Nonlinear Saturation Research Articles

Asynchronous H∞ Control for Continuous-Time Hidden Markov Jump Systems With Actuator Saturation.

In this article, we address the asynchronous H∞ control problem of a class of hidden Markov jump systems (HMJSs) subject to actuator saturation in the continuous-time domain. A bunch of convex hulls is utilized to represent the saturated nonlinearity. Considering that there is an asynchronous mode mismatch between the system and the controller, we establish a hidden Markov model (HMM) to simulate the situation. By means of the Lyapunov theory, sufficient conditions are presented to ensure that the resultant closed-loop HMJS is stochastically mean square stable within the domain of attraction with a prescribed H∞ performance index. Furthermore, the state feedback gain matrix and the estimation of the domain of attraction are given by solving an optimization problem, which is constructed via linear matrix inequality (LMI) techniques. Finally, the reliability and validity of the derived results are examined by a numerical example.

Frequency‐Modulated Combs via Field‐Enhancing Tapered Waveguides

AbstractFrequency‐modulated (FM) combs feature flat intensity spectra with a linear frequency chirp, useful for metrology and sensing applications. Generating FM combs in semiconductor lasers generally requires a fast saturable gain, usually limited by the intrinsic gain medium properties. Here, it is shown how a spatial modulation of the laser gain medium can enhance the gain saturation dynamics and nonlinearities to generate self‐starting FM combs. This is demonstrated with tapered planarized terahertz (THz) quantum cascade lasers (QCLs). While simple ridge THz QCLs typically generate combs presenting a mixture of amplitude and frequency modulation, the on‐chip field enhancement resulting from extreme spatial confinement leads to an ultrafast saturable gain regime, generating a pure FM comb with a flatter intensity spectrum and a clear linear frequency chirp. The observed linear frequency chirp is reproduced using a spatially inhomogeneous mean‐field theory model, which confirms the crucial role of field enhancement. In addition, the modified spatial temperature distribution within the waveguide results in an improved high‐temperature comb operation, up to a heat sink temperature of 115 K, with comb bandwidths of 600 GHz at 90 K. The spatial inhomogeneity leads as well to very intense radio frequency (RF) beatnotes up to ‐30 dBm and facilitates dynamic switching between various harmonic states in the same device.

Optimal tracking control for unknown nonlinear systems with uncertain input saturation: A dynamic event-triggered ADP algorithm

This paper is devoted to proposing a novel dynamic event-triggered adaptive dynamic programming (ADP) algorithm to tackle the tracking control problem of unknown nonlinear systems with uncertain input saturation. Initially, an augmented system is established to address the investigated optimal tracking control issue with a discounted cost function. An online identifier based on neural networks (NNs) is designed to recover the unknown system dynamics. Furthermore, the controller design consists of two parts, including the optimal control policy for the nominal system and the NN-based feedforward compensator. In particular, the latter leverages adaptive NN techniques to cope with uncertain input constraints which can be deemed as uncertain saturation nonlinearities. A critic NN is constructed to obtain the approximate optimal control policy for the nominal system. Moreover, rather than traditional time-triggered and static event-triggered control schemes, an adaptive dynamic event-triggering condition is designed to determine the system sampling as well as the controller execution to further reduce transmission and computation burden. The introduction of an internal dynamic variable in possession of a positive constant lower bound can realize the dynamic adjustment of triggering threshold and effectively exclude Zeno behavior. Notice that the weights of identifier NN and critic NN are updated simultaneously, only at the event-triggering instants. Subsequently, the Lyapunov-based theoretical analysis is conducted to confirm the uniform ultimate boundedness of the tracking error and all the NN weight estimation errors. Eventually, the feasibility and effectiveness of the developed algorithm are validated by means of two simulation examples.

