Abdesselem Boulkroune

Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction

This paper investigates fuzzy adaptive control schemes for a class of multi-input multi-output (MIMO) unknown nonlinear systems with known and unknown sign of the control gain matrix. Three fuzzy adaptive control schemes are developed. In the design of the second and third controller, we will exploit a decomposition of the control gain matrix into a symmetric positive-definite matrix, a diagonal matrix with diagonal entries +1 or -1 and a unity upper triangular matrix. The Nussbaum-type function is used to deal with the unknown control direction (i.e. the unknown sign of the control gain matrix). For updating the parameters of the fuzzy system, an adaptation proportional-integral (PI) law is proposed. Theoretical results are illustrated through two simulation examples.

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.

Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction

This paper aims at investigating the fuzzy adaptive control design for uncertain multivariable systems with unknown actuator nonlinearities and unknown control direction that possibly exhibit time-delay. The actuator nonlinearities involve dead-zone or backlash-like hysteresis, while the control direction is closely related to the sign of the control gain matrix. Two fuzzy adaptive controllers are proposed to deal with such an issue. The design of the first controller is mainly carried out in the free time-delay case, while the second control design is performed assuming that the system exhibits time-varying delays. Of practical interest, the adaptive compensation of the effects of the actuator nonlinearities requires neither the knowledge of their parameters nor the construction of their inverse. Furthermore, the lack of knowledge of the control direction is handled by incorporating in the control law a Nussbaum-type function. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.

Adaptive fuzzy controller for multivariable nonlinear state time-varying delay systems subject to input nonlinearities

In this paper, an adaptive fuzzy variable-structure controller is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear time-delay systems with both sector nonlinearities and dead-zones. A decomposition property of the control-gain matrix is fully exploited in the controller design and the stability analysis. The unknown time-varying delay uncertainties are compensated for using an appropriate Lyapunov-Krasovskii functional. The boundedness of all signals of the closed-loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results.

On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign

In this paper, an observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign is investigated. Because the system states are not available for measurement, a tracking-error observer is constructed. In this controller, the adaptive fuzzy system is used to approximate the unknown nonlinearities and the Nussbaum function is incorporated to deal with the unknown control direction (i.e. with the unknown control gain sign). The stability of the closed-loop system is proven using the strictly positive real (SPR) condition and Lyapunov theory. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed controller.

Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay

This paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict-feedback systems with input delay and output constraint. Input delay is handled based on the information of Pade approximation and output constraint problem is solved by barrier Lypaunov function. Some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub-vectors. A novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop systems are semiglobally uniformly ultimately bounded, and the tracking error can be adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

A fuzzy adaptive variable-structure control scheme for uncertain chaotic MIMO systems with sector nonlinearities and dead-zones

In this paper, a fuzzy adaptive variable-structure controller is investigated for a class of uncertain multi-input multi-output (MIMO) chaotic systems with both sector nonlinearities and dead-zones. A suitable adaptive fuzzy system is used to reasonably approximate the uncertain functions. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the closed-loop errors to an adjustable region. The proposed controller can be applied to the systems with or without sector nonlinearities and/or dead-zones in the input. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results.

Adaptive fuzzy tracking control for a class of MIMO nonaffine uncertain systems

In this paper, a novel fuzzy adaptive controller is investigated for a class of multi-input multi-output (MIMO) nonaffine systems with unknown control direction. An equivalent model in affine-like form is first derived for the original nonaffine system by using a Taylor series expansion. Then, a fuzzy adaptive control is designed based on the affine-like equivalent model. The adaptive fuzzy systems are used to appropriately approximate the unknown nonlinearities, while the lack of knowledge of the control direction being closely related to the sign of control gain matrix is handled by incorporating in the control law a Nussbaum-type function. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. The effectiveness of the proposed fuzzy adaptive controller is illustrated through simulation results.

Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems

This paper deals with the issue of projective synchronization of two distinct fractional-order chaotic systems with the presence of both uncertain dynamics and external disturbances. More precisely, this study is an attempt to investigate a novel fuzzy adaptive controller for achieving an appropriate projective synchronization of uncertain fractional-order chaotic systems. The adaptive fuzzy systems are utilized to online estimate unknown system nonlinearities. The proposed controller, which is derived based on a Lyapunov approach, is continuous and ensures the stability of the closed-loop system and the exponential convergence of the underlying synchronization errors to a small residual set. Finally, three simulation examples are provided to verify the effectiveness of the proposed synchronization method.

Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems

This paper proposes a novel fuzzy adaptive controller for achieving an appropriate generalized projective synchronization (GPS) of two incommensurate fractional-order chaotic systems. The master system and the slave system, considered here, are assumed to be with non-identical structure, external dynamical disturbances, uncertain models and distinct fractional-orders. The adaptive fuzzy systems are used for estimating some unknown nonlinear functions. A Lyapunov approach is adopted for deriving the parameter adaptation laws and proving the stability of the closed-loop system. Under some mild assumptions, the proposed controller can guarantee all the signals in the closed-loop system remain bounded and the underlying synchronization errors asymptotically converge towards a small of neighborhood of the origin. Finally, some numerical experiment results are presented to illustrate the effectiveness of the proposed synchronization scheme.