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.     

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.     

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.     

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 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.     

A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems

In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.     

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.     

Decentralized direct adaptive output feedback fuzzy H ∞ tracking design of large-scale nonaffine nonlinear systems

A novel H _∞ tracking-based decentralized direct adaptive output feedback fuzzy controller is developed for a class of interconnected nonaffine uncertain nonlinear systems in this paper. By virtue of the proper filtering of the observation error dynamics to assure its strictly positive realness, the observer-based decentralized direct adaptive fuzzy control (DAFC) scheme is presented for a class of large-scale nonaffine nonlinear systems by the combination of H _∞ tracking technique, implicit function theorem, a state observer and a fuzzy inference system. The output feedback and adaptation mechanisms for each subsystem depend upon local measurements not only to achieve asymptotical tracking of a reference trajectory but to guarantee arbitrary small attenuation level of the mismatched errors and external disturbances on the tracking error. Simulation results confirm the effectiveness of the proposed decentralized output feedback scheme.     

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.     

A nonlinear high gain observer based input–output control of flexible link manipulator

The input–output control strategy needs all of the states feedback. However, in flexible link robot manipulators, measuring the time rate of elastic degrees of freedom is practically impossible. In this paper, a new nonlinear high gain observer has been developed to estimate the elastic degrees of freedom and their time derivatives. The control strategy is based on an output redefinition approach which stabilizes the zero dynamics of the manipulator. Finally, the results are presented by implementing the proposed observer and controller on a single link flexible manipulator. Numerical simulations will support the validity of our research results.     

Vibration control by nonlocal feedback and jerk dynamics

Jerk dynamics is used for a new method for the suppression of self-excited vibrations in nonlinear oscillators. Two cases are considered, the van der Pol equation and nonlinear oscillator with quadratic and cubic nonlinearities. A nonlocal control force is introduced in such a way to obtain a third order nonlinear differential equation (jerk dynamics). Using the asymptotic perturbation method, two slow flow equations on the amplitude and phase of the response are obtained, and subsequently the performance of the control strategy is investigated. The feedback gains are connected with the stability and response of the system under control. Uncontrolled and controlled systems are compared and the appropriate choices for the feedback gains are found in order to reduce the amplitude peak of the self-excitations. Numerical simulation confirms the validity of the new method.     

Optimal nonlinear observers for chaotic synchronization with message embedded

This paper presents an optimal nonlinear observer for synchronizing the transmitter-receiver pair with guaranteed optimal performance. In the proposed scheme, a generalized nonlinear state-space observer via uniform matrix transformations is constructed to estimate the transmitter state and the information signal, simultaneously. A nonlinear optimal design approach is used to synchronize chaotic systems. Solving the Hamilton–Jacobi–Bellman (H–J–B) equations we can obtain a linear optimal feedback scheme for piecewise-linear chaotic systems. Moreover, a robust scheme derived from the H _∞ optimization theory improves the synchronization performance of general nonlinear chaotic systems by suppressing the influence of their high order residual terms. Finally, two numerical simulation examples are illustrated by the chaotic Chua’s circuit system and the Lorenz chaotic system to demonstrate the effectiveness of our scheme.     

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.     

Decentralized adaptive output feedback fuzzy controller for?a?class of large-scale nonlinear systems

In the previous work of Huang et al., a coordinated decentralized hybrid adaptive output feedback fuzzy control scheme of large-scale nonlinear systems is obtained predicated upon this prerequisite assumption that the local controllers can share the a priori information about their individual reference models. In this note, we concentrate in the absence of the coordination assumption on developing a classical decentralized combined indirect and direct adaptive fuzzy controller for a class of uncertain large-scale nonlinear systems. The output feedback and adaptation mechanisms proposed for each subsystem hinges just upon its individual output, regardless of any other output reference. Neither the famous strictly positive real (SPR) condition nor a high-gain observer (HGO) is required to realize the overall output feedback algorithm. The tracking errors of the closed-loop large-scale system are shown to converge to tunable neighborhoods of the origin. Simulation results on correlated inverted pendulums verify the validity of the decentralized controller modification.     

Fuzzy adaptive output feedback control for robotic systems based on fuzzy adaptive observer

In this paper, a fuzzy adaptive output feedback control scheme based on fuzzy adaptive observer is proposed to control robotic systems with parameter uncertainties and external disturbances. It is supposed that only the joint positions of the robotic system can be measured, whereas the joint velocities are unknown and unmeasured. First, a fuzzy adaptive nonlinear observer is presented to estimate the joint velocities of robotic systems, and the observation errors are analyzed using strictly positive real approach and Lyapunov stability theory. Next, based on the observed joint velocities, a fuzzy adaptive output feedback controller is developed to guarantee stability of closed-loop system and achieve a certain tracking performance. Based on the Lyapunov stability theorem, it is proved that all the signals in closed-loop system are bounded. Finally, simulation examples on a two-link robotic manipulator are presented to show the efficiency of the proposed method.     

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

     

Chaotic interaction dynamics of three structures: Two cylindrical shells nested into each other and their reinforcing local rib

This paper studies the chaotic dynamics of two cylindrical shells nested into each other with a gap and their reinforcing beam, also with a gap, which is subjected to a distributed alternating load. The problem is solved using methods of nonlinear dynamics and the qualitative theory of differential equations. The Novozhilov equations for geometrically nonlinear structures are used as the governing equations. Contact pressure is determined by Kantor’s method. Using finite elements in spatial variables, the partial differential equations for the beam and shells are reduced to the Cauchy problem, which is solved by explicit integration (Euler’s method). The chaotic synchronization of this system is studied.     

Dynamics and control of a self-sustained electromechanical seismographs with time-varying stiffness

This paper is concerned with the nonlinear dynamics and vibration control of an electromechanical seismograph system with time-varying stiffness. The instrument consists of an electrical part coupled to mechanical one and is used to record the vibration during earthquakes. An active control method is applied to the system based on cubic velocity feedback. The electromechanical system is subjected to parametric and external excitations and modeled by a coupled nonlinear ordinary differential equations. The method of multiple scales is used to obtain approximate solutions and investigate the response of the system. The results of perturbation solution have been verified through numerical simulations, where different effects of the system parameters have been reported.     

Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters

The problem of output feedback control for a class of second-order nonlinear systems is investigated in this paper. Using the techniques of finite-time control and finite-time convergent observer, an observer-based finite-time output feedback controller is proposed which can guarantee that the system’s state converges to the equilibrium in a finite time. As an application of the proposed theoretical results, the problem of finite-time control without current signal for the DC–DC buck converters is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.