Large-scale Interconnected Nonlinear Systems Research Articles

Decentralized fuzzy DSC for uncertain large-scale interconnected switched systems in non-strict feedback form with input saturation

This paper demonstrates a fuzzy decentralized dynamic surface control (DSC) scheme for switched large-scale interconnected nonlinear systems under arbitrary switching, which contains non-strict feedback form and unknown input saturation uncertainties. An auxiliary design system is established to handled input saturation. Uncertainties of non-strict feedback form are learned by fuzzy logic systems (FLSs) approximators, DSC method is designed to conquer “explosion of complexity” inherented by repeated differential of virtute controller in backstepping approach. Ii is shown that based on common Lyapunov function (CLF) design and analysis scheme, all the closed-loop systems signals are uniformly ultimately bounded (UUB), simulation results are provided to demonstrate the effectiveness of this proposed strategy.

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.

Adaptive backstepping control for nonlinear interconnected systems with prespecified-performance-driven output triggering

This paper considers a class of nonlinear large-scale interconnected systems and proposes an event-triggered decentralized controller by using adaptive output feedback backstepping. To save the communication resource, the output measurements are transmitted to the controller based on a novel double-events-triggered (DET) mechanism driven by transient performance request. Due to the use of triggered mechanism, only discontinuous output signals can be utilized such that the derived virtual controls are discontinuous, of which the derivatives cannot be computed as often done in standard backstepping design procedure. To overcome this difficulty, a new error signal decomposition and compensation mechanism is proposed to quantify and compensate for the difference between the virtual controls derived by using the event-triggered measurement signals and the real-time system outputs. Through a nonsmooth stability analysis where the closed-loop stability is considered under different conditions of output data transmissions, it is shown that the tracking error remains within a prespecified performance bound all the time. In contrast to the existing backstepping results addressing event-triggered outputs, the designed DET mechanism does not require the virtual control signals to be reversely transmitted to the sensor side from the controller side and guarantees the communication burden can be reduced under tracking performance guarantees.

Decentralized adaptive neural safe tracking control for nonlinear systems with conflicted output constraints

The issue of decentralized adaptive safe tracking control for interconnected large-scale nonlinear systems (ILSNSs) with conflicted output constraints is discussed in this paper. By “conflicted output constraints”, we mean that the output constraint functions conflict with reference signal, i.e., the reference signal is not completely constrained within the constraint range. In existing methods, it is always assumed that the reference signal is constrained within the constraint region. In practice, the constraints may be detected during system operation and conflict with the reference signal given in advance. In this particular case, the existing methods based on barrier Lyapunov function (BLF) or nonlinear transformation function (NTF) are invalid. From a new point of view, this article designs a new safety reference signal (SRS) which is completely restricted within the constraint range by using the boundary protection approach. Meanwhile, a prescribed performance function which can arbitrarily define the convergence time and tracking accuracy is introduced so that the system output can better track the SRS. Then, combining backstepping technique and radial basis function neural network (RBFNN), a new controller is constructed, under which a desired tracking trajectory can be obtained under the premise of ensuring safety performance. Furthermore, by adding a dynamic event triggering mechanism (DETM) between the actuator and the plant, the communication burden is effectively reduced. Simulation results verify the scheme developed.

A Cyclic-Small-Gain-Based Adaptive Fuzzy Control of Interconnected Systems

This article investigates a novel adaptive fuzzy decentralized output-feedback control method for a class of uncertain large-scale interconnected nonlinear systems with unknown dynamics and immeasurable states. By employing fuzzy logic systems, the unknown nonlinear dynamics are estimated. Moreover, the immeasurable states are approximated by constructing a fuzzy decentralized state observer. Based on the Lyapunov stability theory and decentralized backstepping technique, the Lyapunov functions are constructed in a recursive way for each subsystem. In the last step of our process, an overall Lyapunov function is proposed to realize the control objective. Differing from other works, the interconnection influence of the large-scale system is compensated with a more relaxed assumption by introducing the cyclic-small-gain condition. Under the proposed control method, the closed-loop system is capable of being semiglobally uniformly ultimately bounded. Furthermore, the observer and stabilizing errors are able to be bounded by an arbitrarily small residual set around the origin. Finally, a simulation with comparison is provided to illustrate the viability of the presented control scheme.

