Adaptive Backstepping Recursive Design Research Articles

Event‐triggered adaptive neural‐network control of nonlinear MIMO systems

SummaryThis article investigates an adaptive neural networks (NNs) tracking control design issue for nonlinear multi‐input and multi‐output (MIMO) systems involving the sensor‐to‐controller event‐triggered mechanism (ETM). In the design, NNs are utilized to approximate the unknown nonlinear functions. A sensor‐to‐controller ETM is designed to save unnecessary transmission and communication resources. Subsequently, a first‐order filter technique is presented to solve the problem that the virtual control function is not differentiable. Furthermore, an event‐triggered adaptive NNs control strategy is presented by constructing Lyapunov functions and using adaptive backstepping recursive design. It is demonstrated that the presented scheme can ensure the whole closed‐loop signals are uniformly ultimately bounded without exhibiting the Zeno behavior. Finally, a numerical simulation example confirms the effectiveness of the presented adaptive event‐triggered control (ETC) approach.

Adaptive fuzzy fault-tolerant control for active seat suspension systems with full-state constraints

In this paper, an adaptive fuzzy fault-tolerant control (FTC) scheme is proposed for active seat suspension systems. The addressed system contains electromagnetic actuator faults. In addition, the constraints of the displacements of the car seat, active suspension, and wheel, their vertical vibration speeds and current intensity are included. In the control design, since the systems have dynamic characteristics of complexities and spring non-linearities, the fuzzy logic systems are utilized to approximate the unknown nonlinear dynamics. By the aid of Barrier Lyapunov functions and based on the adaptive backstepping recursive design algorithm, a novel adaptive fuzzy FTC scheme is formulated. When the electromagnetic actuator fails, the developed control scheme can guarantee that all the vertical vibration states are stable. Eventually, the effectiveness of the presented control method is offered to illustrate by a random road surface.

Fuzzy Adaptive Finite-Time Consensus Control for High-Order Nonlinear Multiagent Systems Based on Event-Triggered

This article studies the fuzzy adaptive finite-time consensus control problem for high-order nonlinear multiagent systems with unknown nonlinear dynamics. In control design,fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and under the frameworks of adaptive backstepping recursive design and finite-time stability theory, an adaptive fuzzy finite-time consensus control method is developed. To save communication resources and reduce the numbers of controller execution times, a dynamic event-triggered mechanism with a relative threshold is established. Subsequently, an event-triggered-based finite-time fuzzy adaptive control scheme is formulated. Furthermore, by constructing novel integral-type Lyapunov functions and adding a power integrator technique, the finite-time stability of the closed-loop system and the convergence of consensus tracking errors are proved. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed adaptive event-triggered consensus control method.

Adaptive Fuzzy Decentralized Dynamic Surface Control for Fractional-Order Nonlinear Large-Scale Systems

The aim of this article is to study a fuzzy-based decentralized adaptive control strategy for the nonstrict-feedback fractional-order nonlinear large-scale systems with unknown control directions. In each step of the recursive processes, the fuzzy logic systems are employed to identify unknown nonlinear functions. To handle the difficulties caused by unknown control directions, a Nussbaum function technique is adopted. Furthermore, by introducing the dynamic surface control technique into the adaptive backstepping recursive design algorithm, a fuzzy-based decentralized adaptive control strategy is formulated. Both the stability of the controlled system and the convergence of the tracking errors are proved by constructing the fractional-order Lyapunov functions. Finally, the validity and effectiveness of the designed decentralized control scheme are confirmed via two simulation examples.

