A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.     

Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach

In this paper, a direct adaptive fuzzy robust control approach is proposed for single input and single output (SISO) strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamical disturbances. No prior knowledge of the boundary of the nonlinear uncertainties is required. Fuzzy logic systems are used to approximate the intermediate stabilizing functions, and a stable direct adaptive fuzzy backstepping robust control approach is developed by combining the backstepping technique with the fuzzy adaptive control theory. The stability of the closed-loop system and the convergence of the system output are proved based on the small-gain theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.     

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Adaptive fuzzy H/sub /spl infin// stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach

A novel adaptive fuzzy controller with H/sub /spl infin// performance is proposed for a wide class of strict-feedback canonical nonlinear systems. The systems may possess a class of uncertainties referred to as unstructured uncertain functions, which are not linearly parameterized and have no prior knowledge of the bound. The Takagi-Sugeno-type fuzzy logic systems are used to approximate the uncertainties and a systematic design procedure is developed for synthesis of adaptive fuzzy control with H/sub /spl infin// performance, which combines the backstepping technique and generalized small gain approach. The method preserves the three advantages, those are, the semiglobal uniform ultimate bound of adaptive control in the presence of unstructured uncertainties can be guaranteed, the adaptive mechanism with only one learning parameter is obtained and the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.     

动态不确定非线性系统直接自适应模糊backstepping控制

对一类单输入单输出动态不确定非线性系统,提出一种直接自适应模糊backstepping和小增益相结合的控制方法.设计中,首先用模糊逻辑系统逼近虚拟控制器:其次把自适应模糊控制和backstepping控制设计技术相结合.给出了直接自适应模糊控制设计方法.最后基于Lyapunov函数和小增益方法证明了整个闭环系统的稳定性.仿真实例进一步验证了所提方法的有效性.     

Global disturbance rejection of a class of nonlinear systems with unknown exosystems

An asymptotic rejection algorithm is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown disturbances. The disturbances are generated from an unknown exosystem, and are assumed to be sinusoidal disturbances with unknown amplitude and frequency. By using the technique of backstepping and adaptive control, a nonlinear state feedback controller is designed. Under the proposed controller, the system＇s state variables asymptotically converge to zero, and the disturbances are rejected completely. The approach used is an integration of the robust stabilization technique, adaptive technique, and backstepping technique.     

Adaptive neural network output feedback control of stochastic nonlinear systems with dynamical uncertainties

In this paper, a robust adaptive neural network (NN) backstepping output feedback control approach is proposed for a class of uncertain stochastic nonlinear systems with unknown nonlinear functions, unmodeled dynamics, dynamical uncertainties and without requiring the measurements of the states. The NNs are used to approximate the unknown nonlinear functions, and a filter observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function is incorporated into the backstepping recursive design technique, and a new robust adaptive NN output feedback control approach is constructed. It is mathematically proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. The simulation example and comparison results further justify the effectiveness of the proposed approach.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.     

Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach

This paper presents a novel robust adaptive fuzzy tracking controller (RAFTC) for a wide class of perturbed strict-feedback nonlinear systems with both unknown system and virtual control gain nonlinearities. For unknown system nonlinearities, two types for them are included: one naturally satisfies the “triangularity condition” and may possess a class of unstructured uncertain functions which are not linearly parameterized, while the other is partially known and consists of parametric uncertainties and known “bounding functions”. The Takagi–Sugeno type fuzzy logic systems are used to approximate unknown system nonlinearities and a systematic design procedure is developed for synthesis of RAFTC by combining the backstepping technique and generalized small-gain approach. The algorithm proposed is highlighted by three advantages: (i) the semi-global uniform ultimate bound of RAFTC in the presence of perturbed uncertainties and unknown virtual control gain nonlinearities can be guaranteed, (ii) the adaptive mechanism with minimal learning parameterizations is obtained and (iii) the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.     

Fuzzy adaptive output feedback control for a class of switched non-triangular structure nonlinear systems with time-varying delays

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.     

Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays

In this paper, an adaptive backstepping tracking control scheme is proposed for a class of nonlinear state time‐varying delay systems, which are subject to parametric uncertainties and external disturbances. The bounds of the time delays and their derivatives are assumed to be unknown. Tuning functions method is exploited to construct the control law and adaptive laws. Unknown time‐varying delays are compensated by using appropriate Lyapunov–Krasovskii functional. It is shown that the proposed controller can guarantee the boundedness of all the closed‐loop signals. The tracking performance can be adjusted by choosing suitable design parameters. At the end, a simulation example is provided to illustrate the effectiveness of the design procedure. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

In this paper, an adaptive robust controller is designed for a class of uncertain nonlinear cascade systems with multiple time‐varying delays under external disturbance. It is assumed that multiple time‐varying delays are not exactly known and, therefore, the delayed terms must not appear in the adaptation and control laws. Accordingly, by using a Lyapunov‐Krasovskii function, delays are deleted from the adaptation and control laws. A controller based on an adaptive backstepping approach is designed to assure the global asymptotic tracking of the desired output and boundedness of the other states. The proposed controller is proved to be robust against unknown time‐varying delays and external disturbances applying to the system. Simulation results are provided to show the effectiveness of the proposed approach.