Adaptive Fuzzy Output Feedback Control Research Articles

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.

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

In this paper, a new fuzzy adaptive control approach is developed for a class of SISO strict-feedback nonlinear systems, in which the nonlinear functions are unknown and the states are not available for feedback. By fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states. Under the framework of the backstepping design, fuzzy adaptive output feedback control is constructed recursively. It is shown that the proposed fuzzy adaptive control approach guarantees the semi-global boundedness property for all the signals of the resulting closed-loop system. Simulation results are included to illustrate the effectiveness of the proposed techniques.

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.

Direct Adaptive Fuzzy Output Feedback Control for a Class of SISO Nonlinear Systems with Unknown Control Direction

AbstractIn this paper, a direct adaptive output feedback control scheme using fuzzy systems is presented for a class of uncertain SISO nonlinear systems with unknown control direction. Within this scheme, a high-gain observer is employed to estimate the unavailable system states, a fuzzy system is employed to generate directly the control input signal with only output feedback, and the Nussbaum-type function is used to deal with the unknown control direction. The stability of the closed-loop system is performed using a Lyapunov approach. Simulation results are provided to verify the effectiveness of the proposed design.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems

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.

State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems

This paper aims to develop state observer-based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances. An adaptive fuzzy observer is proposed to estimate the system state variables. It is shown that the observation errors obtained from the observer are uniformly ultimately bounded. Applying the estimated system state for design of an output-feedback controller, the uniformly ultimate boundedness of the tracking errors for the resulting closed-loop system can be guaranteed. A typical robot arm system is employed in our simulation studies, and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances.

Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems

The output-feedback control problem of a class of uncertain SISO nonlinear systems is investigated based on an indirect adaptive fuzzy approach. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. Compared with the existing results in the observer design, the main advantages of the proposed adaptive fuzzy output-feedback control approach are as follows: (1) It does not require to assume that the sign of the control gain coefficient is known and Nussbaum-gain technique is utilized to control the nonlinear systems with both the unknown control direction and the unmeasured states; (2) The observer in this paper is designed for the states rather than the tracking errors, then it is convenient to compute; (3) The controller singularity problem is perfectly avoided. The stability of the closed-loop system is analyzed by using Lyapunov method. A simulation example is given to verify the feasibility of the proposed approach.

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy output feedback robust control is constructed recursively, in which nonlinear damping terms and a dynamical signal are introduced to counteract the nonlinear uncertainties and dominate the dynamic disturbances, respectively. It is proved that the proposed adaptive fuzzy control approach guarantees that all the signals of the closed-loop system are semi-globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.

A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.

Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems with unknown backlash-like hysteresis

An output feedback controller is proposed for a class of uncertain nonlinear systems preceded by unknown backlash-like hysteresis, where the hysteresis is modeled by a differential equation. The unknown nonlinear functions are approximated by fuzzy systems based on universal approximation theorem, where both the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. The proposed approach does not need the availability of the states, which is essential in practice, and uses an observer to estimate the states. An adaptive robust structure is used to cope with lumped uncertainties generated by state estimation error, approximation error of fuzzy systems and external disturbances. Due to its adaptive structure the bound of lumped uncertainties does not need to be known and at the same time the chattering is attenuated effectively. The strictly positive real (SPR) Lyapunov synthesis approach is used to guarantee asymptotic stability of the closed-loop system. In order to show the effectiveness of the proposed method simulation results are illustrated.

Adaptive fuzzy controller design for a class of uncertain nonlinear MIMO systems

A combined adaptive fuzzy output feedback control scheme is presented for a class of multiple-input–multiple-output (MIMO) nonlinear systems with the unmeasured states. A state observer is used to estimate the unmeasured states of the systems. The resulting closed-loop system consists of the state observer and four control components, where the control components are the combined adaptive fuzzy controller, supervisory controller, H∞ robust control item and auxiliary compensation item. Compared with the existing results in the observer design, the main advantages of this scheme are that (1) the combined adaptive fuzzy control item, which can trade off the fuzzy descriptions for controlled object rules and control action rules, is designed in the controller; (2) the proposed controller has the supervisory control performance. The stability of the closed-loop system is analyzed by using Lyapunov analysis method. Simulation results validate the effectiveness of the proposed control scheme.

Adaptive Fuzzy Output Feedback Control based on Observer for Nonlinear Heating, Ventilating and Air Conditioning System

A Heating, Ventilating and Air Conditioning (HVAC) system is a nonlinear multi-input multi-output (MIMO) system. This system is very difficult to control the temperature and the humidity ratio of a thermal space because of complex nonlinear characteristics. This paper proposes an adaptive fuzzy output feedback control based on observer for the nonlinear HVAC system. The nonlinear HVAC system is linearized through dynamic extension. State observers are designed for estimating state variables of the HVAC system. Fuzzy systems are employed to approximate uncertain nonlinear functions of the HVAC system with unavailable state variables. The obtained controller compares with an adaptive feedback controller. Simulation is given to demonstrate the effectiveness of our proposed adaptive fuzzy method.

