Non-linear Perturbation Functions Research Articles

Interaction and manipulation for non-autonomous bright soliton solution of the coupled derivative nonlinear Schrödinger equations with Riemann–Hilbert method

Some bright wave solutions of the coupled derivative nonlinear Schrödinger(CDNLS) equations are derived with Riemann–Hilbert(RH) method. We observe some novel non-autonomous bright soliton structures by choosing the different nonlinear perturbation function g(t). It is shown that there are some possibilities to manipulate the interactions of non-autonomous wave solution through choosing nonlinear and gain/loss functions. Some dynamic behaviors of interactions between two bright solitons have been asymptotically analyzed, the two parabolic-type bright solitons propagate with the opposite directions after the interaction. And some interactions of the linear-, parabolic- and periodic-type bright two-solitons are elastic. A general approach is presented to manipulate soliton waves, which has the potential application for the optical self-routing, non-Kerr media and Bose–Einstein condensates(BEC).

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

SummaryThis article addresses the passivity analysis and passification problems for a class of nonlinear singular time‐varying delay systems with the special forms of uncertainties in both derivative matrix and some other system matrices by adopting adaptive sliding mode control (SMC) strategy. First, a distinctive state augmentation technique, which keeps the admissibility and the robust passivity unchanged, is employed due to “left‐singular” form uncertainty in the derivative matrix (ie, ). Next, an integral‐type sliding surface, which involves the SMC gain matrix K, is constructed. By designing an appropriate Lyapunov‐Krasovskii functional and introducing slack matrix approach, in which the slack matrix is not constrained in contrast to most existing literatures, a new sufficient condition is derived to ensure that the resulting sliding mode dynamics is admissible and robustly passive for all admissible uncertainties. Additionally, for the passification problem, a delay‐dependent sufficient condition is proposed in the form of strict linear matrix inequality (LMI), which not only removes the equality constraint but also makes the SMC gain matrix K solvable. Then a novel adaptive SMC law, which does not need to use the assumption that bounds of nonlinear perturbation function and external disturbance are known constants, is synthesized such that the finite‐time reachability can be guaranteed. And the state information before and after state augmented transformation is utilized in SMC law design to help achieve better performance. Finally, four examples are presented to illustrate the effectiveness, superiority, and less conservativeness of the proposed scheme.

Nonlinear time varying perturbation stability analysis of a double diabetes system

Background and objective:The stability problem in double delay differential diabetes system is affected by delay term and meal perturbation. This paper is addressed to assess the stability of such double diabetes system with unknown nonlinear perturbation and bounded time varying delay. Method:The stability of a double diabetes system following a meal function as an unknown nonlinear perturbation function has been analyzed by using a Lyapunov–Krasovskii function. The stability matrices according to linear matrix inequality (LMI) were constructed and solved using YALMIP. Results:The solution of the stability theorem gives semi definite matrices which fulfilled the stability criteria. Simulations observed such oscillation in the early meal intake. Conclusion:Thus, it shows that for given values (30–51 min delay and unknown time varying perturbation) the double diabetes system is stable.

Stochastic Choice and Revealed Perturbed Utility

Perturbed utility functions|the sum of expected utility and a non-linear perturbation function|provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce’s IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across dierent agents and across decision problems. We also show that these representations correspond to a form of ambiguity-averse preferences for an agent who is uncertain about her true utility.

Adaptive neural finite-time control for a class of switched nonlinear systems

This paper investigates the adaptive finite-time stabilization of a class of switched nonlinear systems with unknown nonlinear terms using neural networks. Under the assumption that all the growth conditions for the unknown nonlinear perturbation functions are partially known, the common finite-time controller and adaptive law are constructed by extending the adding-a-power-integrator technique and using the backstepping methodology. The unknown parts of the growth conditions are modeled by the neural networks and the known parts are exploited for the controller design. The bounds of neural network approximation errors are assumed to be unknown and are estimated online. It is shown that the state of the closed-loop system is finite-time stable and the parameter estimations are bounded under arbitrary switching. A simulation example is provided to show the effectiveness of the proposed method.

Further results on adaptive full-order and reduced-order observers for Lur’e differential inclusions

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.

Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System

This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation. The proposed method employs an improved Wirtinger-type inequality for constructing a new Lyapunov functional with triple integral items. By using the convex expression of the nonlinear perturbation function, the original nonlinear Lur'e system is transformed into a linear uncertain system. Based on the Lyapunov stable theory, some novel delay-depended stability criteria for the researched system are established in terms of linear matrix inequality technique. Three numerical examples are presented to illustrate the validity of the main results.

New applications of nonlinear chirp scaling in SAR data processing

New applications of nonlinear chirp scaling (NLCS) have been found in processing monostatic and bistatic SAR data acquired in the strip-map mode. When the effects in impulse response broadenings due to quadratic range migration are negligible for short radar wavelengths, a time domain range cell migration correction (RCMC) can be applied. After the correction, the FM rates of targets confined in a range gate will differ from each other. A nonlinear chirp perturbation function can be applied to each range gate to equalize the targets' FM rates before azimuth compression. This algorithm is analyzed in the paper and is supported by point target simulation experiments.

