Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.     

LMI‐based adaptive output feedback fault‐tolerant controller design for nonlinear systems

This paper presents 2‐novel linear matrix inequality (LMI)‐based adaptive output feedback fault‐tolerant control strategies for the class of nonlinear Lipschitz systems in the presence of bounded matched or mismatched disturbances and simultaneous occurrence of actuator faults, including failure, loss of effectiveness, and stuck. The constructive algorithms based on LMI with creatively using Lyapunov stability theory and without the need for an explicit information about mode of actuator faults or fault detection and isolation mechanism are developed for online tuning of adaptive and fixed output‐feedback gains to stabilize the closed‐loop control system asymptotically. The proposed controllers guarantee to compensate actuator faults effects and to attenuate disturbance effects. The resulting control methods have simpler structure, as compared with most existing recent methods and more suitable for practical systems. The merits of the proposed fault‐tolerant control scheme have been verified by the simulation on nonlinear Boeing 747 lateral motion dynamic model subjected to actuator faults.     

Decentralized output feedback controller design for nonlinear interconnected systems with unknown control direction and time‐varying delays

The decentralized output feedback control problem is considered for a class of large‐scale systems with unknown time‐varying delays. The uncertain interconnections are bounded by general nonlinear functions with unknown coefficients. The control direction parameters are unknown for each subsystem, which brings a challenging issue for decentralized controller design. To deal with this problem, we propose a new decentralized control scheme with the help of Nussbaum function. The decentralized filter is designed at first. By constructing Lyapunov–Krasovskii functional, we design the dynamic output feedback controller. It is rigorously proved that the closed‐loop system is asymptotically stable. Finally, the simulation is performed, and the results verify the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive state feedback stabilization of more general stochastic high‐order nonholonomic systems

This paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method.     

Decentralized adaptive control of nonlinear large‐scale pure‐feedback interconnected systems with time‐varying delays

In this paper, an adaptive decentralized neural control problem is addressed for a class of pure‐feedback interconnected system with unknown time‐varying delays in outputs interconnections. By taking advantage of implicit function theorem and the mean‐value theorem, the difficulty from the pure‐feedback form is overcome. Under a wild assumption that the nonlinear interconnections are assumed to be bounded by unknown nonlinear functions with outputs, the difficulties from unknown interconnections are dealt with, by introducing continuous packaged functions and hyperbolic tangent functions, and the time‐varying delays in interconnections are compensated by Lyapunov–Krasovskii functional. Radial basis function neural network is used to approximate the unknown nonlinearities. Dynamic surface control is successfully extended to eliminate ‘the explosion of complexity’ problem in backstepping procedure. To reduce the computational burden, minimal learning parameters technique is successfully incorporated into this novel control design. A delay‐independent decentralized control scheme is proposed. With the adaptive neural decentralized control, only one estimated parameter need to be updated online for each subsystem. Therefore, the controller is more simplified than the existing results. Also, semiglobal uniform ultimate boundedness of all of the signals in the closed‐loop system is guaranteed. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Finite‐time prescribed performance adaptive fuzzy fault‐tolerant control for nonstrict‐feedback nonlinear systems

This paper focuses on a finite‐time adaptive fuzzy control problem for nonstrict‐feedback nonlinear systems with actuator faults and prescribed performance. Compared with existing results, the finite‐time prescribed performance adaptive fuzzy output feedback control is under study for the first time. By designing performance function, the transient performance of the corresponding controlled variable is maintained in a prescribed area. Combining the finite‐time stability criterion with backstepping technique, a feasible adaptive fault‐tolerant control scheme is proposed to guarantee that the system output converges to a small neighborhood of the origin in finite time, and the closed‐loop signals are bounded. Finally, simulation results are shown to illustrate the effectiveness of the presented control method.     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust adaptive output‐feedback control for a class of nonlinear systems with time‐varying actuator faults

A robust adaptive output‐feedback control scheme is proposed for a class of nonlinear systems with unknown time‐varying actuator faults. Additional unmodelled terms in the actuator fault model are considered. A new linearly parameterized model is proposed. The boundedness of all the closed‐loop signals is established. The desired control performance of the closed‐loop system is guaranteed by appropriately choosing the design parameters. The properties of the proposed control algorithm are demonstrated by two simulation examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Observer‐based adaptive control for stochastic nonstrict‐feedback systems with unknown backlash‐like hysteresis

This paper studies an observer‐based adaptive fuzzy control problem for stochastic nonlinear systems in nonstrict‐feedback form. The unknown backlash‐like hysteresis is considered in the systems. In the design process, the unknown nonlinearities and unavailable state variables are tackled by introducing the fuzzy logic systems and constructing a fuzzy observer, respectively. By using adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy control algorithm is developed. For the closed‐loop system, the proposed controller can guarantee all the signals are 4‐moment semiglobally uniformly ultimately bounded. Finally, simulation results further show the effectiveness of the presented control scheme.     

