Robust adaptive sliding mode control of MEMS gyroscope using T–S fuzzy model

In this paper, a multi-input multi-output Takagi–Sugeno (T–S) fuzzy model is proposed to represent the nonlinear model of micro-electro mechanical systems (MEMS) gyroscope and improve the tracking and compensation performance. A robust adaptive sliding mode control with on-line identification for the upper bounds of external disturbances and an adaptive estimator for the model uncertainty parameters are proposed in the Lyapunov framework. The adaptive algorithm of model uncertainty parameters could compensate the error between the optimal T–S model and the designed T–S model, and decrease the chattering of the sliding surface. Based on Lyapunov methods, these adaptive laws can guarantee that the system is asymptotically stable. For the purpose of comparison, the designed controller is also implemented on the nonlinear model of MEMS gyroscope. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme on the T–S model and the nonlinear model.     

Adaptive nonsingular terminal sliding mode control for synchronization of identical Φ 6 oscillators

The main goal of this paper is to propose the adaptive nonsingular terminal sliding mode controllers for complete synchronization (CS) and anti-synchronization (AS) between two identical ?? ⁶ Van der Pol or Duffing oscillators with presentations of system uncertainties and external disturbances. Unlike directly eliminating the nonlinear items of synchronized error system for sliding mode control schemes in the literature, the proposed adaptive controllers can tackle the nonlinear dynamics without active cancellation. The controllers can be implemented without known bounds of system uncertainties and external disturbances. Meanwhile, the feedback gains are not determined in advance but updated by the adaptive rules. Sufficient conditions are given based on the Lyapunov stability theorem and numerical simulations are performed to verify the effectiveness of presented schemes. The results show that the chaotic synchronization can be achieved accurately by the chattering free control.     

Synchronization and chimeras in a network of photosensitive FitzHugh–Nagumo neurons

Nonlinear Dynamics - Recently, a photosensitive model has been proposed that takes into account nonlinear encoding and responses of photosensitive neurons that are subject to optical signals. In...     

Robust adaptive synchronization of uncertain unified chaotic systems

The problem of synchronizing a unified chaotic system in the presence of parameter variations, unstructured uncertainties, and external disturbances is addressed. To tackle such perturbations whose bounds may be unknown, two robust adaptive algorithms are proposed. The stability analysis is presented based on the Lyapunov stability theorem. Simulation results demonstrate the performance of the developed synchronization schemes.     

Two-terminal feedback circuit for suppressing synchrony of the FitzHugh–Nagumo oscillators

An extremely simple analog technique for desynchronization of neuronal FitzHugh–Nagumo-type oscillators is described. Two-terminal feedback circuit has been developed. The feedback circuit, when coupled to a network of oscillators, nullifies the voltage at the coupling node and thus effectively decouples the individual oscillators. Both numerical simulations and hardware experiments have been performed. The results for an array of three mean-field coupled FitzHugh–Nagumo-type oscillators are presented.     

Secure communication on fractional-order chaotic systems via adaptive sliding mode control with teaching–learning–feedback-based optimization

Nonlinear Dynamics - Due to the significance of secure communication, we do a research about this problem based on fractional-order chaotic systems, where a communication scheme is presented for...     

Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits

This paper presents a dual-stage control system design method for flexible spacecraft attitude maneuvering control by use of on-off thrusters and active vibration suppression by embedded smart material as actuator. As a stepping stone, an adaptive sliding mode controller with the assumption of knowing the upper bounds of the lumped perturbation is designed that ensures exponential convergence or uniform ultimate boundedness (UUB) of the attitude control system in the presence of bounded parameter variation/disturbances and control input saturation as well. Then this adaptive controller is redesigned such that the need for knowing the upper bound in advance is eliminated. Lyapunov analysis shows that this modified adaptive controller can also guarantee the exponential convergence or UUB of the system. For actively suppressing the induced vibration, linear quadratic regulator (LQR) based positive position feedback control method is presented. Numerical simulations are performed to show that rotational maneuver and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty and saturation input.     

Robust $$H_{\infty }$$ H ∞ adaptive output feedback sliding mode control for interval type-2 fuzzy fractional-order systems with actuator faults

Nonlinear Dynamics - This paper addresses the $$H_{\infty }$$ adaptive output feedback sliding mode fault-tolerant control problem for uncertain nonlinear fractional-order $$\hbox {systems}$$...     

