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© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works A number of physical systems allow a complex-valued representation. This article extends the theory of sliding modes to a class of nonlinear systems described by complex-valued variables. Hence, states, parameters, control actions, and sliding manifolds belong, in general, to the complex field. In this article, it is also shown that the proposed design in the complex-valued framework provides shorter reaching times to the sliding manifold than the standard sliding-mode design at equal initial condition and control effort. Different implementation approaches are also evaluated, and numerical examples illustrate the proposal.

This paper introduces a new Takagi–Sugeno (TS) reconfiguration block structure for control reconfiguration of nonlinear systems with sensor and actuator faults represented by TS models and provides conditions for the existence of such blocks that ensures the stability recovery by fault hiding. The proposed reconfiguration block structure consists of a convex sum of linear transformations of the control signals and the sensor measurements hiding the fault occurrence from the nominal controller. Similar static reconfiguration blocks were previously proposed in the literature, however the conditions for their feasibility are more restrictive. This paper presents novel conditions based on the Lyapunov stability theory for obtaining those TS reconfiguration blocks for stability recovery after actuator and sensor faults. These conditions are obtained by assuming that the Lyapunov function that ensures the stability of fault-free closed-loop TS system is a valid Lyapunov candidate for the reconfigured TS system under faulty conditions. In particular, stability recovery conditions for nonlinear systems represented by TS models with nonlinear consequent and networked TS models are provided. Simulation results for a power system and a network of pendulum systems are used to illustrate the effectiveness of the proposed reconfiguration block.

Standard state estimation techniques, either for linear or nonlinear systems, typically assume a perfect knowledge of the system, i.e., known process and measurement functions, and the corresponding noise statistics. The filter performance strongly depends on such knowledge and a possible model mismatch may lead to a significant performance degradation, but closed-form expressions for the resulting bias and covariance are not available. In this contribution, we explore the impact in extended Kalman filter approximations of a parametric model mismatch on both system functions and provide expressions for the estimator bias and covariance error induced by the mismatch. An illustrative example is shown to support the discussion.

The dynamics of gas fluidization is investigated by means of multiresolution analysis. Empirical mode decomposition (EMD) and the Hilbert-Huang transform approach applied to the signals of pressure fluctuation of the bed have been used for this purpose, operating in bubbling and slugging regimes. To elucidate the different components of the different scales, recurrence plots (RP) and recurrence quantification analysis (RQA) have been used. These techniques can distinguish the three different scales of gas fluidization: micro-scale, meso-scale and macro-scale, and classify every mode on its scale. Three modes from the EMD have been related to each dynamic component: particle interaction, local bubble dynamics and bed oscillation, showing evidence of this relationship. To show that the complexity of the modes matches with their characteristics, two measures have been computed: the apparent entropy and Lemped–Ziv complexity.

This paper presents results to assure the almost sure stability of switching stochastic nonlinear systems. The switching rule governing the parameters of the system is driven by independent and identically distributed random variables. In this scenario, we prove that the switching nonlinear system is almost surely stable when appropriate matrices have spectral radius less than one. The result is particularly useful for applications, as shown in the paper by the application for an automotive electronic throttle device. The stability result was used to design a real-time controller for the automotive throttle device, and the experimental data confirm the usefulness of our approach.

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.

When dealing with real control experimentation, the designer has to take into account several uncertainties, such as: time variation of the system parameters, exogenous perturbation and the presence of time delay in the feedback line. In the later case, this time delay behaviour may be random, or chaotic. Hence, the control block has to be robust. In this work, a robust delay-dependent controller based on H&infin, theory is presented by employing the linear matrix inequalities techniques to design an efficient output feedback control. This approach is carefully tuned to face with random time-varying measurement feedback and applied to the Furuta pendulum subject to an exogenous ground perturbation. Therefore, a recent experimental platform is described. Here, the ground perturbation is realised using an Hexapod robotic system. According to experimental data, the proposed control approach is robust and the control objective is completely satisfied.