Command‐filter‐based adaptive output feedback quantized tracking control for switched stochastic nonlinear time‐delay systems with actuator saturation

AbstractThis work addresses the adaptive output feedback quantized control for a class of switched stochastic nonstrict‐feedback nonlinear time‐delay systems with input and output quantization and actuator saturation under arbitrary switching. A novel state observer including the quantized output signal and the saturated input signal is designed to estimate the unknown system states. Then, the command‐filtered backstepping method is introduced to avoid the “explosion of complexity” in the adaptive backstepping recursive design. Moreover, the design challenges from input and output quantization errors and actuator saturation are overcome by combining the auxiliary variable approach and some special techniques. Instead of the traditional quartic Lyapunov–Krasovskii functional, the common quadratic Lyapunov–Krasovskii functional is constructed to develop the adaptive quantized tracking control scheme for such systems. By means of the proposed common controller independent of switching signal, all closed‐loop signals are mean‐square semi‐globally uniformly ultimately bounded, while the tracking error will remain in a small neighborhood of the origin. Finally, stability analysis and simulation results are provided to show the effectiveness and performance of the proposed design methodology.

High‐gain observer‐based adaptive fuzzy finite‐time prescribed performance tracking control for linear stepping motor with event‐triggered strategy

AbstractThis paper considers the tracking problem of linear stepping motor system with unmeasurable states, and a finite‐time prescribed performance controller is designed with dynamic surface control scheme and event‐triggered strategy. In the adaptive backstepping recursive design, fuzzy logic system is used to approximate the nonlinear function, and a high‐gain observer is introduced to estimate the unmeasured states. A finite‐time performance function is developed to improve the transient and transient performance of the system, and a relative threshold event‐triggered strategy is proposed to reduce the communication burden. In addition, the inherent complexity explosion problem of the backstepping process is solved by the dynamic surface control method. Finally, the simulation results prove the effectiveness of the scheme.

Adaptive event-triggered control for new type tyre systems based on vehicles

ABSTRACT In this article, an adaptive event-triggered control scheme is first investigated for new type tyre systems based on vehicle. The intricate systems are transformed into a nonlinear model to research. The improved event-triggered mechanism (ETM) is proposed to enhance effectively the data transmission capacity of the systems and reduce the communication bandwidth. For the sake of conquering the problem of ‘explosion of complexity’ in traditional adaptive backstepping recursive design process, the dynamic surface control (DSC) technique is introduced in control design process. Based on the Lyapunov stability theory, the developed control scheme guarantees all the variables in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). Finally, the simulation results verify the rationality and effectiveness of the proposed control scheme.

Fuzzy Adaptive Event-Triggered Secure Control for Stochastic Nonlinear High-Order MASs Subject to DoS Attacks and Actuator Faults

This article investigates the adaptive event-triggered secure control design problem for a class of stochastic nonlinear high-order multiagent systems (MASs) subject to denial-of-service (DoS) attacks and actuator faults. The considered systems contain not only unknown random interference 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. To solve the problem of wasted communication resources, the control signal with the relative threshold strategy is designed via the event-triggered control technique. As a class of cyber–physical systems, the securities of MASs are vulnerable to actuator faults and DoS attacks. When the system suffers from coupled DoS attacks and actuator failures, its performance will deteriorate rapidly and even the controlled system will collapse. To overcome this difficulty, a novel fault-tolerant and antiattack control method is proposed, which enables the system to achieve the security control objective even in an insecure network and physical environment. The stability analysis of the system is given by combining the adaptive backstepping recursive design process with stochastic Lyapunov stability theory. It is demonstrated that all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded in probability. Finally, a simulation example is given to illustrate the effectiveness and advantages of the presented scheme.

Exponential stability analysis and control design for nonlinear system with time-varying delay

This paper investigates the problem of exponential stability analysis and control design for time delay nonlinear systems with unknown control coefficient. Nussbaum gain function is utilized to solve the problem of unknown control directions at every step. By designing a new Lyapunov-Krasovskii functional, the problem of unknown time-varying delay is solved. Under the frame of adaptive backstepping recursive design, an exponential stabilization control algorithm is developed, which demonstrates that all solutions of controlled system are ultimately uniformly bounded (UUB) and exponential converge to zero. Finally, simulation results are displayed to explain the superiority and effectiveness of the developed control method.

Observer-Based Adaptive Fuzzy Tracking Control for Strict-Feedback Nonlinear Systems With Unknown Control Gain Functions.