Standing Pulse Solutions to FitzHugh–Nagumo Equations

Reaction–diffusion systems serve as relevant models for studying complex patterns in several fields of nonlinear sciences. A localized pattern is a stable non-constant stationary solution usually located far away from neighborhoods of bifurcation induced by Turing’s instability. In the study of FitzHugh–Nagumo equations, we look for a standing pulse with a profile staying close to a trivial background state except in one localized spatial region where the change is substantial. This amounts to seeking a homoclinic orbit for a corresponding Hamiltonian system, and we utilize a variational formulation which involves a nonlocal term. Such a functional is referred to as Helmholtz free energy in modeling microphase separation in diblock copolymers, while its global minimizer does not exist in our setting of dealing with standing pulse. The homoclinic orbit obtained here is a local minimizer extracted from a suitable topological class of admissible functions. In contrast with the known results for positive standing pulses found in the literature, a new technique is attempted by seeking a standing pulse solution with a sign change.     

A Topological Proof of Stability of N-Front Solutions of the FitzHugh–Nagumo Equations

Consideration is devoted to traveling N-front wave solutions of the FitzHugh–Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to detect eigenvalues.     

Logical chaotic resonance in the FitzHugh–Nagumo neuron

Nonlinear Dynamics - It has been shown recently that a chaos-driven bistable system with two square waves as input can consistently work as a reliable logic gate, in an optimal window of chaos...     

Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.     

Nonlinear dynamic analysis and sliding mode control for?a?gyroscope system

This paper employs differential transformation (DT) method to analyze and control the dynamic behavior of a gyroscope system. The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic, quasiperiodic, and chaotic responses of the center of gravity. Furthermore, the results reveal the changes which take place in the dynamic behavior of the gyroscope system as the external force is increased. The current analytical results by DT method are found to be in good agreement with those of Runge?CKutta (RK) method. In order to suppress the chaotic behavior in gyroscope system, the sliding mode controller (SMC) is used and guaranteed the stability of the system from chaotic motion to periodic motion. Numerical simulations are shown to verify the results. The proposed DT method and controlling scheme provide an effective means of gaining insights into the nonlinear dynamics and controlling of gyroscope systems.     

Rebuttal to “Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness”

A paper, “Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness,” was published in the journal Nonlinear Dynamics. The Lyapunov proof is flawed and does not prove stability for the system. It is also unclear how the simulation results in the paper were obtained using the control law. This rebuttal will demonstrate the flaws in the original paper.     

Effect of high-frequency stimulation on nerve pulse propagation in the FitzHugh–Nagumo model

We consider the FitzHugh–Nagumo model axon under action of a homogeneous high-frequency stimulation (HFS) current. Using a multiple scale method and a geometrical singular perturbation theory, we derive analytically the main characteristics of the traveling pulse. We show that the effect of HFS on the axon is determined by a parameter proportional to the ratio of the amplitude to the frequency of the stimulation current. When this parameter is increased, the pulse slows down and shrinks. At some threshold value, the pulse stops and its width becomes zero. The HFS prevents the pulse propagation when the parameter exceeds the threshold value. The analytical results are confirmed by numerical experiments performed with the original system of partial differential equations.     

Simulating the electric activity of FitzHugh–Nagumo neuron by using Josephson junction model

The resistive-capacitive-inductance Josephson junction (RCLSJ) model can simulate the electric activities of neurons. In this paper, the RCLSJ system is controlled to reproduce the dynamical properties of the FitzHugh?CNagumo system neuron by using the improved adaptive synchronization scheme. Improved Lyapunov functions with two controllable gain coefficients (??,??) is constructed, and the controller is approached analytically to realize linear generalized synchronization defined as $x=k\hat{x}+C$ . The summation of error function during the process of synchronization and the power consumption of controller are calculated in the dimensionless model to measure the effect of the two gain coefficients (??,??) by selecting different constants (k,C) to represent different kinds of generalized synchronization. The results are approached as follows: (1) the power consumption of the controller is independent of the selection of the two gain coefficients (??,??); (2) the synchronization region is marked in the phase space of the two gain coefficients; (3) the power consumption of controller is dependent on the selection of constants (k,C), smaller power consumption of the controller is required with larger k at fixed C; larger power consumption costs with larger C at fixed k. The specific case for C=0,k=1 is also discussed to understand the case for complete synchronization.     

The complete synchronization of Morris–Lecar neurons influenced by noise

The influence of noise on the complete synchronization in a Morris–Lecar (ML) model neuronal system is studied in this work. Two individual ML neurons with different initial conditions can discharge completely synchronously when the noise intensity is large enough, and for a smaller reversal potential (V _Ca), the uncoupled neuronal system could be induced to a complete synchronization state under smaller noise intensity. Two coupled ML neurons could be synchronized under very small noise intensity even in the case of weak coupling, the synchronization characteristics of the two coupled neurons are discussed by analyzing the Similarity Function (S(0)) of their membrane potentials, which proves that noise can promote the complete synchronization. The critical noise intensity (D _j ) to induce complete synchronization in coupled ML neurons will decrease with the increase of V _Ca. This result is helpful to study the synchronization and the code of a neural system.