Chronopotentiometry with non-linear perturbation functions at the DME with a preceding blank period: Electrode curvature effects and experimental verification

The effect of electrode curvature on E− t curves obtained in Chronopotentiometry with non-linear perturbation of the form I(itt) = I 0t w ( w ⩾ − 1 2 ) after a blank period, t 1, at the DME, is presented. The cases where the reduction product dissolves both in the electrolyte solution and in the electrode are considered. Concentration profiles have been obtained, and reversibility criteria and methods for determining kinetic parameters of the charge transfer reaction are proposed. The theory has been experimentally verified with Fe(C 2O 4) 3− 3/Fe(C 2O 4) 4− 3, Tl +/Tl(Hg), Cr 3+/Cr 2+ and Zn 2+/Zn(Hg) using a linear currrent scan and a current step. The kinetic parameters of the two last systems have been determined.

Chronopotentiometry with non-linear perturbation functions at the DME with a preceding blank period

A theoretical study on the use of non-linear perturbation functions of the form ( I( t)= I 0 t w (w≥0) after a blank period, t 1, at the DME, is presented. Equations for the potential-time curves are derived and discussed. The general equation obtained here becomes Galvez's equation when t 1→0 and also the generalized Sand equation when t 1⪢ t.

Chronopotentiometry with programmed current at the dropping mercury electrode Part II. Theory for electrode processes with a CE mechanism

A theoretical study of the chronopotentiometric response for the CE mechanism at the DME by using a non-linear perturbation function of the form I=I 0 t q is presented. Equations for the potential-time curves are derived and a method to determine the kinetic parameters of the chemical reaction and of the charge-transfer step is proposed. Comparison with chronopotentiometry at stationary electrodes is also made.

Chronopotentiometry with programmed current at the dropping mercury electrode: Part II. Theory for electrode processes with a ce mechanism

A theoretical study of the chronopotentiometric response for the CE mechanism at the DME by using a non-linear perturbation function of the form I=I 0 t q is presented. Equations for the potential-time curves are derived and a method to determine the kinetic parameters of the chemical reaction and of the charge-transfer step is proposed. Comparison with chronopotentiometry at stationary electrodes is also made.

Chronopotentiometry with non-linear perturbation functions at the dropping mercury electrode

A theoretical study on the use of non-linear perturbation functions of the form I( t)= I 0 t q for Chronopotentiometry at the DME is presented. Equations for the potential-time curves are derived, and their relation with the corresponding equations for chronopotentiometry at stationary electrodes is discussed. Conditions where a transfer charge reaction may be considered as reversible or totally irreversible are given.

Non-linear perturbation functions in the study of electrode kinetics: Part III. The use of the current-time function I(t)= I0t−1/2 in the study of irreversible charge transfer reactions

Theoretical calculations for the study of irreversible charge transfer reactions with the current-time function I(t)= I 0 t −1/2 are given. Methods of determining the kinetic constants from the resulting potential-time functions are proposed. Experimental results obtained by this method for the system Zn 2+/Zn(Hg) with various concentrations of NaNO 3 as supporting electrolyte are presented.

Non-linear perturbation functions in the study of electrode kinetics Part III. The use of the current-time function I(t) = Iot?1/2 in the study of irreversible charge transfer reactions

Non-linear perturbation functions in the study of electrode kinetics Part III. The use of the current-time function I(t) = Iot?1/2 in the study of irreversible charge transfer reactions

Non-linear perturbation functions in the study of electrode kinetics: Part IV. Instrumentation

The construction of a digital function generator with the capability of generating voltage-time functions of the form E= E 0 t −1/2 is described. Some applications of such a device for fast chronopotentiometric measurements employed for the study of the mechanism of electrode reactions and superimposed non-faradaic charging processes are suggested.

Non-linear perturbation functions in the study of electrode kinetics Part IV. Instrumentation

The construction of a digital function generator with the capability of generating voltage-time functions of the form E=E0t−1/2 is described. Some applications of such a device for fast chronopotentiometric measurements employed for the study of the mechanism of electrode reactions and superimposed non-faradaic charging processes are suggested.

Nonlinear perturbation functions in the study of electrode kinetics II. Some theoretical aspects concerning the e.c.e. mechanism

Theoretical calculations for the simple e.c.e. mechanism are presented using as current functions an arbitrary power of time function. General relations are given which enable the calculations of the total current from the two partial currents and vice versa for any predetermined current—time function to be performed. The influence of the separation of the formal potentials of the charge transfer steps is treated taking as an example the constant current case and criteria for the simple e.c.e. mechanism are derived.

Nonlinear perturbation functions in the study of electrode kinetics: II. Some theoretical aspects concerning the E.C.E. mechanism

Theoretical calculations for the simple e.c.e. mechanism are presented using as current functions an arbitrary power of time function. General relations are given which enable the calculations of the total current from the two partial currents and vice versa for any predetermined current—time function to be performed. The influence of the separation of the formal potentials of the charge transfer steps is treated taking as an example the constant current case and criteria for the simple e.c.e. mechanism are derived.

Non-linear perturbation functions in the study of electrode kinetics I. Some theoretical aspects concerning the e., e.c. and catalytic mechanisms

The possibilities offered by the use of nonlinear perturbation functions in electrochemical measurements are presented using as examples the e., e.c. and catalytic reaction mechanisms. The solutions for the diffusion equations are given in particular for two current-time functions: one containing an arbitrary power of time, and the other an exponential function of time.