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This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.

The article presents an adaptive fuzzy control approach to the problem of control of electrostatically actuated MEMS, which is based on differential flatness theory and which uses exclusively output feedback. It is shown that the model of the electrostatically actuated MEMS is a differentially flat one and this permits to transform it to the so-called linear canonical form. For the new description of the system's dynamics the transformed control inputs contain unknown terms which depend on the system's parameters. To identify these terms an adaptive fuzzy approximator is used in the control loop. Thus an adaptive fuzzy control scheme is implemented in which the unknown or unmodeled system dynamics is approximated by neurofuzzy networks and next this information is used by a feedback controller that makes the electrostatically activated MEMS converge to the desirable motion setpoints. This adaptive control scheme is exclusively implemented with the use of output feedback, while the state vector elements which are not directly measured are estimated with the use of a state observer that operates in the control loop. The learning rate of the adaptive fuzzy system is suitably computed from Lyapunov analysis, so as to assure that both the learning procedure for the unknown system's parameters, the dynamics of the observer and the dynamics of the control loop will remain stable. The Lyapunov stability analysis depends on two Riccati equations, one associated with the feedback controller and one associated with the state observer. Finally, it is proven that for the control scheme that comprises the feedback controller, the state observer and the neurofuzzy approximator, an H-infinity tracking performance can be achieved. The functioning of the control loop has been evaluated through simulation experiments.

In this paper, a novel adaptive fuzzy variable-structure control approach is proposed for a class of multivariable nonaffine uncertain systems subject to dynamic nonlinear disturbances and actuator nonlinearities (dead zone and sector nonlinearities). By using the Taylor series expansion, an equivalent model in affine-like form is first derived for the nonaffine system. Then after, an adaptive fuzzy variable-structure controller is designed based on this affine-like equivalent model. The adaptive fuzzy systems are used to appropriately approximate the unknown nonlinear functions. The so-called SDU decomposition of the control gain matrix is exploited in the controller design and the stability analysis. It is proved that the proposed adaptive fuzzy control scheme can guarantee that all involved signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Finally, simulation results are presented to illustrate the effectiveness of this adaptive control system.

In this paper, a new direct adaptive controller for nonlinear SISO systems with unknown control gain sign is investigated. The controller design is based on the approximation capability of fuzzy systems. A Nussbaum function is incorporated in the adaptation laws 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 a Lyapunov approach. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed controller.

This paper deals with the active fault tolerant control (AFTC) problem for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems subject to sensor faults and external disturbances. The proposed AFTC method can tolerate three additive (bias, drift and loss of accuracy) and one multiplicative (loss of effectiveness) sensor faults. By employing backstepping technique, a novel adaptive backstepping-based AFTC scheme is developed using the fact that sensor faults and system uncertainties (including external disturbances and unexpected nonlinear functions caused by sensor faults) can be on-line estimated and compensated via robust adaptive schemes. The stability analysis of the closed-loop system is rigorously proven using a Lyapunov approach. The effectiveness of the proposed controller is illustrated by two simulation examples.

In this paper, a projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive controller is investigated for a projective synchronization of uncertain multivariable chaotic systems. The adaptive fuzzy-logic systems are used to approximate the unknown functions. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. 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 synchronization errors to an adjustable region. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

In this paper, a projective synchronization scheme for a class of master–slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. To practically achieve this synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed projective synchronization scheme.

In this paper, a novel stable adaptive fuzzy sliding–mode controller (AFSMC) is investigated for a class of uncertain underactuated nonlinear dynamic systems. The underactuated system is decoupled into two subsystems. In the controller design, a sliding surface for each subsystem is defined and a suitable adaptive fuzzy system is used to reasonably approximate the uncertain functions. The stability of the closed-loop system is proven by Lyapunov approach. The effectiveness of the proposed AFSMC is illustrated throughout simulation results.

