Uncertain Nonlinear Large-scale Systems Research Articles

A dual-gain scaling approach to event-triggered adaptive tracking for large-scale nonlinear systems via output feedback

A novel non-backstepping output feedback control approach, called as the dual-gain scaling approach, is proposed by combining the extended Lyapunov matrix inequalities with dual-domination idea. This approach provides partially decentralised adaptive output feedback controllers with three event-triggered mechanisms to achieve the global practical tracking of a family of uncertain large-scale nonlinear systems subject to unknown control coefficients and strongly interconnected nonlinearities with output-polynomial growth rate. The dual gains are embedded in the observers and controllers, which can effectively compensate for time-varying control coefficients and unknown constant growth rate multiplied by output-polynomial function. Three different threshold schemes including fixed threshold, relative threshold and time-varying threshold are introduced to save communication resources. The stability analysis shows that the solutions of the closed-loop system are globally uniformly bounded and the tracking error converges to a preset compact set after a finite time; also, there will be no zeno behaviour in the closed-loop response.

Adaptive Decentralized Finite-Time Fuzzy Secure Control for Uncertain Nonlinear CPSs Under Deception Attacks

This article addresses the adaptive secure control problem for a class of uncertain nonlinear large-scale cyber-physical systems (CPSs) subjected to deception attacks. Specifically, a novel adaptive fuzzy control scheme for each subsystem of CPSs is designed to mitigate the effects of cyber-attacks that intentionally tamper with control signals from controllers to actuators and the state signals from sensors to controllers, and a Nussbaum function is proposed to tackle unknown time-varying control directions. Moreover, a finite-time converging secure control scheme is designed for compromised CPSs to guarantee all the states converge to a predetermined small set in finite time. It is shown that with the proposed control scheme, all the signals of the closed-loop system are proved to be semi-globally bounded. Two simulation examples are provided to illustrate the effectiveness of the proposed secure control method.

Feasibility Conditions-Free Prescribed Performance Decentralized Fault-Tolerant Neural Control of Constrained Large-Scale Systems

This article investigates the command filter-based decentralized prescribed performance adaptive fault-tolerant compensation control strategy for uncertain nonlinear large-scale systems subject to asymmetric time-varying full-state constraints. Via integrating the performance function with command filter-based backstepping technique, the prescribed performance control problem is addressed, under which the complexity of controller design is reduced. Under the prescribed performance control framework, the nonlinear transformed function is constructed so as to ensure that the asymmetric time-varying full-state constraints free from feasibility conditions imposed on virtual control signals are not violated. Besides, the effect of infinite number of time-varying actuator faults is compensated with the aid of projection adaption design. Furthermore, based on the piecewise Lyapunov function analysis, it is rigorously testified that entire involved signals are bounded, desired constraints are not breached and tracking errors within the predefined domains. Finally, the effective performances of the developed control algorithm are confirmed by some simulation results.

Output-Feedback Prescribed Performance Decentralized Controller for Interconnected Large-Scale Uncertain Nonlinear Systems With Unknown Input Gain Sign

A novel decentralized output-feedback controller is proposed in this paper for large-scale uncertain general nonautonomous nonlinear systems without prior knowledge of the input gain’s sign. The subsystems are considered to be completely unknown and nonautonomous, except for their known full relative degree. The proposed controller uses a higher-order switching differentiator to estimate the time-derivatives of the output tracking error, resulting in a low-complexity output-feedback prescribed performance controller that compensates for uncertainties, including high-frequency gain sign and unstructured uncertainties. It is mathematically proven that the output tracking error and its time-derivatives are all maintained within the prescribed regions. To demonstrate the effectiveness of the proposed controller, numerical simulations of two interconnected inverted pendulums are conducted. To the best of the authors’ knowledge, this paper presents the first results on this problem.