Reinforcement learning-based saturated adaptive robust output-feedback funnel control of surface vessels in different weather conditions

This article tackles the problem of saturated adaptive robust actor–critic learning PID tracking control design guaranteeing a prescribed funnel performance for ships with multiple dead bands in which the ship’s velocities/accelerations and dynamic parameters are unknown and time-variant subject to the availability of external disturbances. The controller is proposed by integrating an observer, adaptive actor–critic multi-layer neural networks, generalized saturation functions, the prescribed performance funnel control, an adaptive robust controller and multiple dead bands. The observer calculates the estimation of ship’s velocities/accelerations, in which the peaking phenomenon is prevented by limiting the observer signals. Within the structure of adaptive actor–critic design, adaptive multi-layer neural networks are exerted, which counteracts against ship’s time-variant uncertainties and the actuator saturation nonlinearity. In order to reduce the likelihood of actuator saturation well, generalized saturation functions are taken into account. To realize prespecified transient and steady-state performance of the tracking errors, the prescribed performance control is applied. With the purpose of avoiding the corner cutting to increase the trajectory tracking accuracy, curvature of the circular trajectories is calculated and the angle of arc is compensated. An adaptive robust controller is utilized to resist against external disturbances, and a scheme of multiple dead bands is devised in this paper to protect the actuator system in heavy seas.

Discrete-time state delayed systems with saturation arithmetic: overflow oscillation-free realization

ABSTRACT In many smart systems, such as cloud computing, networked control, manufacturing, and telecommunication, the effects of time delays are unavoidable. Saturation nonlinearity is common in many smart systems (e.g. electric systems with limited actuator power supplies, mechanical systems with position and speed constraints, fixed-point digital filters, etc.). Therefore, the study of stability of discrete-time systems (DTSs) with time delay and saturation is of high importance in practice. The global asymptotic stability (GAS) problem of such systems is investigated in this paper. The saturation nonlinearity is constrained by a convex hull with a free matrix whose infinity norm is smaller than or equal to unity. A new Lyapunov-based GAS criterion for DTSs with time-varying delay and state saturation is established. The GAS problem for DTSs with constant delay and saturation is also discussed. The obtained results can be used to ensure the absence of overflow oscillations in the considered system. In comparison to several existing criteria, the approach yields improved stability results. An example is provided to demonstrate the importance of the presented results.

Highly nonlinear optic nucleic acid thin-solid film to generate short pulse laser

Using aqueous precursors, we report successfully fabricating thin-solid films of two nucleic acids, ribonucleic acid (RNA) and deoxyribonucleic acid (DNA). We investigated the potential of these films deposited on a fiber optic platform as all-fiber integrated saturable absorbers (SAs) for ultrafast nonlinear optics. RNA-SA performances were comparable to those of DNA-SA in terms of its nonlinear transmission, modulation depth, and saturation intensity. Upon insertion of these devices into an Erbium-doped fiber ring-laser cavity, both RNA and DNA SAs enabled efficient passive Q-switching operation. RNA-SA application further facilitated robust mode-locking and generated a transform-limited soliton pulse, exhibiting a pulse duration of 633 femtoseconds. A detailed analysis of these pulsed laser characteristics compared RNA and DNA fiber optic SAs with other nonlinear optic materials. The findings of this research establish the feasibility of utilizing RNA as a saturable absorber in ultrafast laser systems with an equal or higher potential as DNA, which presents novel possibilities for the nonlinear photonic applications of nucleic acid thin solid films.

The Wave Growth, Saturation, and Electron Heating of Lower Hybrid Waves in the Magnetic Reconnection Exhaust

Lower hybrid waves are commonly observed in magnetic reconnection. Based on in situ measurements and the application of an extended quasi-linear model, we investigate the occurrence, saturation, and electron heating of lower hybrid waves in the region of magnetopause reconnection outflows. Lower hybrid waves are statistically favored when the density gradient length scale (L n ) normalized by the ion gyroradius (ρ i ) is small. The occurrence of lower hybrid waves is significantly higher in the regime of L n /ρ i < 1 and plasma beta β < 1. These features of wave occurrence are consistent with the linear theory of the wave growth rate. Evidence indicates that the saturation level and the parallel electron heating of waves both increase as the normalized gradient scale L n /ρ i decreases. The parallel electron temperature increases ∼30%–70% as L n /ρ i < 1. We show that the observation of saturation and electron heating is consistent with an extended quasi-linear model. In this scenario, lower hybrid waves are driven by density gradients and then quickly saturate in tens of ion gyroperiods. The parallel electron heating from lower hybrid waves is achieved through Landau damping before the nonlinear saturation. Our results provide comprehensive evidence for an end-to-end process of electron heating through lower hybrid waves in reconnection exhausts. L n /ρ i is the key parameter that determines the extent of the wave growth, saturation energy, and electron heating in this wave–particle interaction process.

