Springer Science and Business Media LLC

This paper studies the adaptive neural fault-tolerant control (FTC) problem of a class of switched nonstrict-feedback nonlinear systems (NFNSs) via adopting the hierarchical sliding mode control (HSMC) method and the average dwell time (ADT) switching strategy. First, the original system is transformed into a new system with unknown compound nonlinear functions. Then, by utilizing the robust approximation capability of neural networks (NNs), the compound nonlinear functions are identified online. Furthermore, a novel hierarchical sliding mode surface-based adaptive neural fault-tolerant controller is designed, in which the denominator singular issue is successfully handled by using a modified projection algorithm. By means of the Lyapunov stability theory, it is proved that the proposed control method can ensure the boundedness of all signals of the considered NFNS. Eventually, a practical continuous stirred tank reactor example is given to verify the validity of the proposed HSMS-based adaptive neural FTC method.

We made an attempt to provide a realistic picture of the localization of energy in microtubules (MTs), and we intend to model the nonlinear dynamics of MTs using the “double-well” $$\phi ^4$$ form of the potential describing the dipole–dipole interactions. We investigate the modulational instability (MI) of the nonlinear plane wave solutions by considering both the wave vector (q) of the basic states and the wave vector (Q) of the perturbations as free parameters. A set of explicit criteria of MI is derived, and under the plane-wave perturbation, the constant amplitude solution becomes unstable and localized discrete breathers (DBs) solutions appear. We show numerically that MI is also an indicator of the presence of discrete breathers. We suggest that an electric field favourably leads the DB excitations towards the properly aligned end triggering a dissembly of the protofilament due to the energy release. These DBs could catalyse MT-associated proteins attachment/detachment and promote or inhibit the kinesin walk. We establish that the electromechanical vibrations in MTs can generate an electromagnetic field in the form of an electric pulse (breathers) which propagates along MT serving as signalling pathway in neuronal cells. The DBs in MT can be viewed as a bit of information whose propagation can be controlled by an electric filed. They might perform the role of elementary logic gates, thus implementing a subneuronal mode of computation. The generated DBs present us with novel possibilities for the direct interaction between the local electromagnetic field and the cytoskeletal structures in neurons. Thus, we emphasize that the effect of discreteness and electric field plays a significant role in MTs.

We study power harvesting using MEMS capacitors with single and dual air cavities that have been fabricated in our laboratory. Our goal is to achieve power harvesting from vibration sources with limited amplitude and with frequencies that are well below the resonance frequency of the fabricated device. The mathematical model includes the electrostatic forces and the forces provided by stoppers which are designed to prevent the direct contact between the capacitive plates. Global bifurcation analysis of the model illustrates the effect of the electrostatic force on the static equilibrium, the resonance frequency, and the regions of stability surrounding the equilibrium. The electrostatic forces are shown to reduce the resonance frequency at the cost of shrinking the stable domain of oscillation near the equilibrium. The inclusion of the mechanical stoppers make power harvesting still possible when the plate motion exceeds the stable domain so long as the two capacitive plates are kept at a distance to prevent the electrostatic force to dominate. Moreover, when the two plates are kept sufficiently separated, rocking instability—the instability leading to non-parallel motion between the two plates—is also prevented.

In this paper, a cascaded piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance (CPUAUTSR) system is proposed to improve the detection capability of the classical tri-stable system and addresses the output saturation problem. Firstly, it demonstrates the good unsaturated characteristics of the piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance (PUAUTSR) system. Then, the steady-state probability density (SPD), mean first passage time (MFPT) of PUAUTSR system are derived, respectively. Based on the adiabatic approximation theory, the spectral amplification (SA) coefficient of CPUAUTSR system is derived for the first time. The effects of different system parameters on the performance indexes are also investigated. The parameters are optimized using the adaptive genetic algorithm (AGA) and used to measure the stochastic resonance performance using signal-to-noise ratio (SNR). Finally, the piecewise unsaturated asymmetric over-damped tri-stable stochastic resonance (PUAOTSR) and CPUAUTSR system are applied to diagnose the fault signal of bearing. The results show that CPUAUTSR system provides better enhancement and detection of bearing fault signals. In particular, in the detection of bearing inner and outer ring faults, the SNR of the second stage CPUAUTSR system is higher than that of PUAOTSR and first stage CPUAUTSR systems by 8.107 dB, 2.733 dB, 1.879 dB, and 0.185 dB, respectively. These findings provide valuable theoretical support and application prospects for practical engineering.

Generating pseudorandom numbers with good statistical performance based on chaotic maps has become a topic of interest in chaotic cryptography. Several high-order polynomial chaotic maps with special forms are proposed by the Li–Yorke theorem in this paper, and chaotic conditions and intervals are given. The dynamical behaviors of chaotic maps satisfying the chaotic conditions are numerically analyzed, such as the bifurcation and Lyapunov exponent, the analysis results show the correctness of the related chaos criterion theorems. Chaotic maps are essential for the design of pseudorandom number generator and are widely used in many applications. Based on the superposition of chaotic maps, a pseudorandom number generator is designed, and the available chaotic parameters of the pseudorandom number generator are increased through the superposition of chaotic maps. This paper tests and analyses the performance of pseudorandom sequences produced by the pseudorandom number generator, and the analysis results show that pseudorandom sequences produced by pseudorandom number generator have good randomness, uniformity, complexity, and sensitivity to the initial parameters. Performance analyses show that the pseudorandom number generator in this paper can generate sequences with high quality. Several high-order polynomial chaotic maps we constructed based on the Li–Yorke theorem enrich the chaotic map and provide the possibility for its application in the field of cryptography.

During deepwater riserless drilling operations, the vibration behavior of drill string may have a significant impact on wellbore pressure, which leads to serious drilling accidents such as well leakage and collapse in shallow risk areas. In order to solve this problem, based on Hamilton's principle, a three-dimensional nonlinear coupling dynamics model of drill string in deepwater riserless drilling is established, taking into account the following factors: heave and offset motion of offshore platform, ocean current load, drill string-borehole contact and bit-rock interaction. The Newmark-β method is used to solve the nonlinear discrete equations of the system. The effectiveness of the model and calculation program is verified by the field test data. Meanwhile, a model of wellbore pressure field is established under the influence of axial-lateral-torsional coupling vibration of drill string. The 3D nonlinear coupling vibration characteristic of drill string and its influence on wellbore pressure fluctuation are investigated. The results indicate that the collision between the drill string system and the borehole usually occurs in the middle of the formation and at the bit, which is easy to cause drilling tools failure. The maximum pressure fluctuation along the wellbore is mainly affected by lateral vibration. The mean value of wellbore pressure fluctuation is mainly determined by torsional vibration. The results may be useful to predict the risks of well leakage and collapse in deepwater riserless drilling operations.

This paper focuses on the iterative identification problems for a class of Hammerstein nonlinear systems. By decomposing the system into two fictitious subsystems, a decomposition-based least squares iterative algorithm is presented for estimating the parameter vector in each subsystem. Moreover, a data filtering-based decomposition least squares iterative algorithm is proposed. The simulation results indicate that the data filtering-based least squares iterative algorithm can generate more accurate parameter estimates than the least squares iterative algorithm.