In this paper, an adaptive fuzzy variable structure control approach is developed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The MIMO system under study is a strict-feedback uncertain nonlinear system with non-symmetric input nonlinearities. Variable structure control (VSC) technique in combination with backstepping is proposed to tackle the input saturation and dead-zone. The adaptive fuzzy systems are used to appropriately approximate the unknown nonlinear functions. The so-called SDU decomposition of the control gain matrix is exploited in the controller design and the stability analysis. It is proved that the proposed adaptive fuzzy control scheme can guarantee that all involved signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighbourhood of the origin. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

A fuzzy approximation-based indirect adaptive control is investigated for a class of unknown non-affine non-linear systems with unknown control direction. An equivalent model in affine-like form is first derived for the original non-affine system by using a Taylor series expansion. Next, a fuzzy indirect adaptive control is designed based on this affine-like equivalent model. In this control scheme, the adaptive fuzzy systems are used to appropriately approximate the equivalent affine model’s unknown non-linearities, whereas the Nussbaum gain function is used to deal with the unknown control directions (being closely related to the sign of control gain matrix). A decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis. It is proven that, under some appropriate assumptions, the proposed control scheme can achieve that all the signals in the closed-loop control system are bounded and the tracking errors converge to a small neighbourhood around zero. Effectiveness of the developed scheme is illustrated by two simulation examples.

Chaos in nonlinear dynamics occurs widely in physics, chemistry, biology, ecology, secure communications, cryptosystems and many scientific branches. Chaotic systems have important applications in science and engineering. In this work, we derive a twelve-term novel 4-D hyperchaotic system by introducing a state feedback control to the 3-D chemical chaotic reactor obtained by Huang, Yang, J Math Chem 38(1):107–117, 2015, [11]. The phase portraits of the twelve-term novel hyperchaotic chemical reactor system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The Lyapunov exponents of the novel hyperchaotic chemical reactor system are obtained as \(L_1 = 0.2263\), \(L_2 = 0.0365\), \(L_3 = 0\) and \(L_4 = -10.8396\). Also, the Kaplan–Yorke dimension of the novel hyperchaotic chemical reactor system is obtained as \(D_{KY} = 3.0240\). Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic system with unknown parameters. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical hyperchaotic systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work.

International audience; 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.

In this paper, a novel adaptive fuzzy backstepping control scheme is developed for induction machines with unknown model, uncertain load-torque and nonlinear friction. fuzzy systems are used to online approximate the uncertain nonlinearities and an adaptive backstepping technique is employed to systematically construct the control law. The proposed adaptive fuzzy controller guarantees the tracking error converge to a small neighborhood of the origin and the boundedness of all closed-loop signals. These neuro-fuzzy systems are adjusted on-line according to some adaptation laws deduced from the stability analysis in the sense of Lyapunov. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

In this paper, a practical projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive slave chaotic system subject to dead-zone nonlinearity in the input channel is proposed using only the measurable output of the master system thanks to a suitable observer. A practical projective synchronization between the master and slave systems is achieved by an adequate fuzzy adaptive control system. The underlying parameter adaptation design as well as stability analysis are carried out using a Lyapunov based approach. Unlike the previous works, in the design of the proposed synchronization scheme, we do not require to know the uncertainties function and that the dynamics of the original synchronization error are strictly positive real (SPR). In fact, herein, the uncertainties function is estimated by a fuzzy adaptive system and the dynamics of the original synchronization error are augmented by a low pass filter designed to satisfy the SPR condition. Simulation results are given to show the effectiveness of the proposed practical projective synchronization scheme.

International audience; 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.

This work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. A qualitative analysis of the properties of the novel 4-D hyperchaotic system is presented. A special feature of our novel hyperchaotic system is that it has three equilibrium points of which two are unstable and one is locally asymptotically stable. The Lyapunov exponents of the novel hyperchaotic system are obtained as L1 = 1.5146, L2 = 0.2527, L3 = 0 and L4 = -12.7626. The Kaplan-Yorke dimension of the novel hyperchaotic system is derived as DKY. = 3.1385. Next, this work describes the design of an adaptive controller for the global hyperchaos synchronisation of identical novel hyperchaotic systems with unknown parameters. MATLAB simulations are shown to describe all the main results derived in this work.