Assuming that many physical models can be decoupled, an anti-windup control scheme for nonlinear cascade systems is proposed. Taking into account that saturation appears frequently, in order to overcome this difficulty, an efficient control approach is developed. The paper is divided into two parts; First, the design of a cascade control system with dynamic controllers in the inner and outer loops, considering the closed-loop stability in the controller design with a suitable anti-windup compensator; Secondly, a PID cascade controller design in the inner and outer loop is presented, when the parameter tuning in both control schemes is done by particle swarm optimization (PSO). However, in this case, the implementation of an anti-windup compensator is not needed. Apart from the theoretical background, two numerical examples are shown to corroborate the provided results.

We present a set of phase-space portraits illustrating the extraordinary oscillatory possibilities of the dynamical systems through the so-called generalized Landau scenario. In its simplest form the scenario develops in N dimensions around a saddle-node pair of fixed points experiencing successive Hopf bifurcations up to exhausting their stable manifolds and generating N-1 different limit cycles. The oscillation modes associated with these cycles extend over a wide phase-space region by mixing ones within the others and by affecting both the transient trajectories and the periodic orbits themselves. A mathematical theory covering the mode-mixing mechanisms is lacking, and our aim is to provide an overview of their main qualitative features in order to stimulate research on it., Comment: 24 pages, 10 figures and 1 table. Submitted to Physica D and then to Physical Review E. Minor corrections added

DOI: 10.1063/1.4954273 Link: http://scitation.aip.org/content/aip/journal/chaos/26/9/10.1063/1.4954273 Filiació URV: SI The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types, comment on the potential failures of the method.

We propose a versatile ``stabilization on demand'' method for the suppression of modulation instability in oscillatory spatially extended nonlinear systems, based on a genetically optimized multifrequency spatiotemporal modulation of the potential. The method, which ensures full stabilization even for very strong nonlinearities, forms a powerful tool allowing for an arbitrary design of the instability spectrum. The stabilization method is universal for complex oscillatory systems, based on a general complex Ginzburg-Landau model with varying degrees of nonlinearity, and could lead to the stabilization of arbitrarily complex systems---from high power lasers and Bose-Einstein condensates of attracting atoms, to spatially extended chemical and biological pattern-forming systems.

This is the accepted version of the following article: Mossaiby, F., Ghaderian, M., Rossi, R. Implementation of a generalized exponential basis functions method for linear and non-linear problems. International Journal for Numerical Methods in Engineering [on line]. Jul 2015, which has been published in final form at http://dx.doi.org/10.1002/nme.4985. In this paper, we address shortcomings of the method of exponential basis functions (EBF) by extending it to general linear and non-linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non-linear problems, they are converted to into a succession of linear ones using a Newton-Kantorovich approach. The generalized exponential basis functions method (GEBF) developed can be implemented with greater ease compared to EBF, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. We compare GEBF on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also in a 3D problem, we report the run time of the proposed method compared to Kratos, a parallel, highly optimized finite element code. The results show that in this example, to obtain the same level of error much less computational effort is needed in the proposed method. Practical limitations might be encountered however for large problems because of dense matrix operations involved.

We developed multi-step iterative method for computing the numerical solution of nonlinear systems, associated with ordinary differential equations (ODEs) of the form L(x(t)) + f(x(t)) = g(t) : here L(.) is a linear differential operator and f(.) is a nonlinear smooth function. The proposed iterative scheme only requires one inversion of Jacobian which is computationally very efficient if either LU-decomposition or GMRES-type methods are employed. The higher-order Frechet derivatives of the nonlinear system stemming from the considered ODEs are diagonal matrices. We used the higher-order Frechet derivatives to enhance the convergence-order of the iterative schemes proposed in this note and indeed the use of a multi-step method dramatically increases the convergence-order. The second-order Frechet derivative is used in the first step of an iterative technique which produced third-order convergence. In a second step we constructed matrix polynomial to enhance the convergence-order by three. Finally, we freeze the product of a matrix polynomial by the Jacobian inverse to generate the multi-step method. Each additional step will increase the convergence-order by three, with minimal computational effort. The convergence-order (CO) obeys the formula CO = 3m, where m is the number of steps per full-cycle of the considered iterative scheme. Few numerical experiments and conclusive remarks end the paper.