Decentralized Adaptive Funnel Control of Uncertain Large-Scale Interconnected Nonlinear System

In this paper, a decentralized adaptive funnel control for a class of uncertain large-scale nonlinear systems is studied. By using a new funnel control method with a barrier Lyapunov function, a new adaptive decentralized funnel controller is recursively constructed to achieve output tracking of given transient behavior. To solve the interconnection terms issues in controller design, an auxiliary nonlinear function is introduced. Meanwhile, dynamic surface control is applied to the backstepping design in order to avoid the “explosion of complexity” problems in backstepping procedure. It is demonstrated that the proposed control scheme proves that all signals of the closed-loop system are bounded and that the tracking error always evolves in the funnel. Finally, the effectiveness of the scheme is verified by a numerical example and a third-order power network system model.

Event-based adaptive fuzzy fixed-time control for nonlinear interconnected systems with non-affine nonlinear faults

This article studies the event-based adaptive practical fixed-time decentralized control problem for a class of large-scale uncertain nonlinear systems subject to non-affine nonlinear faults. By fusing the techniques of fixed-time control and command filter, the problems such as singular-value and computational explosion in fixed-time control based on backstepping design framework are solved. Based on the fuzzy approximation theory and Butterworth low-pass filter (BLPF) technique, the non-affine nonlinear fault terms are processed and fault-tolerant controllers are designed to realize fault compensation. In order to relieve the communication the pressure between system components, a novel switching event-triggering mechanism (SETM) based on user-set threshold parameters is proposed. This switching threshold design the scheme combines the advantages of the traditional fixed threshold and relative threshold design strategies, providing greater flexibility in balancing system performance and network constraints. By combining the practical fixed-time stability criterion with the Lyapunov stability theory, it is demonstrated that both the tracking performance and the closed-loop stability can be ensured in a fixed-time. Finally, two simulation examples are given to verify the effectiveness of the proposed fixed-time switching event-triggered control (SETC) scheme.

Command filter-based event-triggered adaptive fixed-time output-feedback control for large-scale nonlinear systems

This paper studies the issue of event-triggered adaptive fixed-time control for uncertain large-scale nonlinear systems. A state observer is employed to estimate unknown states. By combining the technologies of command filter and backstepping control, a command filtered-based fixed-time adaptive control approach is proposed, which can cope with the issue of ‘complexity explosion’ in the backstepping design scheme. Meanwhile, a novel continuous hyperbolic tangent function is designed to handle the difficulty of fixed-time stability analysis with output-feedback control form, where two types of observer errors are needed in the designed Lyapunov function to achieve the fixed-time stability. Further, based on the event-triggered strategy, an event-triggered fixed-time adaptive controller is designed. Based on Lyapunov stability theory, it is proven that all signals of the closed-loop system are bounded. Finally, the effectiveness of the presented approach is validated by a simulation.

Privatized Distributed Anomaly Detection for Large-Scale Nonlinear Uncertain Systems

In this article two limitations in current distributed model based approaches for anomaly detection in large-scale uncertain nonlinear systems are addressed. The first limitation regards the high conservativeness of deterministic detection thresholds, against which a novel family of set-based thresholds is proposed. Such set-based thresholds are defined in a way to guarantee robustness in a user-defined probabilistic sense, rather than a deterministic sense. They are obtained by solving a chance-constrained optimization problem, thanks to a randomization technique based on the Scenario Approach. The second limitation regards the requirement, in distributed anomaly detection architectures, for different parties to regularly communicate local measurements. In settings where these parties want to preserve their privacy, communication may be undesirable. In order to preserve privacy and still allow for distributed detection to be implemented, a novel privacy-preserving mechanism is proposed and a so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">privatized communication</i> protocol is introduced. Theoretical guarantees on the achievable level of privacy, along with a characterization of the robustness properties of the proposed distributed threshold set design, taking into account the privatized communication scheme, are provided. Finally, simulation studies are included to illustrate our theoretical developments.