A Fuzzy-Logic-System-Based Cooperative Control for the Multielectromagnets Suspension System of Maglev Trains With Experimental Verification

A maglev train is a sustainable public transport method with the characteristics of being green, pollution-free, and low-noise, as well as providing environmental protection. However, the performance of existing maglev control strategies for maglev trains may be deteriorated by various challenges, including disregard of the coordination and synchronization between multiple electromagnets, control input unidirectionality, dead zones, saturation, and finite time stability ability, etc. In this paper, an adaptive fuzzy-based suspension control method based on a multi-electromagnets dynamic coupling model is proposed that can cope with dead zone and saturation problems and guarantee the finite-time of the airgap tracking errors of multiple electromagnets simultaneously. Specifically, a fuzzy-logic system (FLS) is utilized to compensate for the nonlinear input unidirectionality, dead zone, saturation and unmodeled dynamics. Moreover, considering the coupling dynamic characteristics of adjacent electromagnet control modules, a fuzzy-based cooperative suspension controller with adaptive update law is designed. The finite time stability of the presented control strategy is proven with the Lyapunov method. Finally, the suspension frame experimental results are illustrated to validate the effectiveness and robustness of the developed method, whose superior performance is shown by being experimentally compared with some baseline methods.

Distributed Adaptive-Neural Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems Subject to Saturated Inputs.

In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.

The Effect of Hydrogen on Nonlinear Flame Saturation

Abstract We investigate the effect of increasing levels of hydrogen enrichment on the nonlinear response and saturation of premixed bluff-body stabilized methane/hydrogen flames submitted to acoustic forcing. The thermal power is kept approximately constant to preserve the nozzle velocity while increasing the flame speed through hydrogen enrichment. The flame describing function (FDF) is measured for a fixed frequency and three hydrogen–methane blends ranging from 10% to 50% by power, corresponding to 25% to 75% by volume. We show that when the flame is forced at the same frequency at similar power and bulk velocities, increasing levels of hydrogen enrichment increase the saturation amplitude of the flame. To provide insight into the flame dynamics responsible for the change in the global nonlinear response and saturation amplitude, the flames were investigated using high-speed imaging in combination with OH planar laser-induced fluorescence (OH-PLIF) at a range of forcing amplitudes. At lower hydrogen concentrations, the flame is stabilized along the inner shear layer and saturation in the heat release rate (HRR) occurs at lower forcing amplitudes due to large-scale flame–vortex interactions causing flame annihilation as observed in several previous studies. At increased levels of hydrogen enrichment, distinctly different flame dynamics are observed. In these cases, the flame accelerates and propagates across to the outer shear layer, which acts to suppress large-scale flame annihilation during roll-up of both the inner and outer shear layers. This results in a coherent increase in flame surface area with forcing amplitudes significantly increasing the saturation amplitude of the flame. These results show that high levels of hydrogen increase the amplitude response to acoustic forcing leading to higher saturation amplitudes. This suggests that substituting natural gas with hydrogen in gas turbines increases the risk of much higher limit-cycle amplitudes if self-excited instabilities occur.

Nonlinear saturation of resistive tearing modes in a cylindrical tokamak with and without solving the dynamics

We show that the saturation of resistive tearing modes in a cylindrical tokamak, as well as the corresponding island width, can be directly calculated with a magnetohydrodynamics (MHD) equilibrium code without solving the dynamics and without considering resistivity. The results are compared with initial-value resistive MHD simulations and to an analytical nonlinear theory. For small enough islands, the agreement is remarkable. For sufficiently large islands, the equilibrium calculations, which assume a flat current profile inside the island, overestimate the saturation amplitude. On the other hand, excellent agreement between nonlinear resistive MHD simulations and nonlinear theory is observed for all the considered tearing unstable equilibria.

