Class Of Large-scale Nonlinear Systems Research Articles

Decentralized Implicit Inverse Control for Large-Scale Hysteretic Nonlinear Time-Delay Systems and Its Application on Triple-Axis Giant Magnetostrictive Actuators.

This article proposes fuzzy-logic systems (FLSs)-based decentralized adaptive implicit inverse control scheme for a class of large-scale nonlinear systems with time delays and multihysteretic loops. Our novel algorithms feature hysteretic implicit inverse compensators designed to effectively mitigate multihysteretic loops in large-scale systems. In this article, hysteretic implicit inverse compensators can replace the traditional hysteretic inverse models, which are exceedingly difficult to construct, and no longer necessary. The authors provide three contributions: 1) a searching mechanism to obtain the approximate value of the practical input signal from the so-called hysteretic temporary control law; 2) the arbitrarily small L∞ norm of the tracking error attained by utilizing the proposed initializing technique, which applies the combination of FLSs and a finite covering lemma to deal with time delays; and 3) the construction of a triple-axis giant magnetostrictive motion control platform, which validates the effectiveness of the proposed control scheme and algorithms.

Composite adaptive exponential tracking control for large-scale nonlinear systems with sensor faults

The issue of composite adaptive exponential tracking control for a class of large-scale nonlinear systems under model uncertainties, external disturbances, along with multiplicative and additive time-varying sensor faults is considered in this paper. The command filtered backstepping approach is employed to address the “explosion of terms” issue inherent in standard backstepping method. A novel compensating system is incorporated to mitigate the effects of filtering errors and enhance the convergence of tracking errors. The composite estimation laws are designed by integrating the compensated tracking errors, prediction errors stemming from output estimators, along with the proportional and integral estimation errors of faulty terms. This on-line estimation framework enables achieving fast, robust and accurate estimation, even when employing low learning and modification gains. By incorporating modification terms with appropriate time-varying gains, it is demonstrated that the resulting system is globally exponentially stable. Finally, the effectiveness of the presented FTC approach is illustrated through two simulation examples.

Event-triggered impulsive control of lower-triangular large-scale nonlinear systems based on gain scaling technique

This paper investigates the event-triggered impulsive control problem for a class of large-scale nonlinear systems in lower-triangular form. Based on gain scaling technique and impulsive control theory, a novel decentralized event-triggered impulsive control strategy is first put forward by introducing a static scaling gain, where no control input exists between two consecutive triggering points. Moreover, when the large uncertainties exist in system nonlinearities, we further develop a new control strategy by introducing a time-varying scaling gain. It is proved that the proposed closed-loop control strategies exclude the Zeno behavior without sacrificing the global convergence of system states. Compared with the existing results, it is the first time to apply impulsive control to lower-triangular large-scale nonlinear systems, and the advantages of event-triggered impulsive control and gain scaling technique are subtly combined in the proposed control strategies. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed schemes.

Decentralized Adaptive Control of Large-Scale Nonlinear Systems With Time-Delay Interconnections and Asymmetric Dead-Zone Input

In this article, a decentralized adaptive control strategy is proposed for a class of large-scale nonlinear systems with interconnections. Each subsystem contains multiple state delays, asymmetric dead-zone inputs, and bounded time-varying disturbances. Every error subsystem is first decomposed according to input matrix assumption. Then, the decentralized adaptive controller is developed to handle uncertain functions in the subsystem. The nonlinear control gain function is constructed and used in adaptive control design. Two robust adaptive control schemes are, respectively, addressed for the cases of matched and mismatched time-delay nonlinearities. It is proved that all closed-loop signals are bounded, and the tracking error converges to an adjustable region. A simulation example is presented to show the effectiveness of the proposed method.