Unknown Input Observer-Based Decentralized PID- BFO Algorithm for Interconnected Systems Against Fault Actuator

This article presents a decentralized controller/observer for nonlinear large-scale interconnected systems with actuator fault. The proposal integrates a robust proportional-integral-derivative (PID) controller with the unknown input observer (UIO) to achieve closed-loop robustness against the interactions and the actuator faults. In this scheme, the PID controller is tuned using the Bacterial foraging optimization algorithm (BFO) algorithm. On the other hand, the unknown input observer can diagnose the actuator faults from the controller input. A numerical example consisting of two subsystems is adopted to clarify the effectiveness of the suggested method with a guarantee that the state estimation error is asymptotically converged to zero. The actuator faults have been added to the second subsystem, keeping the first subsystem free of fault. The simulation results demonstrated the influence of the interactions between subsystems, verifying that the unknown input observer can detect the actuator faults despite the presence of these interactions between the subsystems. Index Terms—Fault Diagnosis (FD), Unknown Input Observer (UIO), Proportional- Integral- Derivative (PID), Bacterial Foraging Optimization (BFO).

Decentralized adaptive neural two-bit-triggered control for nonstrict-feedback nonlinear systems with actuator failures

This article studies the adaptive neural decentralized two-bit-triggered control problem for interconnected large-scale nonlinear systems in nonstrict-feedback forms (NFF) with actuator failures. Since actuator failures occur frequently in practical systems, it will affect the stability of the interconnected large-scale systems under consideration. Combining radial basis function neural networks (RBF NNs) and a command filter, an adaptive decentralized two-bit-triggered (TBT) control method based on backstepping recursive design is presented to deal with this problem. Different from the traditional event-triggered control, the problem of control signal transmission bit is further considered to save system transmission resources. The proposed control scheme can guarantee that all signals are bounded and have good tracking performance. Finally, two simulation examples are provided to verify the validity of the presented control scheme.

Decentralized robust control for T-S fuzzy bi-linear interconnected system

This paper presents decentralized fuzzy robust control for a class of nonlinear interconnected large-scale systems which is composed of a number of Takagi-Sugeno (T-S) fuzzy bilinear subsystems with interconnections. Based on the Lyapunov stability analysis theory and the parallel distribute compensation scheme, some robust stabilization sufficient conditions are derived for the whole close-loop fuzzy interconnected systems. The corresponding decentralized fuzzy controller design is converted into a convex optimization problem with linear matrix inequality (LMI) constraints.

Compositional stability criteria based on cyclically neutral supply conditions

In this paper we consider stability of large scale interconnected nonlinear systems that satisfy a strict dissipativity property in terms of local storage and supply functions. Existing compositional stability criteria certify global stability by constructing a global Lyapunov function as the (weighted) sum of local storage functions. We generalize these results by unifying spatial composition, i.e., (weighted) sum of local supply functions is neutral, with temporal composition, i.e., (weighted) sum of supply functions over a time cycle is neutral. Two benchmark examples illustrate the benefits of the developed compositional stability criteria in terms of reducing conservatism and constrained distributed stabilization.

Neural-network-based adaptive secure control for nonstrict-feedback nonlinear interconnected systems under DoS attacks

This paper investigates the problems of decentralized adaptive neural network (NN) secure control for a class of nonstrict-feedback nonlinear interconnected large-scale systems (NILSs) under denial-of-service (DoS) attacks. The considered systems contain not only unknown interconnected terms but also general nonlinear functions that are not required to be globally Lipschitz, in contrast to most of the existing results in the area. When the system subject to the DoS attack, the sampled data can neither be sent by the sensors nor received by the actuators due to the appearance of DoS in the sensor-to-controller (S-C) and the controller-to-actuator (C-A) communication channels. The data packets sent from the sensors are blocked and the traditional backstepping technology cannot be adopted. In order to solve this difficulty, a novel dynamic gain observer is constructed, which can obtain the desired states from the NILSs under DoS attacks. Considering the energy limitation of attackers, two reasonable Assumptions of DoS attack intensity are given. The stability is proven based on the Lyapunov stability theory (LST) and the improved average dwell time (ADT) method. The proposed controller guarantees that all signals in closed-loop systems are bounded, while the tracking error signals converge to a small residual set. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed control method.