Bipartite Consensus of Heterogeneous Multi-Agents Under Input Saturation Over Signed Graphs

This brief addresses the problem of bipartite consensus for linear multi-agent systems (MASs) with heterogeneous dynamics susceptible to input saturation over a signed graph under antagonistic interactions. Prior to extending the findings to directed signed graphs, a theoretical examination of the bipartite consensus for undirected signed graphs is conducted. Input saturation is addressed by using a generalized sector condition. With the aid of the Lyapunov theory, it has been shown that for the MASs with heterogeneous dynamics stability and bipartite consensus can be accomplished. To the best of our knowledge, a bipartite consensus control approach for heterogeneous MASs with input saturation nonlinearity, connected via directed signed graphs, has been considered for the first time. The validity of the given results is demonstrated by a numerical example.

Nonlinear verification of the resistive-wall boundary modules in the specyl and pixie3d magneto-hydrodynamic codes for fusion plasmas

A nonlinear verification benchmark is reported between the three-dimensional magneto-hydrodynamic (3D MHD) codes specyl [Cappello and Biskamp, Nucl. Fusion 36, 571 (1996)] and pixie3d [Chacón, Phys. Plasmas, 15, 056103 (2008)]. This work substantially extends a former successful verification study between the same two codes [Bonfiglio et al., Phys. Plasmas, 17, 082501 (2010)] and focuses on the verification of thin-shell resistive-wall boundary conditions, recently implemented in both codes. Such boundary conditions feature a thin resistive shell in contact with the plasma and an ideal wall placed at a finite distance, separated from the resistive shell by a vacuum region, along with a 3D boundary flow consistent with Ohm’s law. This setup allows the study of MHD modes that are influenced by the plasma magnetic boundary, such as external kink modes. The linear growth and nonlinear saturation of external kink modes are studied in both the tokamak and reversed-field pinch magnetic configurations, demonstrating excellent agreement between the two codes. For the tokamak, we present a comparison with analytical linear stability results for the external kink mode, demonstrating remarkable agreement between numerical and analytical growth rates.

Steady states of the Parker instability

ABSTRACT We study the linear properties, non-linear saturation, and a steady, strongly non-linear state of the Parker instability in galaxies. We consider magnetic buoyancy and its consequences with and without cosmic rays. Cosmic rays are described using the fluid approximation with anisotropic, non-Fickian diffusion. To avoid unphysical constraints on the instability (such as boundary conditions often used to specify an unstable background state), non-ideal magnetohydrodynamic equations are solved for deviations from a background state representing an unstable magnetohydrostatic equilibrium. We consider isothermal gas and neglect rotation. The linear evolution of the instability is in broad agreement with earlier analytical and numerical models; but we show that most of the simplifying assumptions of the earlier work do not hold, such that they provide only a qualitative rather than quantitative picture. In its non-linear stage the instability has significantly altered the background state from its initial state. Vertical distributions of both magnetic field and cosmic rays are much wider, the gas layer is thinner, and the energy densities of both magnetic field and cosmic rays are much reduced. The spatial structure of the non-linear state differs from that of any linear modes. A transient gas outflow is driven by the weakly non-linear instability as it approaches saturation.

Charged biexciton polaritons sustaining strong nonlinearity in 2D semiconductor-based nanocavities

Controlling the interaction between light and matter at micro- and nano-scale can provide new opportunities for modern optics and optoelectronics. An archetypical example is polariton, a half-light-half-matter quasi particle inheriting simultaneously the robust coherence of light and the strong interaction of matter, which plays an important role in many exotic phenomena. Here, we open up a new kind of cooperative coupling between plasmon and different excitonic complexes in WS2-silver nanocavities, namely plasmon-exciton-trion-charged biexciton four coupling states. Thanks to the large Bohr radius of up to 5 nm, the charged biexciton polariton exhibits strong saturation nonlinearity, ~30 times higher than the neutral exciton polariton. Transient absorption dynamics further reveal the ultrafast many-body interaction nature, with a timescale of <100 fs. The demonstration of biexciton polariton here combines high nonlinearity, simple processing and strong scalability, permitting access for future energy-efficient optical switching and information processing.

