Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO uncertain nonlinear strict-feedback systems. The considered nonlinear systems contain unknown nonlinear functions, unknown time-varying delays and unmeasured states. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and then a high-gain filter is designed to estimate the unmeasured states. Combining the backstepping recursive design technique and adaptive fuzzy control design, an adaptive fuzzy output feedback backstepping control method is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and both the observer error and tracking error converge to a small neighborhood of the origin. Two key advantages of our scheme are that (i) the high-gain filter is designed to estimate unmeasured states of time-delay nonlinear system, and (ii) the virtual control gains are functions. A simulation is included to illustrate the effectiveness of the proposed approach.     

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multiinput and multioutput (MIMO) uncertain stochastic nonlinear strict-feedback 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. Utilizing the designed the fuzzy state observer and by combining the adaptive backstepping control design, an adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. A simulation example is provided to show the effectiveness of the proposed approach.     

Adaptive robust fuzzy control for a class of uncertain chaotic systems

In this paper, the output feedback control of uncertain chaotic systems is addressed via an adaptive robust fuzzy approach. Fuzzy logic systems are employed to approximate uncertain nonlinear functions in the chaotic systems. Because only partial information of the system’s states is needed to be known, an observer is given to estimate the unmeasured states. Compared with the existing results in the observer design, the prior knowledge on dynamic uncertainties is relaxed and a class of more general chaotic systems is considered as well as robustness to the approximation error is improved. It can be proven that the closed-loop system is stable in the sense that all the variables are bounded. Simulation example for the unified chaotic systems is given to verify the effectiveness of the proposed method. This work was supported in part by the National Natural Science Foundation of China (60874056) and the Foundation of Educational Department of Liaoning Province (2008312).     

Observer-based adaptive fuzzy backstepping dynamic surface control design and stability analysis for MIMO stochastic nonlinear systems

In this paper, an adaptive fuzzy backstepping output feedback dynamic surface control (DSC) approach is developed for a class of multiinput and multioutput (MIMO) stochastic nonlinear systems with immeasurable states. Fuzzy logic systems are firstly utilized to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive backstepping technique and dynamic surface control (DSC) technique, an adaptive fuzzy output feedback backstepping DSC approach is developed. The proposed control method not only overcomes the problem of ??explosion of complexity?? inherent in the backstepping design methods, but also the problem of the immeasurable states. It is proved that all the signals of the closed-loop adaptive control stochastic system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties

In this paper, a fuzzy adaptive output feedback control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states, unmodeled dynamics, and dynamical disturbances. In the backstepping recursive design, fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states; a dynamic signal is incorporated into the control scheme to dominate the dynamic uncertainties. Using the states estimates and combining the backstepping design technique, a fuzzy adaptive output feedback control is constructed recursively. It is proved that the proposed fuzzy adaptive output feedback control scheme can guarantee the all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SUUB), and the observer and tracking error converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated via an example.     

Prescribed performance adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback control approach is proposed for a class of uncertain nonlinear systems with unknown nonlinear functions, unmodeled dynamics, and 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. To solve the problem of unmodeled dynamics, the dynamical signal combined with changing supply function is incorporated into the backstepping recursive design technique. Under the framework of the backstepping control design technique and incorporated by the predefined performance technique, a new robust adaptive fuzzy output feedback control scheme is constructed. It is shown that all the signals of the resulting closed-loop system are bounded, and the system output remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach.     

Property and evolution of the running-in attractor in an actual dynamic system

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

     

Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multiinput and multioutput (MIMO) nonlinear systems with time delays and immeasurable states. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and an adaptive fuzzy high-gain observer is developed to estimate the unmeasured states. Using the designed high-gain observer, and combining the fuzzy adaptive control theory with the backstepping approach, an adaptive fuzzy output feedback control is constructed recursively. It is proved that all the signals of the closed-loop adaptive control system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighborhood of the origin.     