This article investigates the adaptive fuzzy output-feedback backstepping control design problem for uncertain strict-feedback nonlinear systems in the presence of unknown virtual and actual control gain functions and unmeasurable states. A fuzzy state observer is designed via fuzzy-logic systems, thus the unmeasurable states are estimated based on the designed fuzzy state observer. By constructing the logarithm Lyapunov functions and incorporating the property of the fuzzy basis functions and bounded control design technique into the adaptive backstepping recursive design, a novel observer-based adaptive fuzzy output-feedback control method is developed. The proposed fuzzy adaptive output-feedback backstepping control scheme can remove the restrictive assumptions in the previous literature that the virtual control gains and actual control gain functions must be constants. Furthermore, it can make the control system be semiglobally uniformly ultimately boundedness (SGUUB) and keep the observer and tracking errors to remain in a small neighborhood of the origin. The numerical simulation example is presented to validate the effectiveness of the proposed control scheme and theory.

Neural network based adaptive dynamic surface control of nonaffine nonlinear systems with time delay and input hysteresis nonlinearities

In this paper, neural networks (NNs)-based adaptive dynamic surface control is investigated for a class of pure-feedback nonlinear systems with unknown time delay and input hysteresis nonlinearities. The design difficulty appeared in this paper due to time delay is handled by combining neural networks with finite covering lemma instead of using Krasovskii functionals, and the assumptions on the time-delay functions are removed based the finite covering lemma and NNs. Meanwhile, completely unknown backlash-like hysteresis control input that frequently exists in practice is also considered. By combining the adaptive backstepping recursive design technique with the universal approximation ability of neural networks, an adaptive neural control algorithm is systemically designed for the system under consideration, and the explosion of complexity exists in traditional backstepping design is avoided by using dynamic surface technique. It is shown that the designed adaptive controller can guarantee that all the signals are ultimately uniformly bounded and the desired signal can be tracked with a small domain of the origin. A numerical example and an example of a real plant for adjustable metal cutting system are provided to show the feasibility of the proposed method.

Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method

This paper considers the problem of adaptive fuzzy backstepping-based output-feedback controller design for a class of uncertain switched nonlinear stochastic systems in lower-triangular form without the measurements of the system states. By combining fuzzy logic systems’ universal approximation ability and dynamic surface control technique in the adaptive backstepping recursive design with a modified average dwell-time scheme, a new adaptive fuzzy control approach is presented for the switched system. More specifically, a switched observer is constructed to reduce the conservativeness aroused by the employ of a common observer, and individual coordinate transformations for subsystems are given up by adopting a common coordinate transformation of all subsystems. It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters. Finally, simulation studies are provided to demonstrate the validity of the proposed control method.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

SUMMARYIn this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

Adaptive Fuzzy Output Feedback Tracking Backstepping Control of Strict-Feedback Nonlinear Systems With Unknown Dead Zones

In this paper, an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict-feedback systems with unknown functions, unknown dead zones, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy filters state observer is designed to estimate the immeasurable states. By using the adaptive backstepping recursive design technique and constructing the dead-zone inverse, a new adaptive fuzzy backstepping output-feedback control approach is developed. It is mathematically proved that all the signals of the resulting closed-loop adaptive control system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters. The proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement. Two simulation examples are provided to show the effectiveness of the proposed approach.

Adaptive Fuzzy Control for Nonlinear Time-Delay Systems with Dynamical Uncertainties

In this paper, an adaptive fuzzy backstepping robust control approach is proposed for a class of SISO nonlinear strict-feedback systems. The nonlinear systems addressed in this paper are assumed to possess three uncertainties: (i) the unstructured uncertainties; (ii) the time delays; and (iii) the dynamics uncertainties. In adaptive backstepping recursive design, fuzzy logic systems are used to approximate the unstructured uncertainties. A nonlinear damping technique and Lyapunov–Krasovskii functions are introduced to cancel the effects of the dynamics uncertainties and deal with the time delays, respectively. Combining the backstepping technique and a small gain approach, a stable adaptive fuzzy robust control approach is developed. It is proved that all the signals of the closed-loop system are semi-golablly uniformaly ultimately bounded (SUUB). The effectiveness of the proposed approach is illustrated by a simulation example.