Reliable Fault Detection and Diagnosis of Large-Scale Nonlinear Uncertain Systems Using Interval Reduced Kernel PLS

Kernel partial least squares (KPLS) models are widely used as nonlinear data-driven methods for faults detection (FD) in industrial processes. However, KPLS models lead to irrelevant performance over long operation periods due to process parameters changes, errors and uncertainties associated with measurements. Therefore, in this paper, two different interval reduced KPLS (IRKPLS) models are developed for monitoring large scale nonlinear uncertain systems. The proposed IRKPLS models present an interval versions of the classical KPLS model. The two proposed IRKPLS models are based on the Euclidean distance between interval-valued observations as a dissimilarity metric to keep only the more relevant and informative samples. The first proposed IRKPLS technique uses the centers and ranges of intervals to estimate the interval model, while the second one is based on the upper and lower bounds of intervals for model identification. These obtained models are used to evaluate the monitored interval residuals. The aforementioned interval residuals are fed to the generalized likelihood ratio test (GLRT) chart to detect the faults. In addition to considering the uncertainties in the input-output systems, the new IRKPLS-based GLRT techniques aim to decrease the execution time when ensuring the fault detection performance. The developed IRKPLS-based GLRT approaches are evaluated across various faults of the well-known Tennessee Eastman (TE) process. The performance of the proposed IRKPLS-based GLRT methods is evaluated in terms of missed detection rate, false alarms rate, and execution time. The obtained results demonstrate the efficiency of the proposed approaches, compared with the classical interval KPLS.

Observer-Based Adaptive Fuzzy Decentralized Control of Uncertain Large-Scale Nonlinear Systems with Full State Constraints

In this paper, the problem of observer-based adaptive fuzzy decentralized control is studied for uncertain large-scale nonlinear systems with full state constraints, input saturation and unmeasurable state. Compared with the existing literature, the state directly measurable problem is relaxed, and the systems with full state constraints and input saturation problem are further considered. In order to solve the controller design difficulties caused by input saturation and state constraints, the auxiliary design functions and the barrier Lyapunov functions are employed, respectively. By utilizing adaptive backstepping technique and Lyapunov stability theorem, an observer-based adaptive fuzzy decentralized control approach is developed. It is proved that all the signals of the closed-loop systems are semi-globally uniformly ultimately bounded and the observer errors are converged on a small neighborhood of the origin. The tracking errors are remained in the bounded compact set, and the full state constraints are not violated. Two practical examples are given to demonstrate the usefulness of the proposed control scheme.

Adaptive Dynamic Programming for Decentralized Stabilization of Uncertain Nonlinear Large-Scale Systems With Mismatched Interconnections

This paper presents a novel decentralized control strategy for a class of uncertain nonlinear large-scale systems with mismatched interconnections. First, it is shown that the decentralized controller for the overall system can be represented by an array of optimal control policies of auxiliary subsystems. Then, within the framework of adaptive dynamic programming, a simultaneous policy iteration (SPI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations associated with auxiliary subsystem optimal control policies. The convergence of the SPI algorithm is guaranteed by an equivalence relationship. To implement the present SPI algorithm, actor and critic neural networks are applied to approximate the optimal control policies and the optimal value functions, respectively. Meanwhile, both the least squares method and the Monte Carlo integration technique are employed to derive the unknown weight parameters. Furthermore, by using Lyapunov’s direct method, the overall system with the obtained decentralized controller is proved to be asymptotically stable. Finally, the effectiveness of the proposed decentralized control scheme is illustrated via simulations for nonlinear plants and unstable power systems.

Finite-Time Filter Decentralized Control for Nonstrict-Feedback Nonlinear Large-Scale Systems

This paper solves the finite-time decentralized control problem for uncertain nonlinear large-scale systems in nonstrict-feedback form. The considered controlled plants are different from the previous results of finite-time control systems, which are the nonstrict-feedback large-scale systems with the unknown functions consisting of all states, interactions, and immeasurable states. Fuzzy logic systems and a filter-based state observer are utilized to model uncertain systems and deal with the immeasurable states, respectively. By combining the backstepping recursive design with Lyapunov function theory, a finite-time adaptive fuzzy decentralized control approach is raised. It is testified that the developed control strategy can guarantee that the closed-loop signals are bounded, and the outputs of systems have satisfactory tracking performance in a finite time. A quadruple-tank process system is given to testify the effectiveness and applicability of the proposed approach.