The effects of a disordered medium in the growth of unstable interfaces are studied by means of two local models with multiplicative and additive quenched disorder, respectively. For short times and large pushing the multiplicative quenched disorder is equivalent to a time-dependent noise. In this regime, the linear dispersion relation contains a destabilizing contribution introduced by the noise. For long times, the interface always gets pinned. We model the systematics of the pinned shapes by means of an effective nonlinear model. These results show good agreement with numerical simulations. For the additive noise we find numerically that a depinning transition occurs.

We consider the evaporation of periodic arrays of initially equal droplets in two-dimensional systems with open ~absorbing! boundaries. Our study is based on the numerical solution of the Cahn-Hilliard equation. We show that due to cooperative effects the droplets which are further from the boundary may evaporate earlier than those in the boundary’s vicinity. The time evolution of the overall amount of matter in the system is also studied.

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Nonlinearities have been shown to play an important role in increasing the extracted energy of energy harvesting devices at the macro and micro scales. Vibration-based energy harvesting on the nano scale has also received attention. In this paper, we characterize the nonlinear dynamical behavior of a strained nanostructured graphene for its potential use in energy harvesting applications. A compressed vibrating membrane graphene sheet free from any external excitation is first studied. We present a continuous time dynamical model of the system in the form of a double-well single degree of freedom system. Equilibrium points are obtained and their stability analysis is carried out. Then, random vibrations are considered as the main ambient energy source for the system and its performances in terms of the well occupation zones, RMS value of the position, and the corresponding energy harvested are presented in the steady state non-equilibrium regime when the noise level is considered as a control parameter. From this model, nonlinear analysis is carried out by computing state space trajectories, probability density and FFT spectra under a deterministic excitation. The ultimate goal of this parameter space exploration based upon a behavioral model is to provide design-oriented guidelines for engineering graphene-based mechanical harvesters.

The dynamics of an interface separating the two coexistent phases of a binary system in the presence of external fluctuations in temperature is studied. An interfacial instability is obtained for an interface that would be stable in the absence of fluctuations or in the presence of internal fluctuations. Analytical stability analysis and numerical simulations are in accordance with an explanation of these effects in terms of a quenchlike instability induced by fluctuations.

This article discusses several different implementations of Volterra seriesmodels, and performs a fair comparison between them using measured data and well known figures of merit. Among the implemented models, an approach that uses sub-sampling techniques together with Volterra series in a parallel cascade structure shows an improved performance compared to the other variations of Volterra seriesmodels.Based on the results, new trends in RF power amplifier behavioral modeling are suggested.

Optimizing the thermal production of electricity in the short term in an integrated power system when a thermal unit commitment has been decided means coordinating hydro and thermal generation in order to obtain the minimum thermal generation costs over the time period under study. Fundamental constraints to be satisfied are the covering of each hourly load and satisfaction of spinning reserve requirements and transmission capacity limits. A nonlinear network flow model with linear side constraints with no decomposition into hydro and thermal subproblems was used to solve the hydrothermal scheduling. Hydrogeneration is linearized with respect to network variables and a novel thermal generation and transmission network is introduced. Computational results are reported. >

International audience; Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a uni ed framework for the identi cation of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein.

Canal systems are complex nonlinear, distributed parameter systems with changing parameters according to the operating point. In this paper, a linear parameter-varying LPV state-space canal control model is obtained by identification in a local way using a multimodel approach. This LPV identification procedure is based on subspace methods for different operating points of an irrigation canal covering the full operation range. Different subspace algorithms have been used and compared. The model that best represents the canal behavior in a precise manner has been chosen, and it has been validated by error functions and analysis correlation of residuals in a laboratory multireach pilot canal providing satisfactory results

A second-order sliding mode strategy to control the breathing subsystem of a polymer electrolyte membrane fuel cell stack for transportation applications is presented. The controller is developed from a design model of the plant derived from open literature, and well suited for the design of second-order sliding mode strategies. Stability issues are solved using a super twisting algorithm. The resulting approach exhibits good dynamic characteristics, being robust to uncertainties and disturbances. Simulations results are provided, showing the feasibility of the approach., This work was supported by the project 'Avances en el modelo y diseño de controladores para sistemas basados en pila de combustible PEM' (4800). This work was supported by UNLP, CONICET, CICPBA, and CECyT, UPC, and AECI.