Adaptive Decentralized Tracking Control for a Class of Large-Scale Nonlinear Systems with Dynamic Uncertainties Using Multi-dimensional Taylor Network Approach

Adaptive Decentralized Tracking Control for a Class of Large-Scale Nonlinear Systems with Dynamic Uncertainties Using Multi-dimensional Taylor Network Approach

An Overview on Modelling of Complex Interconnected Nonlinear Systems

This paper proposes new mathematical models of representation, which can describe the dynamic behavior of large-scale nonlinear systems, such as an extended mathematical model of Volterra series, interconnected Hammerstein structures, and interconnected Wiener structures. In this research, we focus on the class of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. In this context, a discrete nonlinear mathematical model with unknown time-varying parameters, mono-variable, characterizes each interconnected subsystem operating in a deterministic or stochastic environment. An illustrative numerical simulation example of two interconnected nonlinear processes is provided to prove the validity and the performance of the developed theoretical results.

Adaptive Decentralized Asymptotic Tracking Control for Large-Scale Nonlinear Systems With Unknown Strong Interconnections

An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections, unknown time-varying parameters, and disturbances. First, by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time, all extra signals in the framework of decentralized control are filtered out, thereby removing all additional assumptions imposed on the interconnections, such as upper bounding functions and matching conditions. Second, by introducing two integral bounded functions, asymptotic tracking control is realized. Moreover, the nonlinear filters with the compensation terms are introduced to circumvent the issue of “explosion of complexity”. It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically. In the end, a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

Global decentralized control for uncertain large-scale feedforward nonlinear time-delay systems via output feedback

Abstract In this paper, the problem of global decentralized output feedback control is addressed for a class of large-scale nonlinear systems with zero dynamics and unknown time-varying delay. System disturbance nonlinearities are subject to feedforward growth restrictions with unknown growth rate. In the spirit of dynamic scaling change technique, a novel pair of time-varying-gain observer and controller is proposed. Compared with the existing results, the controller proposed is capable of handling the difficulties caused by the zero-dynamics, the uncertainties and the unknown time-varying delay. With the help of the Razumikhin theorem, it is shown that the closed-loop states asymptotically converge to zero. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example.

Differential-game for resource aware approximate optimal control of large-scale nonlinear systems with multiple players

In this paper, we propose a novel differential-game based neural network (NN) control architecture to solve an optimal control problem for a class of large-scale nonlinear systems involving N-players. We focus on optimizing the usage of the computational resources along with the system performance simultaneously. In particular, the N-players’ control policies are desired to be designed such that they cooperatively optimize the large-scale system performance, and the sampling intervals for each player are desired to reduce the frequency of feedback execution. To develop a unified design framework that achieves both these objectives, we propose an optimal control problem by integrating both the design requirements, which leads to a multi-player differential-game. A solution to this problem is numerically obtained by solving the associated Hamilton-Jacobi (HJ) equation using event-driven approximate dynamic programming (E-ADP) and artificial NNs online and forward-in-time. We employ the critic neural networks to approximate the solution to the HJ equation, i.e., the optimal value function, with aperiodically available feedback information. Using the NN approximated value function, we design the control policies and the sampling schemes. Finally, the event-driven N-player system is remodeled as a hybrid dynamical system with impulsive weight update rules for analyzing its stability and convergence properties. The closed-loop practical stability of the system and Zeno free behavior of the sampling scheme are demonstrated using the Lyapunov method. Simulation results using a numerical example are also included to substantiate the analytical results.

Adaptive decentralized fuzzy dynamic surface control scheme for a class of nonlinear large-scale systems with input and interconnection delays

This paper is focused on the decentralized tracking control problem of nonlinear large-scale systems with immeasurable states and unknown nonlinearities in each subsystems and their interconnections in the presence of unknown interconnection delays and uncertain input delays. To deal with inaccessible states and unknown nonlinearities, a fuzzy state observer is firstly constructed. Then, appropriate changes of coordinates are defined to cope with the problem of uncertain input delays and design dynamic surface control strategy for unknown nonlinear interconnected systems. In the design procedures, appropriate Lyapunov–Krasovskii functions are introduced to conquer the difficulties arising from interconnection delays with unknown upper bounds. it is also proven that the proposed method can ensure that all signals of the closed loop large-scale systems in the presence of both interconnection and input delays which have not been considered in previous literature are uniformly ultimately bounded. Furthermore, by appropriate selection of design parameters and matrices, the observation errors as well as the tracking errors converge to small desired values. Finally, to illustrate the effectiveness and efficiency of the proposed decentralized control scheme, numerical simulations are performed.

