Fuzzy Backstepping Output Feedback Control Research Articles

Adaptive decentralized fuzzy output feedback tracking control for a class of nonlinear large-scale systems with input delays

In this paper, the decentralized tracking control problem of nonlinear large-scale systems with immeasurable states and unknown nonlinearities in each subsystem and their interconnections subject to input delays is proposed. Based on the universal approximation properties of fuzzy systems, a fuzzy observer is designed to estimate the inaccessible states of the system. Subsequently, by defining the appropriate change of coordinates and employing the backstepping technique, an adaptive fuzzy backstepping output feedback control scheme is proposed for nonlinear interconnected systems subject to input delays. Owing to the problem of so-called explosion of complexity that inherently arises in the design procedures of the traditional backstepping technique, an adaptive fuzzy dynamic surface output feedback control approach is also presented for this class of large-scale systems. Moreover, it is shown that the two proposed adaptive decentralized fuzzy observer-based control approaches ensure all the signals of the closed loop system uniformly ultimately bounded and the norms of the tracking errors as well as the norms of the observation errors can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are carried out on the chemical reactor recycle system to illustrate and compare the effectiveness of the two proposed approaches.

Command filter-based adaptive fuzzy backstepping control for a class of switched nonlinear systems

This paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems. The considered switched nonlinear systems contain unknown nonlinearities, the switching signals with average dwell time, and without requiring that state variables are available for measurement. Fuzzy logic systems are used to approximate the unknown nonlinearities, and a fuzzy switched state observer is designed to estimate the immeasurable states. In the framework of observer-based output feedback control design technique, and by introducing a command filter into the backstepping design algorithm, a command filter-based adaptive fuzzy backstepping output feedback control scheme is developed. The stability of the closed-loop system and the convergence of the tracking error are proved via average dwell time and multiple Lyapunov function. A numerical example is provided to illustrate the effectiveness of the proposed approach.

Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of SISO nonaffine nonlinear systems with unknown dead-zone input and immeasurable states. Within this scheme, the original nonaffine system is firstly transformed into an affine-like form by using Taylor series expansion, the unknown dead-zone input is treated as a combination of a linear and a bounded disturbance-like term, and a state observer is introduced to estimate the system states. The fuzzy logic systems are utilized to directly approximate the desire virtual control law, and a novel adaptive fuzzy output feedback controller is designed via backstepping. A main advantage of the proposed controller is that only one adaptive parameter needs to be updated online in backstepping design process. Theoretically, it is proved that the presented adaptive fuzzy controller can guarantee that the tracking error converges to a small neighborhood of the origin and all signals in closed-loop are bounded. Finally, the simulation results validate the effectiveness of the proposed scheme.

Adaptive fuzzy backstepping output feedback control for a class of uncertain stochastic nonlinear system in pure-feedback form

This paper is concerned with the problem of adaptive fuzzy output feedback for a class of uncertain stochastic pure-feedback nonlinear systems with immeasurable states. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By incorporating the filtered signals into the backstepping recursive design, a fuzzy adaptive output feedback control scheme is developed. It is proven that all the signals of the closed-loop system are bounded in probability, and also that 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 studies are included to illustrate the effectiveness of the proposed approach.

Adaptive fuzzy output feedback control of MIMO nonlinear uncertain systems with time-varying delays and unknown backlash-like hysteresis

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multi-input and multi-output (MIMO) nonlinear systems with time-varying delays and unknown backlash-like hysteresis. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and an adaptive fuzzy state observer is designed to estimate the unmeasured states. By utilizing the adaptive fuzzy observer, and combining the fuzzy adaptive control theory with backstepping approach, an adaptive fuzzy output feedback control approach is developed. The proposed control approach can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the observer error and tracking error are proved to converge to a small neighborhood of the origin. Two simulation examples are included to illustrate the effectiveness of the proposed approach.

Adaptive Fuzzy Output Feedback Tracking Backstepping Control of Strict-Feedback Nonlinear Systems With Unknown Dead Zones

In this paper, an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict-feedback systems with unknown functions, unknown dead zones, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy filters state observer is designed to estimate the immeasurable states. By using the adaptive backstepping recursive design technique and constructing the dead-zone inverse, a new adaptive fuzzy backstepping output-feedback control approach is developed. It is mathematically proved that all the signals of the resulting closed-loop adaptive control system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters. The proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement. Two simulation examples are provided to show the effectiveness of the proposed approach.

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.

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

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.

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 fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO nonlinear uncertain systems with unmeasured states and unknown virtual control coefficients. The fuzzy logic systems are used to model the uncertain nonlinear systems. The MT-filters and the state observer are designed to estimate the unmeasured states. Using backstepping design principle and combining the Nussbaum gain functions, an adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of origin. A simulation is included to illustrate the effectiveness of the proposed approach.

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.