Online [formula omitted] control for continuous-time nonlinear large-scale systems via single echo state network

In this article, the H∞ optimal control for nonlinear large-scale interconnected systems is designed using novel adaptive/approximate dynamic programming (ADP) method and single echo state network (ESN). All subsystems of the large-scale systems are combined into an augmented system. Subsequently, the H∞ problem is transformed into a zero-sum game problem, where a nonlinear partial differential Hamilton-Jacobi-Isaacs (HJI) equation is required to be solved. However, the HJI equation has no analytically solution, so this paper develops a novel online ADP algorithm to approximatively obtain the index function and control policy simultaneously employing single ESN without requiring the initial admissible control. The stability of the closed-loop augmented system and the ESN output weights is analyzed using the Lyapunov theorem and guaranteed to be uniformly ultimate boundedness (UUB). A large-scale system example including three subsystems is simulated to show the feasibility of the suggested control scheme.

Distributed model predictive control for nonlinear large-scale systems based on reduced-order cooperative optimisation

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems’ cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system.

Composite adaptive fuzzy decentralized tracking control for pure-feedback interconnected large-scale nonlinear systems

This paper focuses on a problem of composite adaptive fuzzy decentralized tracking control for a class of uncertain pure-feedback interconnected large-scale nonlinear systems with unmeasurable states. A fuzzy state observer is designed by using fuzzy logic systems; thus, the unmeasurable states of pure-feedback nonlinear systems are estimated based on the designed fuzzy state observer. A serial–parallel estimation model is designed by using the fuzzy state observer. To avoid the analytic computation, the command filters are employed to produce the command signals and their derivatives. The fuzzy adaptive laws are constructed by using prediction errors and compensating tracking errors. Finally, a controller is constructed by dynamic surface control technique. Through the proposed control method, all the signals in the closed-loop system are bounded, and the output of the system can track the given reference signal. The simulation studies verify the effectiveness of the proposed control method in this paper.

Finite-Time Adaptive Fuzzy Decentralized Control for Nonstrict-Feedback Nonlinear Systems With Output-Constraint

This paper addresses the finite time adaptive fuzzy decentralized control problem for interconnected large scale nonlinear systems in nonstrict feedback forms with output-constraint. The fuzzy logic systems are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable states. In order to deal with the output constraint problem, the barrier Lyapunov function is introduced. By combining backstepping recursion design with a command filter, a finite time fuzzy adaptive decentralized control method is presented. The stability analysis can be obtained based on the finite time Lyapunov stability theory, which demonstrates that the closed-loop system are semi-global practical finite-time stability, the system outputs can track the given reference signals and keep in the given constraint bounds in a finite time. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control scheme.

Decentralized Event-Triggered Online Adaptive Control of Unknown Large-Scale Systems Over Wireless Communication Networks.

In this article, a novel online decentralized event-triggered control scheme is proposed for a class of nonlinear interconnected large-scale systems subject to unknown internal system dynamics and interconnected terms. First, by designing a neural network-based identifier, the unknown internal dynamics of the interconnected systems is reconstructed. Then, the adaptive critic design method is used to learn the approximate optimal control policies in the context of event-triggered mechanism. Specifically, the event-based control processes of different subsystems are independent, asynchronous, and decentralized. That is, the decentralized event-triggering conditions and the controllers only rely on the local state information of the corresponding subsystems, which avoids the transmissions of the state information between the subsystems over the wireless communication networks. Then, with the help of Lyapunov's theorem, the states of the developed closed-loop control system and the critic weight estimation errors are proved to be uniformly ultimately bounded. Finally, the effectiveness and applicability of the event-based control method are verified by an illustrative numerical example and a practical example.