Differentially-Private Distributed Fault Diagnosis for Large-Scale Nonlinear Uncertain Systems

Distributed fault diagnosis has been proposed as an effective technique for monitoring large scale, nonlinear and uncertain systems. It is based on the decomposition of the large scale system into a number of interconnected subsystems, each one monitored by a dedicated Local Fault Detector (LFD). Neighboring LFDs, in order to successfully account for subsystems interconnection, are thus required to communicate with each other some of the measurements from their subsystems. Anyway, such communication may expose private information of a given subsystem, such as its local input. To avoid this problem, we propose here to use differential privacy to pre-process data before transmission.

Cascade Training Multilayer Fuzzy Model for Nonlinear Uncertain System Identification Optimized by Differential Evolution Algorithm

This paper proposes a new cascade training multilayer fuzzy logic for identifying forward model of multiple-inputs multiple-outputs (MIMO) nonlinear double-coupled fluid tank system based on experiment platform. The novel multilayer fuzzy model consists of multiple MISO model; for each MISO model, it composes of multiple single fuzzy Takagi–Sugeno (T–S) models. The cascade training using optimization algorithms optimally trained multilayer fuzzy model one by one. All parameters of multilayer fuzzy model were optimally and comparatively identified using DE, GA and PSO optimization algorithms. Then, the proposed method results are compared with normal training method results. The experimental results show that proposed method gives better performance than the normal training. Hence, the novel proposed optimized multilayer fuzzy model is efficiently applied for identifying MISO system. The experiment cascade training is clearly presented. It proves more accurate and takes less time to compute than the normal training, and it seems promisingly scalable as a simple and efficient method to successfully identify and control various uncertain nonlinear large-scale MIMO systems.

Decentralized adaptive fuzzy control for nonlinear large-scale systems with random packet dropouts, sensor delays and nonlinearities

This paper investigates the adaptive fuzzy decentralized control problem for a class of uncertain nonlinear large-scale systems. Different from the conventional backstepping-based adaptive output feedback control technique, the output measurements are imperfect and considered to suffer random packet dropouts (RPDs), random sensor delays (RSDs) and random sensor nonlinearities (RSNs), which result typically from a network environment such as sensor networks. A novel sensor model is established for describing the random phenomena within a unified representation by introducing a multi-Markovian variable. Based on this sensor model, two main difficulties arise: first is that the system output cannot be used directly for controller design due to the randomly occurring phenomena; second is how to deal with the complex nonlinear stochastic terms with unknown interconnections, unknown time-varying delays and unknown sensor nonlinearities entangled together. With the help of new coordinate transformations and mean value theorem, by using appropriate Lyapunov–Krasovskii functionals, a new adaptive decentralized memoryless output feedback controller is designed. It is proved that the constructed controller ensures the boundedness in probability of all the closed-loop signals in presence of RPDs, RSDs and RSNs. The simulation results are presented to show the effectiveness of the proposed scheme.

Low-complexity differentiator-based decentralized fault-tolerant control of uncertain large-scale nonlinear systems with unknown dead zone

This paper investigates a low-complexity robust decentralized fault-tolerant prescribed performance control scheme for uncertain larger-scale nonlinear systems with consideration of the unknown nonlinearity, actuator failures, dead-zone input, and external disturbance. Firstly, a new simple finite-time-convergent differentiator is developed to obtain the unmeasurable state variables with arbitrary accuracy. Then, a time-varying sliding manifold involving the output tracking error and its high-order derivatives is constructed to tackle the high-order dynamics of subsystems. Sequentially, a robust decentralized fault-tolerant control scheme is proposed for each sliding manifold with prescribed convergence rate. The prominent advantage of the proposed fault-tolerant control scheme is that any specialized approximation technique, disturbance observer, and recursive procedure of backstepping technique are avoided, which dramatically alleviates the complexity of controller design. Finally, two groups of illustrative examples are employed to demonstrate the effectiveness of the low-complexity decentralized fault-tolerant control scheme under the developed finite-time-convergent differentiator.