Adaptive decentralized tracking control of a class of large-scale nonlinear systems with unknown dead-zone inputs using neural network

In this paper, an adaptive decentralized control approach is proposed for a class of large-scale nonlinear systems with unknown dead-zone inputs using neural network. Firstly, the dead-zone outputs are firstly represented as simple linear systems with a static time-varying gain and bounded disturbance by introducing characteristic function. Secondly, in the controller design, neural networks are utilized to approximate the unknown nonlinear functions. Thirdly, an adaptive decentralized tracking control approach is constructed via backstepping design technique. It is shown that the proposed control approach can assure that all the signals of the closed-loop system semi-globally uniformly ultimately bounded and the tracking errors finally converge to a small domain around the origin. The proposed method can get precise tracking results with low computational cost, and have a good real-time performance and convergence. Finally, two examples are given to demonstrate the effectiveness of the proposed control scheme.

Observer-Based Event-Triggered Adaptive Decentralized Fuzzy Control for Nonlinear Large-Scale Systems

For a class of large-scale nonlinear systems in nonstrict-feedback structure with immeasurable states, an adaptive decentralized fuzzy control strategy on the basis of event-triggered mechanism is investigated in this paper. Fuzzy logic systems are implemented to construct an observer, which approximates the unknown nonlinear function in the controller. In light of backstepping control technique and event-triggered mechanism, a decentralized adaptive fuzzy control approach is proposed to compensate for the effects of actuator faults. When the triggering condition is satisfied, the communication burden can be reduced. Moreover, the whole signals of the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Furthermore, the outputs of subsystems can track the desired reference signals. Finally, some simulation results are utilized to testify the effectiveness of the proposed control scheme.

Decentralized fault-tolerant MRAC for a class of large-scale systems with time-varying delays and actuator faults

This paper considers the decentralized fault-tolerant model reference adaptive control (MRAC) problem for a class of nonlinear large-scale systems with matched unknown nonlinearity and uncertain time delay interconnections and mismatched interconnections. A novel cyclic-small-gain condition is achieved to show the boundedness of tracking errors. Furthermore, by introducing adaptive mechanisms, a new decentralized fault-tolerant controller is developed. In addition, it is shown that the matched unknown nonlinear functions and the matched uncertain time delay functions can be compensated by the developed controller. Compared with existing large-scale systems results, the proposed method is effective to solve the fault-tolerant MRAC problem for large-scale systems with time-varying delays and mismatched interconnections. Finally, the validity is shown by applying the proposed method to a chemical reactor system with two subsystems.

Decentralized reliable guaranteed cost control for large-scale nonlinear systems using actor-critic network

Abstract In this paper, the decentralized reliable guaranteed cost control problem of large-scale nonlinear systems with mismatched interconnection and time-varying actuator fault is investigated. The unknown actuator fault is assumed to be with known upper bounds. Under the case that the interconnection term is unknown and mismatched, the guaranteed cost control problem for a class of large-scale nonlinear systems can be transformed into design an optimal control strategy of the isolated system, which is necessary to solve the HJB (Hamilton–Jacobi–Bellman) equations by using adaptive dynamic programming (ADP) of actor-critic networks. The convergence property of the neural network weights and the stability of the closed-loop system have been strictly proved even if time-varying actuator faults and unknown interconnection coexist. Finally, simulation examples are given to show the effectiveness of the proposed approach.

Decentralized adaptive fuzzy tracking control for a class of uncertain large-scale systems with actuator nonlinearities

This paper studies the problem of decentralized adaptive tracking control for a class of nonlinear large-scale systems with unmeasurable states and actuator nonlinearities. For each subsystem, a novel decentralized disturbance rejection filter is designed to estimate both system states and external disturbances. The decentralized controller with adaptive laws is designed based on back-stepping techniques. It is proved that all the signals of the resulting closed-loop system are bounded, and the output tracking errors of subsystems converge to a desired neighborhood of origin. Simulation results illustrate the effectiveness of the method proposed in this paper.