Fuzzy adaptive observer backstepping control for MIMO nonlinear systems

In this paper, a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi-input and multi-output (MIMO) nonlinear systems with unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is designed for state estimation as well as system identification. Combining with the backstepping design techniques, a fuzzy adaptive output feedback control is constructed recursively. It is proved that the proposed fuzzy adaptive control approach can guarantee the semi-global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin. Simulation studies illustrate the effectiveness of the proposed approach.

Observer-based fuzzy adaptive control for strict-feedback nonlinear systems

In this paper, a new fuzzy adaptive control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is introduced for state estimation as well as system identification. Under the framework of the backstepping design, fuzzy adaptive output feedback control is constructed recursively. It is proven that the proposed fuzzy adaptive control approach guarantees the semi-global boundedness property for all the signals and the tracking error to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.

A unified approach for design of indirect adaptive output-feedback fuzzy controller

In this paper, an indirect adaptive fuzzy output-feedback control based on the observer is presented for Single-Input Single-Output (SISO) uncertain non-linear systems. On the basis of the estimation of the tracking error, and without resorting to the famous Strictly Positive Real condition or the filtering of the observation error, a Proportional-Integral law for updating the adjustable parameters is proposed. Then, a unified observer is used to estimate the tracking error. Indeed, the corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used High-Gain (HG)-based observers, namely, for the usual HG observers and the Sliding Modes observers together with their implementable versions. The Lyapunov synthesis approach is used to guarantee a Uniformly Ultimately Bounded property of the observation and tracking errors, as well as of all other signals in a closed-loop system. The viability and the efficiency of the obtained fundamental results are clearly illustrated through a numerical simulation involving the usual benchmark example of the fuzzy control community.

How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems

This paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer (high-gain (HG) observer, sliding mode (like) observer, etc.) for a class of single-input–single-output (SISO) uncertain or ill-defined affine nonlinear systems. Indeed, the corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used HG based observers, namely for the usual HG observers and the sliding mode observers together with their implementable versions. The design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error. This particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real (SPR) condition.

Combined indirect and direct method for adaptive fuzzy output feedback control of nonlinear system

Abstract A novel control method for a general class of nonlinear systems using fuzzy logic systems (FLSs) is presertted. Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.

Robust adaptive fuzzy control scheme for nonlinear system with uncertainty

In this paper, a robust adaptive fuzzy control scheme for a class of nonlinear system with uncertainty is proposed. First, using prior knowledge about the plant we obtain a fuzzy model, which is called the generalized fuzzy hyperbolic model (GFHM). Secondly, for the case that the states of the system are not available an observer is designed and a robust adaptive fuzzy output feedback control scheme is developed. The overall control system guarantees that the tracking error converges to a small neighborhood of origin and that all signals involved are uniformly bounded. The main advantages of the proposed control scheme are that the human knowledge about the plant under control can be used to design the controller and only one parameter in the adaptive mechanism needs to be on-line adjusted.

Fuzzy adaptive output feedback control for MIMO nonlinear systems

In this paper, two observer-based adaptive fuzzy output feedback control schemes are presented for a class of uncertain continuous-time multi-input–multi-output (MIMO) nonlinear dynamics systems whose states are not available. Within these schemes, fuzzy logic systems are employed to approximate the plant's unknown nonlinear functions and then the state observer is designed for estimating the states of the plant, upon which a fuzzy adaptive output feedback controller is firstly investigated. In order to overcome the controller singularity problem and relax the requirement of bounding parameter values, a second modified fuzzy adaptive output feedback controller is proposed by using a regularized inverse and a robustifying control term. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that convergence to zero of tracking errors and boundedness of all signals in the closed-loop system can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

Direct adaptive fuzzy output tracking control of nonlinear systems

A stable direct adaptive fuzzy output tracking control scheme is developed for the single-input–single-output (SISO) unknown nonlinear systems. Using a high-gain observer, the proposed adaptive fuzzy algorithm does not require the state variables to be measurable. First, a direct adaptive fuzzy state controller is constructed with the aid of its H ∞ control technique to achieve the H ∞ tracking performance. Afterwards, a high-gain observer is used to estimate the system states, by which the above adaptive fuzzy state controller becomes an adaptive fuzzy output feedback control. The proposed control scheme can guarantee the stability of the closed-loop system and the good tracking performance as well.