Adaptive Fuzzy Decentralized Tracking Control for Large-Scale Interconnected Nonlinear Networked Control Systems

This article investigates the problem of adaptive fuzzy decentralized tracking control design for a class of large-scale interconnected nonlinear systems with network-induced input time delay. First, fuzzy logic systems are used to approximate the unknown nonlinear functions. Then, a newly defined filtered error is introduced to compensate the network-induced delay, and a novel adaptive fuzzy decentralized control strategy is proposed to guarantee the uniform ultimate boundedness of the closed-loop nonlinear system. Finally, a simulation example is given to further demonstrate the effectiveness of the proposed method.

A Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite interval

This paper presents a Laguerre homotopy method for quadratic optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, the spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagin's maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from the literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency.

Dynamic output feedback control for nonlinear large-scale interconnected systems

Purpose This paper aims to focus on the design of a decentralized observation and control method for a class of large-scale systems characterized by nonlinear interconnected functions that are assumed to be uncertain but quadratically bounded. Design/methodology/approach Sufficient conditions, under which the designed control scheme can achieve the asymptotic stabilization of the augmented system, are developed within the Lyapunov theory in the framework of linear matrix inequalities (LMIs). Findings The derived LMIs are formulated under the form of an optimization problem whose resolution allows the concurrent computation of the decentralized control and observation gains and the maximization of the nonlinearity coverage tolerated by the system without becoming unstable. The reliable performances of the designed control scheme, compared to a distinguished decentralized guaranteed cost control strategy issued from the literature, are demonstrated by numerical simulations on an extensive application of a three-generator infinite bus power system. Originality/value The developed optimization problem subject to LMI constraints is efficiently solved by a one-step procedure to analyze the asymptotic stability and to synthesize all the control and observation parameters. Therefore, such a procedure enables to cope with the conservatism and suboptimal solutions procreated by optimization problems based on iterative algorithms with multi-step procedures usually used in the problem of dynamic output feedback decentralized control of nonlinear interconnected systems.

Observer-Based Adaptive Neural Networks Control for Large-Scale Interconnected Systems With Nonconstant Control Gains.

In this article, an adaptive neural network (NN) decentralized output-feedback control design is studied for the uncertain strict-feedback large-scale interconnected nonlinear systems with nonconstant virtual and control gains. NNs are utilized to approximate the unknown nonlinear functions, and the immeasurable states are estimated via designing an NN decentralized state observer. By constructing the logarithm Lyapunov functions, an observer-based NN adaptive decentralized backstepping output-feedback control is developed in the framework of the decentralized backstepping control. The proposed adaptive decentralized backstepping output-feedback control can make that the closed-loop system is semiglobally uniformly ultimately bounded (SGUUB) and that the tracking and observer errors converge to a small neighborhood of the origin. The most important contribution of this article is that it removes the restrictive assumption in the existing results that both virtual and control gain functions in each subsystem must be constants. A numerical simulation example is provided to validate the effectiveness of the proposed control method and theory.

Echo State Network-Based Decentralized Control of Continuous-Time Nonlinear Large-Scale Interconnected Systems

This article addresses the decentralized control problem of continuous-time nonlinear large-scale interconnected systems by the means of echo state network (ESN). The interconnected terms between the subsystems are treated as the disturbances added to the system dynamics, then the control problem is solved by the proposed robust controllers. By designing a cost function for the nominal subsystems, the robust controller is obtained by solving optimal controllers. The stability of the interconnected systems is proved by a composite Lyapunov function. The online adaptive dynamic program (ADP) method is employed to solve the transformed optimal problem, where a single ESN is utilized to approximate the critic cost and control policy. The optimal control policies of all the isolated subsystems are obtained simultaneously. The closed-loop stability of the feedback nominal systems is also proved, in a uniformly ultimately boundedness (UUB) manner. In the simulation, a large-scale interconnected system with four subsystems is provided to verify the effectiveness of the proposed decentralized controllers.