Stimulated Raman blockade in coherent phonon generation

We theoretically investigate the behavior of coherent optical phonons in an electron–phonon coupled system at moderate laser intensity: below GW/cm2. We calculate the coherent phonons from impulsive stimulated Raman scattering (ISRS) and impulsive absorption (IA) mechanisms with a nonperturbative model. The generation efficiency of coherent phonons in single-pulse excitation exhibits gradual nonlinear saturation with increasing optical intensity in a nonperturbative regime. The ISRS mechanism exhibits substantial saturation at relatively low pulse intensity, whereas the IA mechanism remains roughly linear. We further examine the influence of double-pulse excitation on quantum path interference. The ISRS mechanism exhibits a pronounced saturation effect near 0 fs of pump–pump delay, whereas the IA process exhibits negligible saturation behavior. These results reproduce well experimental data obtained by double-pulse excitation and support our proposal that ISRS is the primary quantum path for the observed coherent phonons in gallium arsenide.

Adaptive event-triggered filtering for semi-Markov jump systems under communication constraints

This paper investigates the problem of adaptive event-triggered filtering for a class of semi-Markov jump systems. A more general scenario of semi-Markov jump systems under communication constraints is explored, where the output signal occurs with saturation nonlinearity, packet loss, and quantization. The saturation nonlinearity and packet dropout are described by two random variables subject to Bernoulli distribution. The mode-dependent adaptive event-triggered mechanism is designed by combining the system mode information. Based on the output error, the trigger threshold adaptive law is designed to make the threshold change dynamically. The mode-dependent time-varying filter is constructed and sufficient conditions for the desired filter with H∞ performance are obtained. Finally, a single-link robot arm system verifies the effectiveness of the proposed filter design method, and the adaptive event-triggered protocol can effectively reduce the number of data transmissions.

Performance-enhanced time-delayed photonic reservoir computing system using a reflective semiconductor optical amplifier.

We propose a time-delayed photonic reservoir computing (RC) architecture utilizing a reflective semiconductor optical amplifier (RSOA) as an active mirror. The performance of the proposed RC structure is investigated by two benchmark tasks, namely the Santa Fe time-series prediction task and the nonlinear channel equalization task. The simulation results show that both the prediction and equalization performance of the proposed system are significantly improved with the contribution of RSOA, with respect to the traditional RC system using a mirror. By increasing the drive current of the RSOA, the greater nonlinearity of the RSOA gain saturation is achieved, as such the prediction and equalization performance are enhanced. It is also shown that the proposed RC architecture shows a wider consistency interval and superior robustness than the traditional RC structure for most of the measured parameters such as coupling strength, injection strength, and frequency detuning. This work provides a performance-enhanced time-delayed RC structure by making use of the nonlinear transformation of the RSOA feedback.

Improved Stability and Passivity Results for Discrete Time-Delayed Systems with Saturation Nonlinearities and External Disturbances

Improved Stability and Passivity Results for Discrete Time-Delayed Systems with Saturation Nonlinearities and External Disturbances

Nonlinear saturation of whistler modes driven by runaway electrons

Runaway electrons exhibit kinetic instabilities with potentially beneficial consequences. The anomalous Doppler resonance between the electrons and whistler modes is a primary underlying mechanism. These instabilities require a first-principle nonlinear theoretical analysis, which would ultimately enable assessment of their impact on disruption mitigation and diagnostics, especially in ITER-relevant conditions. This paper presents recent progress in developing the required theoretical framework for isolated nonlinear resonances. By employing the generic bump-on-tail model, we predict the wave saturation levels in both near-threshold and strongly driven regimes. Remarkably, for the waves of interest, the parallel component of the wave vector dictates the parallel momentum of the resonant particles. This feature, together with the expected wave saturation level, provides a complete description of the resonance impact on the runaway electron distribution function. We show that the parametric dependence of the nonlinearly saturated mode provides a way to recover certain features of the runaway momentum distribution function.