Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone.

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

In this paper, an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict-feedback systems without the requirement of states measurement. The stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties (unknown nonlinear functions) and, in the presence of unmodeled dynamics, dynamics disturbances. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique with the stochastic small-gain approach, a new adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) 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. Simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance. In addition, the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the 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.

In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme 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, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients.

Adaptive fuzzy tracking controller design is addressed for a class of uncertain nonlinear system in strict-feedback form. The system dynamics are unknown, and external disturbances satisfy triangular bounds. We utilize Tagaki-Sugeno (T-S) fuzzy logic system to approximate the unknown system functions. The proposed scheme can guarantee the ultimate uniform boundedness of all the signals in the closed-loop system. Compensated tracking errors are employed to construct Lyapunov candidate function. The proposed design circumvents the repeated differential of virtual control law, which renders the controller structures simple and easy to implement. Simulation researches are carried out. The simulation results demonstrate the effectiveness and usage of the proposed design.

Finite-time stabilization of stochastic nonlinear systems in strict-feedback form

In this paper, by incorporating this dynamic structure control technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of explosion of complexity inherent in the existing method. Taking the neural network as a model of the system, control signals are directly obtained by minimizing the cumulative differences between a setpoint and output of the model. The applicability in nonlinear system is demonstrated by simulation experiments.

In this paper, an adaptive fuzzy robust output feedback control problem is considered for a class of single-input and single-output nonlinear systems in a strict-feedback form. The considered systems possess the unstructured uncertainties, unknown dead zone, and the dynamics uncertainties, and they do not assume the states being available for the controller design. In the controller design, fuzzy logic systems are first used to approximate the unstructured uncertainties, and by utilizing the information of the bounds of the dead-zone slopes and treating the time-varying inputs coefficients as a system uncertainty, a fuzzy state observer is designed to estimate the unmeasured states. By combining a backstepping technique with a nonlinear small-gain approach, a new adaptive fuzzy robust output feedback control has been developed. It is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed-loop systems. Simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach.

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

In this paper, a novel robust adaptive tracking control approach is presented for a class of strict-feedback single-input single-output nonlinear systems. By employing radial basis function neural network to account for system uncertainties, the proposed scheme is developed by combining “command filter” and “minimal learning parameter” techniques. The main advantages of the proposed controller are that: (1) the problem of “explosion of complexity” inherent in the conventional backstepping method is avoided; (2) the problem of “dimensionality curse” is solved, and only one adaptive parameter needs to be updated online. These advantages result in a much simpler adaptive control algorithm, which is convenient to implement in applications. In addition, stability analysis shows that uniform ultimate boundedness of the solution of the closed-loop system can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.

In this paper, a partial tracking error constrained fuzzy output-feedback dynamic surface control (DSC) scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design. With the help of fuzzy logic systems identifying the MIMO unknown nonlinear systems, a fuzzy adaptive observer is established to estimate the unmeasured states. By transforming the tracking errors into new virtual error variables and based on the DSC backstepping recursive design technique, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds. The simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme.

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults based on dynamic surface technique

This paper presents a finite-time fault-tolerant fuzzy adaptive controller for uncertain interconnected nonlinear systems in strict-feedback form. The controller addresses input saturation, state-dependent actuator faults, external disturbances, and unavailable states for measurement. To avoid any unexpected alteration due to failures, the proposed control scheme design addresses all types of actuator faults that are bias, drift, and loss of accuracy as additive faults, as well as a multiplicative fault that results in loss of effectiveness with nonaffine state-dependency. Restrictions on control gains and unmatched interconnections are eliminated, and the explosion complexity caused by recursive back-stepping designs is avoided. Fuzzy Systems approximate the unknown ideal control laws along side the acutator faults and disturbances. The stability analysis guarantees that tracking errors converge to a small compact set around the origin in finite time. Simulation results on a quad-rotor UAV and a mathematical system confirm the effectiveness of the proposed approach.

SUMMARY This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict-feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non-switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.