinear interconnected systems with output measurements. First, through combining an adaptive high gain observer with the deterministic learning theory, the system states and unknown dynamics are estimated simultaneously. However, large value of gain may let the estimator becomes noise sensitive. Thus, the observer structure is modified to avoid this issue. Second, by reusing the estimated knowledge which is stored in the constant radial basis function (RBF) neural networks, a bank of dynamic estimators are constructed. Then, the average [Formula: see text] norms of residuals are generated. The smallest residual principle is considered for decision-making in the detection phase. Third, the fault detection conditions and detection time are analyzed under the influence of observer gain. A simulation example is utilized to illustrate the effectiveness of this scheme.

Decentralized adaptive tracking control for a class of interconnected nonlinear systems via dynamic high‐gain technique

AbstractIn this article, the problem of decentralized adaptive tracking control for a class of interconnected nonlinear systems is investigated, in which the interconnection term in each subsystem is related to the states of all subsystems. By utilizing the backstepping controller design method and dynamic high‐gain technique, two kinds of decentralized adaptive control schemes are developed. Some dynamic parameters are introduced into the controllers to counteract the effects of interactions among subsystems. Moreover, with the aid of graph theory, it is shown that all signals of the closed‐loop system are bounded. The novelty of the proposed method lies in that the tracking accuracy of each subsystem can be preset without adjusting the controller parameters. Finally, two illustrative examples are presented to demonstrate the efficiency of the proposed schemes.

Distributed observer design for interconnected nonlinear systems with faults and disturbances based on dynamic event conditions

AbstractThis study investigated the observer design schemes for interconnected nonlinear systems with actuator faults, sensor faults, external disturbances, and limited measured resources. A novel effective distributed estimation scheme is presented for the interconnected nonlinear system to estimate the states, faults, and lumped disturbances, simultaneously. To save communication resources and to improve information utilization, an adaptive event condition is designed in the sensor channel, and the triggered values are utilized to design the observer. Especially, to handle the sensor fault, the output is separated into two parts, and the estimation is realized with the help of a normal one. In the first part of this study, a class of interconnected nonlinear systems with partial loss of effectiveness of sensor fault is considered, and an event‐based distributed estimation scheme is established. In the second part, a class of more universal feedback interconnected nonlinear with both partial loss sensor fault and bias sensor fault is investigated. An augment system is formulated by an augmented vector composed of state and sensor faults. And then the estimation scheme is realized by utilizing the presented event‐based distributed observer. The convergence abilities of both the two conditions are proved and, finally, the estimation performances of the presented observer are verified by a numerical simulation system and an inverted pendulum system.

A predefined time decentralized adaptive tracking control method for interconnected nonlinear systems

SummaryIn this paper, the problem of predefined time adaptive decentralized tracking control for a class of interconnected nonlinear systems is investigated. Firstly, a time‐varying constraint function is introduced to convert the tracking control problem into one with a constraint on tracking error, which can successfully remove the restriction of initial conditions. Secondly, the asymmetric constraint requirements on tracking error are achieved via defining a novel coordinate transformation function. Then, based on the proposed constraint function and the backstepping method, a decentralized adaptive controller is constructed. Furthermore, it is proved that all signals of the closed‐loop system are globally uniformly ultimately bounded (GUUB) via Lyapunov stability theory. Finally, the effectiveness of the proposed scheme is confirmed by two simulation examples.

Extended dissipative filter design for discrete-time interconnected fuzzy systems with time-varying delays subject to cyber attacks

This article addresses the problem of extended dissipative filtering design for the class of nonlinear interconnected systems with time-varying delays under the cyber attacks. The dynamics of proposed interconnected systems (ISs) is modeled by the Takagi-Sugeno fuzzy (TSF) IF-THEN rules. The relevant practical model is used to describe the network connectivity between the plant and the filter. In addition, to develop the filter for nonlinear systems in more practical sense, the sensor delays and the influence of cyber attacks are taken into account during the signal transmission. In order to verify that the developed closed-loop system is asymptotically stable with extended dissipative, sufficient conditions are derived by constructing the delay-dependent Lyapunov-Krasovskii functional (LKF) and employing the summation inequalities through the linear matrix inequalities (LMIs) approach. The outcomes of theoretical results can be used to analyze the various performances like H∞ performance, (Υ1,Υ2,R)−α−dissipativity, passivity, mixed H∞/passivity, and l2−l∞ performance in a single framework. At last, a numerical example is presented to demonstrate the proposed method and to validate the theoretical findings in a practical sense.

Neural network‐based decentralized adaptive fault‐tolerant control for a class of nonlinear interconnected systems with unknown input powers

SummaryThis article studies the output tracking control for a class of interconnected nonlinear systems with actuator faults, where each subsystem has unknown powers. Based on Lyapunov stability theory, a neural‐network‐based decentralized adaptive fault‐tolerant control scheme is proposed so that each tracking error can be constricted in a small adjustable neighborhood of the origin. In existing results, interconnections and actuator bias faults have been addressed. But the systems' input powers are required to be a known positive integer and preferably one. So in our article, we relax the restrictions and consider more general systems whose input powers are extended to larger than one and unknown at the same time. Finally, two numerical simulation examples are shown to explain the validity of control strategy proposed in our article.

Finite-time boundedness and finite-time stabilization boundedness for nonlinear interconnected systems with Atangana–Baleanu–Caputo fractional derivative

In this paper, we consider the finite-time boundedness (FTB) and finite-time stabilization boundedness (FTSB) problems for a class of nonlinear interconnected systems with Atangana–Baleanu–Caputo (ABC) fractional derivative. By employing the FTB theory and some properties of ABC fractional derivative, and some basic mathematical transformations, we derive new conditions for the FTB and FTSB problems of ABC fractional-order nonlinear interconnected systems. These conditions are formed in linear matrix inequalities (LMIs), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, two numerical examples with simulations are provided to illustrate the efficiency of the proposed method.