Adaptive Fuzzy Decentralized Control for a Class of Large-Scale Nonlinear Systems With Actuator Faults and Unknown Dead Zones

This paper studies the fault-tolerant control problem for a class of uncertain large-scale nonlinear systems with unknown dead zones and actuator failures, including outage, loss of effectiveness, and stuck. It is assumed that the lower and upper bounds of actuator efficiency factor, the unparametrizable time-varying stuck fault, the system coefficient, and the uncertain functions of our considered systems are unknown. By introducing a smooth function, fuzzy logic systems and a bound estimation approach, a decentralized backstepping design method of fault-tolerant tracking controller is developed for the systems under consideration. The proposed controller can compensate the effects of actuator faults and dead zones completely. It is proved that all the signals in the closed-loop systems are ultimately bounded, and the tracking control performance can be achieved by the proposed controller. In comparing with the existing results, the restrictions on the number of failures are removed and the stuck fault is allowed to be time-varying. Finally, simulation results show the efficiency of the proposed control scheme.

Decentralized Adaptive Neural Output-Feedback DSC for Switched Large-Scale Nonlinear Systems

In this paper, for a class of switched large-scale uncertain nonlinear systems with unknown control coefficients and unmeasurable states, a switched-dynamic-surface-based decentralized adaptive neural output-feedback control approach is developed. The approach proposed extends the classical dynamic surface control (DSC) technique for nonswitched version to switched version by designing switched first-order filters, which overcomes the problem of multiple "explosion of complexity." Also, a dual common coordinates transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme. Nussbaum-type functions are utilized to handle the unknown control coefficients, and a switched neural network observer is constructed to estimate the unmeasurable states. Combining with the average dwell time method and backstepping and the DSC technique, decentralized adaptive neural controllers of subsystems are explicitly designed. It is proved that the approach provided can guarantee the semiglobal uniformly ultimately boundedness for all the signals in the closed-loop system under a class of switching signals with average dwell time, and the tracking errors to a small neighborhood of the origin. A two inverted pendulums system is provided to demonstrate the effectiveness of the method proposed.

Adaptive decentralized fault-tolerant tracking control of a class of uncertain large-scale nonlinear systems with actuator faults

We are concerned with the fault-tolerant tracking control affair for a class of large-scale multi-input and multi-output (MIMO) nonlinear systems suffering from actuator failures. Taking advantage of the mean-value theory and the implicit function theorem, the non-affine subsystems are transformed into affine forms. Neural networks (NNs) are utilized to approximate unknown virtual control signals, and then an adaptive NN-based decentralized tracking control strategy is exploited recursively by combining backstepping methods as well as the dynamic surface control (DSC) methodology. In theory, the stability of the resulting whole system is rigorously analysed, where it is proven that all signals remain uniformly ultimately bounded (UUB) and the designed strategy can guarantee the convergence of tracking errors via a suitable choice of control parameters. Finally, two simulation examples, both practical and numerical examples, are illustrated to verify the feasibility of the theoretical claims.

Adaptive fuzzy output constrained decentralized control for switched nonlinear large-scale systems with unknown dead zones

In this paper, an adaptive fuzzy output-feedback control design with output constrained is investigated for a class of switched uncertain nonlinear large-scale systems with unknown dead zones and immeasurable states. Based on dynamic surface backstepping control design technique and incorporated by the average dwell time method and the prescribed performance theory, a new adaptive fuzzy output-feedback control method is developed. It is strictly proved that the resulting closed-loop system is stable in the sense of uniformly ultimately boundedness and both transient and steady-state performances of the outputs are preserved. Comparison simulation studies illustrate the effectiveness of the proposed approach.