Adaptive neural network command filtered backstepping control of pure‐feedback systems in presence of full state constraints

An adaptive neural network (NN) command filtered backstepping control is proposed for the pure‐feedback system subjected to time‐varying output/stated constraints. By introducing a one‐to‐one nonlinear mapping, the obstacle caused by full stated constraints is conquered. The adaptive control law is constructed by command filtered backstepping technology and radial basis function NNs, where only one learning parameter needs to be updated online. The stability analysis via nonlinear small‐gain theorem shows that all the signals in closed‐loop system are semiglobal uniformly ultimately bounded. The simulation examples demonstrate the effectiveness of the proposed control scheme.     

Direct adaptive neural tracking control for a class of stochastic pure‐feedback nonlinear systems with unknown dead‐zone

This paper considers the problem of adaptive neural tracking control for a class of nonlinear stochastic pure‐feedback systems with unknown dead zone. Based on the radial basis function neural networks' online approximation capability, a novel adaptive neural controller is presented via backstepping technique. It is shown that the proposed controller guarantees that all the signals of the closed‐loop system are semi‐globally, uniformly bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the suggested control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint

This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed‐loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated.     

Observer‐based nonlinear feedback decentralized neural adaptive dynamic surface control for large‐scale nonlinear systems

This paper presents a nonlinear gain feedback technique for observer‐based decentralized neural adaptive dynamic surface control of a class of large‐scale nonlinear systems with immeasurable states and uncertain interconnections among subsystems. Neural networks are used in the observer design to estimate the immeasurable states and thus facilitate the control design. Besides avoiding the complexity problem in traditional backstepping, the new nonlinear feedback gain method endows an automatic regulation ability into the pioneering dynamic surface control design and improvement in dynamic performance. Novel Lyapunov function is designed and rigorous stability analysis is given to show that all the closed‐loop signals are kept semiglobally uniformly ultimately bounded, and the output tracking errors can be guaranteed to converge to sufficient area around zero, with the bound values characterized by design parameters in an explicit manner. Simulation and comparative results are shown to verify effectiveness.     

Adaptive neural network output feedback stabilization of nonlinear non‐minimum phase systems

This paper presents an adaptive output feedback stabilization method based on neural networks (NNs) for nonlinear non‐minimum phase systems. The proposed controller comprises a linear, a neuro‐adaptive, and an adaptive robustifying parts. The NN is designed to approximate the matched uncertainties of the system. The inputs of the NN are the tapped delays of the system input–output signals. In addition, an appropriate reference signal is proposed to compensate the unmatched uncertainties inherent in the internal system dynamics. The adaptation laws for the NN weights and adaptive gains are obtained using Lyapunov's direct method. These adaptation laws employ a linear observer of system dynamics that is realizable. The ultimate boundedness of the error signals are analytically shown using Lyapunov's method. The effectiveness of the proposed scheme is shown by applying to a translation oscillator rotational actuator model. Copyright © 2009 John Wiley & Sons, Ltd.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

This research addresses the stability analysis and adaptive state‐feedback control for a class of nonlinear discrete‐time systems with multiple interval time‐varying delays and symmetry dead zone. The multiple interval time‐varying delays and symmetry dead zone are considered in the nonlinear discrete‐time system. The multiple interval time‐varying delays are bounded by the nonlinear function with unknown coefficients, and the symmetry dead zone is considered without the knowledge of the dead zone parameters. The adaptive state‐feedback controller is designed for the nonlinear discrete‐time systems with multiple interval time‐varying delays and dead zone. The discrete Lyapunov‐Krasovskii functional is introduced, such that the solutions of the closed‐loop error system converge to an adjustable bounded region and the state errors can be rendered arbitrarily small by adjusting the adaptive parameters. The designed adaptive state‐feedback controller does not require the knowledge of maximum and minimum values for the characteristic slopes of the dead zone. Finally, three simulation examples are given to show the effectiveness of the proposed methods.     

Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

In this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.