International audience; In this article, the direct adaptive fuzzy control problem is investigated for a class of general non-linear systems with zero dynamics. The direct adaptive fuzzy controller is developed based on a unified observer which is used to estimate the time derivatives of the output. 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-based observers, namely for the usual high-gain observers and the sliding-mode observers together with their implementable versions. By using a general error function, and without resorting to the famous strictly positive real condition or the filtering of the observation error, a general proportional-integral (PI) law for updating the fuzzy parameters is proposed. Ultimately boundedness of the error signals is shown through Lyapunov's direct method. Theoretical results are illustrated through two simulation examples.

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.

This paper proposes a fuzzy approximation-based adaptive sliding-mode controller for uncertain nonlinear perturbed underactuated systems. The fuzzy logic system is used for approximating the unknown nonlinear functions. For estimating the parameters of the fuzzy systems and some unknown bounds, a set of adaptation laws are appropriately designed. The boundedness of all signals of the closed-loop system as well as the asymptotic convergence of the underlying tracking errors to the origin are established based on a Lyapunov analysis. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results

This paper proposes an adaptive fuzzy control system based on sliding mode like observer for a class of unknown chaotic systems. The design of the underlying update law as well as the robust control term is based on an appropriate filtering of the sliding surface. This particularly allows to overcome the output observation error filtering or the necessity of the famous SPR condition. The performances of the proposed control system are illustrated throughout a simulation results involving a Duffing forced oscillation system.

International audience; A fuzzy approximation-based indirect adaptive control is investigated for a class of unknown non-affine non-linear systems with unknown control direction. An equivalent model in affine-like form is first derived for the original non-affine system by using a Taylor series expansion. Next, a fuzzy indirect adaptive control is designed based on this affine-like equivalent model. In this control scheme, the adaptive fuzzy systems are used to appropriately approximate the equivalent affine model's unknown non-linearities, whereas the Nussbaum gain function is used to deal with the unknown control directions (being closely related to the sign of control gain matrix). A decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis. It is proven that, under some appropriate assumptions, the proposed control scheme can achieve that all the signals in the closed-loop control system are bounded and the tracking errors converge to a small neighbourhood around zero. Effectiveness of the developed scheme is illustrated by two simulation examples.

International audience; 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.

International audience; 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.

International audience; 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.

International audience; In this paper, a fuzzy adaptive control system is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with both unknown dead-zone and unknown sign of the control gain matrix (i.e. unknown control direction). To deal with the unknown sign of the control gain matrix, the Nussbaum-type function is used. In the designing of the fuzzy adaptive control scheme, we will fully exploit a decomposition property of the control gain matrix. To compensate for the effects of the dead-zone, we require neither the knowledge of dead-zone parameters nor the construction of its inverse. Simulation results demonstrate the effectiveness of the proposed control approach.

In this paper, a fuzzy adaptive control system is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with both unknown dead-zone and unknown sign of the control gain matrix (i.e. unknown control direction). To deal with the unknown sign of the control gain matrix, the Nussbaum-type function is used. In the designing of the fuzzy adaptive control scheme, we will fully exploit a decomposition property of the control gain matrix. To compensate the effects of the dead-zone, we require neither the knowledge of dead-zone parameters nor the construction of its inverse. Simulation results demonstrate the effectiveness of the approach.

In this paper, a fuzzy adaptive control system is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with both unknown backlash hysteresis and unknown sign of the control gain matrix. To deal with the unknown sign of the control gain matrix, the Nussbaum-type function is used. In the designing of the fuzzy adaptive control scheme, we will exploit a decomposition property of the control gain matrix. To compensate the effects of the backlash, we require neither the knowledge of backlash parameters nor the construction of its inverse.

In this paper, an adaptive feedback controller with observer is developed for a class of chaotic systems. This controller does not need the availability of state variables. It can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. This adaptive feedback controller is constructed with H∞ control technique. Based on Lyapunov stability theorem, the proposed adaptive feedback control system can guarantee the stability of whole closed-loop system and achieve the H∞ tracking performance as well. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems namely Duffing-Holmes system and Lur'e-like system are considered as illustrative examples.

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.