Adaptive dynamic surface neural network control for nonstrict-feedback uncertain nonlinear systems with constraints

This paper presents an adaptive dynamic surface neural network control for a class of nonstrict-feedback uncertain nonlinear systems subjected to input saturation, dead zone and output constraint. The problem of input saturation is solved by designing an anti-windup compensator, and the issue of output constraint is addressed by introducing tan-type Barrier Lyapunov function. Furthermore, based on adaptive backstepping technique, a series of novel stabilizing functions are derived. First-order sliding mode differentiator is introduced into backstepping design to obtain the first-order derivative of virtual control. The real control input is obtained using dead-zone inverse method. It is proved that the proposed control scheme can achieve finite time convergence of the output tracking error into a small neighbor of the origin and guarantee all the closed-loop signals are bounded. Simulation results demonstrate the effectiveness of the proposed control scheme.     

Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input

In this paper, we present an adaptive control scheme for a class of uncertain nonlinear system with unknown nonsymmetric dead-zone nonlinearity. It is assumed that the system states are unmeasurable. Therefore, an observer is designed to estimate those unmeasured states. The controller is designed by using the backstepping control design procedure. The proposed adaptive scheme requires only the information that the dead-zone slopes are bounded. The new control scheme ensures bounded-error trajectory tracking and the boundedness of all the signals in the closed-loop. The feasibility is investigated by an illustrative simulation example.     

Chaos control and modified projective synchronization of unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control

This paper proposes the chaos control and the modified projective synchronization methods for unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a regular or periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise-like, synchronized chaotic systems can be used as cipher generators for secure communication. Obviously, the importance of obtaining these objectives is specified when the dynamics of gyroscope system are unknown. In this paper, using the neural backstepping control technique, control laws are established which guarantees the chaos control and the modified projective synchronization of unknown chaotic gyroscope system. In the neural backstepping control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimators are derived in the sense of Lyapunov function. Thus, the unknown chaotic gyroscope system can be guaranteed to be asymptotically stable. Also, the control objectives have been achieved.     

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

A new design scheme of directly adaptive fuzzy control for a class of discrete-time chaotic systems is proposed in this paper. The T-S fuzzy model is employed to represent the discrete-time chaotic systems. Then a fuzzy controller is designed and the unknown coefficients of the controller are identified by least squares algorithm with dead-zone. By Lyapunov method, all the signals involved in the closed-loop systems are shown to be bounded and the error between the system output and the reference output is proved to converge to a small neighborhood of zero. Simulation results demonstrate the effectiveness of the theoretical results.     

Reduced-order observer-based backstepping tracking control for a class of stochastic nonlinear systems

In this paper, an output feedback tracking control scheme is put forwarded for a class of stochastic nonlinear systems, whose dynamics involve not only unknown parameters but also unmeasured states multiplied by output nonlinearities. A type of reduced-order observer is first developed. By adding some output related items in the observer, the estimation error realize global asymptotic convergence under disturbance free condition, and global bounded convergence when considering disturbance. Besides, the dimension of the closed-loop system is reduced, and the update law of this observer gain is beneficial for steady tracking. After the observer was established, the controller is constructed by employing the adaptive backstepping approach, and a smooth nonsingular robust item is proposed to handle the influence of stochastic disturbance. All the signals in the closed system is proved to be globally bounded in probability. Moreover the output tracking error converges to an arbitrary small neighborhood of the origin by proper choosing of the design parameters. The simulation results based on current control scheme and the comparison with the previous method illustrate that the proposed output feedback scheme realizes good tracking performance and strong ability on stochastic disturbance attenuation.     

Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity

Existence of unknown time-delay in the systems is a drastic restriction that it can menace the stability criteria and even deteriorate the performance system. This undesired case would be more intensified if that the uncertain input nonlinearity effects are also considered. To handle the input nonlinearities effects (results in dead-zone and/or hysteresis phenomena) and also unknown time-delay in the chaotic systems, this paper presents an observer-based Model Reference Adaptive Control (MRAC) scheme for a class of unknown time-delay chaotic systems with disturbances. This new method is a delay-independent variable-structure control method which is integrated with an observer system. The main task of the proposed approach is to accomplish a perfect tracking procedure such that unknown parameters are adapted via output estimation error. Furthermore, stability of the closed-loop system is achieved by means of the Lyapunov stability theory. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.     