Observer-Based Adaptive Fuzzy Decentralized Optimal Control Design for Strict-Feedback Nonlinear Large-Scale Systems

In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

Adaptive Optimal Control for Large-Scale Nonlinear Systems

In this paper, we present an adaptive optimal control approach applicable to a wide class of large-scale nonlinear systems. The proposed approach avoids the so-called loss-of-stabilizability problem and the problem of poor transient performance that are typically associated with adaptive control designs. Moreover, it does not require the system model to be in a certain parameterized form, and most importantly, it is able to efficiently handle systems of large dimensions. Theoretical analysis establishes that the proposed methodology guarantees stability and exponential convergence to state trajectories that can be made as close as desired to the optimal ones. A numerical example demonstrates the capability of the proposed approach to overcome loss-of-stabilizability problems. Moreover, simulation experiments for energy-efficient climate control performed on a ten-office building demonstrate the effectiveness of the proposed approach in large-scale nonlinear applications.

Adaptive decentralized fuzzy output feedback tracking control for a class of nonlinear large-scale systems with input delays

In this paper, the decentralized tracking control problem of nonlinear large-scale systems with immeasurable states and unknown nonlinearities in each subsystem and their interconnections subject to input delays is proposed. Based on the universal approximation properties of fuzzy systems, a fuzzy observer is designed to estimate the inaccessible states of the system. Subsequently, by defining the appropriate change of coordinates and employing the backstepping technique, an adaptive fuzzy backstepping output feedback control scheme is proposed for nonlinear interconnected systems subject to input delays. Owing to the problem of so-called explosion of complexity that inherently arises in the design procedures of the traditional backstepping technique, an adaptive fuzzy dynamic surface output feedback control approach is also presented for this class of large-scale systems. Moreover, it is shown that the two proposed adaptive decentralized fuzzy observer-based control approaches ensure all the signals of the closed loop system uniformly ultimately bounded and the norms of the tracking errors as well as the norms of the observation errors can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are carried out on the chemical reactor recycle system to illustrate and compare the effectiveness of the two proposed approaches.

Backstepping-based decentralized adaptive neural $$H_{\infty }$$ H ∞ control for a class of large-scale nonlinear systems with expanding construction

In this paper, a backstepping-based robust decentralized adaptive neural \( H_{\infty }\) connective stabilization approach is proposed for a class of large-scale interconnected nonlinear systems with expanding construction and external disturbances. First, the decentralized adaptive neural \(H_{\infty }\) controllers for the original nonlinear interconnected system are deduced and obtained by using backstepping technique, which can guarantee the connective stability of the nonlinear interconnected system. Then, the expansion of the system is considered. It is needed that the decentralized control laws and adaptive laws of the original system are kept to be unchanged, and only the control and adaptive laws for the new subsystem needs to be designed. Based on this requirement, a backstepping-based decentralized adaptive neural \(H_{\infty }\) control design method for the new subsystem is given. The decentralized control law and adaptive law of the new subsystem can stabilize the resultant expanded large-scale nonlinear system. The proposed method can guarantee the connective stability of the expanded large-scale nonlinear system. In this paper, neural networks are used to approximate the packaged nonlinear terms. As a result, the calculation of the control laws and adaptive laws is simplified. The effect of external disturbances and approximation errors is attenuated by \( H_{\infty }\) performance. All of the signals in the expanded closed-loop system are bounded. Two numerical examples are provided to show the effectiveness of the proposed control approach.

Distributed agent-based control and estimation over unreliable networks for a class of nonlinear large-scale systems

ABSTRACTA new technique for distributed estimation and control of large-scale systems is presented in this paper. The proposed method makes use of a set of agents that implement local H∞ controllers and Luenberger-like observers, improved with consensus-based corrections that incorporate information received from other agents. The communication between agents is assumed to be unreliable, this is modelled by time-varying delays and packet dropouts. The proposed methodology is an application for a class of nonlinear system affected by external disturbances. Some simulations are presented to illustrate the performance of this technique compared to the centralised case.