We study the interaction between two independent nonlinear oscillators competing through a neutral excitable element. The first oscillator, completely deterministic, acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses. The second oscillator, endowed with some randomness, though unable to make the excitable element to beat, leads to the occasional suppression of its firing. The missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators. This study is inspired in some complex rhythms such us a particular class of heart arrhythmia.

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

We present a numerical study of classical particles diffusing on a solid surface. The particles’ motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady state finger the width of which goes to one half of the channel width as the velocity increases.

In this paper aspects of non linear systems and flat control are studied for a specific application of a satellite fine pointing breadboard based on semi active magnetic bearings actuators. Authors propose a complete 6 degrees of freedom mechanical model which describes the system dynamics. A completely non linear and unstable system is obtained leading to implement non linear control laws. A combination of flat control, which ensures trajectory tracking and path planning, with a linear controller which rejects uncertainties and additive noise is implemented and simulated. Simulations proves the efficiency of control law, leading to a system which is stable and reaching the high precision performances desired for the application.

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

In this paper, modern numerical continuation methodologies are presented as a way of understanding and computing multiplicity of solutions in undergraduate physics problems. Mechanical and thermodynamical problems are used as a storyline to introduce the mathematical formalism required to clarify the distinction between the uniqueness and multiplicity of equilibrium solutions and the critical states of a nonlinear physical problem, as well as to illustrate how these novel numerical continuation techniques are implemented in practice. The paper provides simple numerical Matlab codes that are easily adaptable to other problems, as well as updated software and literature resources.

Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons. Within these equation we identify two types of long-wave instabilities and study the ensuing dynamics using numerical simulations of the three coupled Ginzburg-Landau equations., Comment: 25 pages, 7 figures

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)]. \textcopyright{} 1996 The American Physical Society.

Phase separation dynamics in the presence of externally imposed stirring is stuidied. The stirring is assumed independent of the concentration and it is generated with a well-defined energy spectrum. The domain growth process is either favored or frozen depending on the intensity and correlation length of this advective flow. This behavior is explained by analytical arguments.

We study nonstationary non‐Markovian processes defined by Langevin‐type stochastic differential equations with an Ornstein–Uhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non‐Markovian process, and we discuss its consequences. Non‐Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non‐Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Many natural systems display transitions among different dynamical regimes, which are difficult to identify when the data is noisy and high dimensional. A technologically relevant example is a fiber laser, which can display complex dynamical behaviors that involve nonlinear interactions of millions of cavity modes. Here we study the laminar-turbulence transition that occurs when the laser pump power is increased. By applying various data analysis tools to empirical intensity time series we characterize their persistence and demonstrate that at the transition temporal correlations can be precisely represented by a surprisingly simple model., 10 pages, 13 figures

The objective of this chapter is to introduce the technology of Microelectromechanical Systems, MEMS, and their application to emerging energy harvesting devices. The chapter begins with a general introduction to the most common MEMS fabrication processes. This is followed with a survey of design mechanisms implemented in MEMS energy harvesters to provide nonlinear mechanical actuations. Mechanisms to produce bistable potential will be studied, such as introducing fixed magnets, buckling of beams or using slightly slanted clamped-clamped beams. Other nonlinear mechanisms are studied such as impact energy transfer, or the design of nonlinear springs. Finally, due to their importance in the field of MEMS and their application to energy harvesters, an introduction to actuation using piezoelectric materials is given. Examples of energy harvesters found in the literature using this actuation principle are also presented.

We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement.

Frictionless sliding conditions between two bodies are usually defined using either the method of Lagrangian multipliers or by prescribing an artificial (penalty) stiffness which resists the penetration at the contact point. Both of these methods impose the condition that the contact force should be normal to the contact surface, with the Lagrangian multiplier or the penalty parameter serving as a measure of this force. In this work, an alternative approach is undertaken: the frictionless sliding condition is defined through a relationship between nodal parameters of the virtual displacements of a discretised principle of virtual work. This method, which does not involve additional force parameters or degrees of freedom, is known as the master–slave or the minimum-set method and is particularly convenient for displacement-based finite-element implementation. The method is analysed in detail in context of bilateral sliding constraints characteristic of prismatic and cylindrical joints in flexible beam assemblies undergoing large overall motion. Two numerical examples are presented and assessed against the results in the literature.