Disturbance-observer-based robust synchronization control of uncertain chaotic systems

In this paper, a robust synchronization control scheme is proposed for chaotic systems in the presence of system uncertainties and unknown external disturbances. For the synchronization error system, the compound disturbance which is estimated using the disturbance observer cannot be directly measured. If the gain matrix is properly chosen, the disturbance observer can approximate the unknown compound disturbance well. And then, the constrained robust synchronization control scheme is presented for uncertain chaotic systems based on the output of disturbance observer. In the design of a robust synchronization control scheme, the effect of unknown control input constraint has been explicitly considered to guarantee the synchronization performance. Numerical simulation results are presented to illustrate the effectiveness of the proposed constrained synchronization control scheme for uncertain chaotic systems.     

Nonlinear adaptive neural network control for a model-scaled unmanned helicopter

In this paper, a nonlinear adaptive neural network control is proposed for trajectory tracking of a model-scaled helicopter. The purpose of this research is to reduce the ultimate bounds of tracking errors resulted from small coupling forces (or small parasitic body forces) and aerodynamic uncertainties. The proposed control is designed under backstepping framework, with neural network compensators being added. Updating laws of neural networks are designed through projection algorithm, so that adaptive parameters are bounded. Derivatives of virtual controls are obtained through command filters. It is proved that, by using neural network compensators, tracking errors of the closed-loop system can be restricted within very small ultimate bounds. Superiority of the proposed nonlinear adaptive neural network control over a backstepping control is demonstrated by simulation results.     

Robust nonlinear control for a model-scaled helicopter with parameter uncertainties

A robust nonlinear controller is designed for the trajectory tracking of a model-scaled helicopter with uncertain parameters (including uncertain inertial parameters, uncertain structural parameters and uncertain aerodynamic parameters). The proposed controller is based upon the backstepping technique, with modifications to accommodate helicopter dynamics. Aerodynamic uncertainties are addressed by dynamic inverters, and derivatives of virtual controls in the backstepping process are calculated through command filters to avoid complex analytical solutions. Errors resulted from dynamic inverters, command filters, and uncertain parameters are then regarded as disturbances, and treated by nonlinear damping terms. With the proposed controller, it can be proved that tracking errors of the closed-loop system are ultimately bounded with tunable ultimate bounds. Performances of the proposed controller are evaluated by simulation results.     

Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot

In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i)?the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii)?the problem of ??explosion of complexity?? is avoided.     

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter–receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua’s system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.     

Backstepping control for the optoelectronic stabilized platform based on adaptive fuzzy logic system and nonlinear disturbance observer

A composite controller based on a backstepping controller with an adaptive fuzzy logic system and a nonlinear disturbance observer is proposed in this paper to address the disturbance and uncertainty issues in the control of the optoelectronic stabilized platform. The matched and unmatched disturbances and system uncertainty are included in the stabilized platform model. The system's uncertainty and disturbance are approximated and estimated using an adaptive fuzzy logic system and a nonlinear disturbance observer. Moreover, the backstepping control algorithm is utilized to control the system. The simulations are performed in four states to confirm the viability of the proposed control technique. The proportional integral controller, proportional integral-disturbance observer controller, and fuzzy backstepping controller are contrasted with the proposed controller. It has been noted that the proposed controller's instantaneous disturbance's highest value is 5.1°/s. The maximal value of the coupling output for the two gimbals utilizing the proposed controller, however, is 0.0008°/s and 0.0018°/s, respectively. The findings presented here demonstrate that the backstepping controller, which is based on an adaptive fuzzy logic system and a nonlinear disturbance observer, is capable of precise tracking and dynamic tracking of a stabilized platform under disturbance and uncertainty.