Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.

Calibration of CO and CO2 Monitors Used in Periodic Inspection of Vehicles at Fixed Stations for Environmental Control

Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuring the quantitative assessment of emissions for informed decisions on environmental treatments. This paper describes a method for the calibration of CO/CO2 monitors used for periodic inspections of vehicles in cites. The calibration was performed in the selected ranges: 900 - 12,000 µmol/mol for CO and 2000 - 20,000 µmol/mol for CO2. The traceability of the measurement results to the SI units was ensured by using certified reference materials from CO/N2 and CO2/N2 primary gas mixtures. The method performance was evaluated by assessing its linearity, accuracy, precision, bias, and uncertainty of the calibration results. The calibration data exhibited a strong linear trend with R² values close to 1, indicating an excellent fit between the measured values and the calibration lines. Precision, expressed as relative standard deviation (%RSD), ranged from 0.48 to 4.56% for CO and from 0.97 to 3.53% for CO2, staying well below the 5% threshold for reporting results at a 95% confidence level. Accuracy measured as percent recovery, was consistently high (≥ 99.1%) for CO and ranged from 84.90% to 101.54% across the calibration range for CO2. In addition, the method exhibited minimal bias for both CO and CO2 calibrations and thus provided a reliable and accurate approach for calibrating CO/CO2 monitors used in vehicle inspections. Thus, it ensures the effectiveness of exhaust emission control for better environment.

THE 2-ERROR LINEAR COMPLEXITY OF 2~n-PERIODIC BINARY SEQUENCES WITH LINEAR COMPLEXITY 2~n-1

Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Noise destroys the coexistence of periodic orbits of a piecewise linear map

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.

POSITIVE PERIODIC SOLUTION FOR A NONAUTONOMOUS LOGISTIC MODEL WITH LINEAR FEEDBACK REGULATION

A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model

Robust Stabilization for Linear Time-varying Uncertain Periodic Descriptor Systems

这个问题赶出为线性变化时间的不明确的周期的描述符系统的稳定被重游。为线性变化时间的不明确的周期的描述符系统基于柔韧的稳定性的概念，为柔韧的稳定性的一个必要、足够的条件被提出。柔韧的稳定问题也被学习，相应必要、足够的条件用双系统的符号被给。获得的矩阵不平等条件能被转变到与一些免费矩阵的介绍的线性矩阵不平等一，它使分析和设计过程简单、可靠。

The k-Error Linear Complexity and the Linear Complexity for pq^n-Periodic Binary Sequences

The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd（p-1, q-1） = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.

Analysis and control of a class of uncertain linear periodic discrete-time systems

Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.

Periodic solutions and flip bifurcation in a linear impulsive system

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.

Satisfactory control of discrete-time linear periodic systems

In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.

PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

Consider the linear neutral FDEd/dt[x(t) + Ax(t - r)] = R [dL(s)]x(t + s) + f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.

THE DISTRIBUTION FUNCTIONS FOR THE LINEAR COMPLEXITY OF PERIODIC SEQUENCES

Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given complexity measure value. In this paper, we mainly determine the distribution function of sequences with period over using Discrete Fourier Transform (DFT), where and the characteristics of are odd primes, gcd and is a primitive root modulo The results presented can be used to study the randomness of periodic sequences and the analysis and design of stream cipher.

Analysis of the Mode of the Periodically Time-varying Vibration Systems

By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode of the periodically time-varying vibration system has been discussed. The paper defines the mode and analyzes its characteristics. It can be found that the mode of the periodically time-varying system is periodically time-varing but has such characteristics as orthogonality. Finally, a method is given to solve the mode. By solving the eigenvalues and the eigenvectors of the state transition matrix in one period, the periodically time-varying mode can be obtained.

Periodic Modulation of Nonlinearity in a Two-Core Photonic Crystal Fiber: A Numerical Investigation

We present a numerical investigation of the propagation and the switching of ultra-short pulses (100 fs) in a two-core nonlinear coupler of photonic crystal fibers constructed with periodically modulated the non-linearity fiber (PMNL-PFC). Our simulations are taking into account different amplitude and frequency modulations of the PMNL-PFC. A coupler for coupling whose length is Lc = 1.8 cm, the transmission characteristics, the compression factor, the crosstalk (Xtalk) and extinction ratio (Xratio) levels of the first order solitons were studied for low to high pump energies considering 2Lc. By an analysis on the reference channel (channel 2), it is observed that at low modulation frequencies an increase occurs in the switching power increasing transmission efficiency. For high modulation frequencies, the transmitted energy efficiency loses. The switching pulses are stronger for low frequency and high amplitude modulation. The Xtalk is a function of the measurement made on the secondary channel (channel 1). It was observed that this unwanted high-frequency energy increases to lessen the measure of the amplitude modulation. In summary, we have demonstrated that introduction of a non-linearity profile takes the periodically modulated PMNL-PFC to strong variations at transmission efficiency, Xtalk, Xratio a function of frequency and modulation amplitude and the input power.

A TWO-STEP EXPLICIT METHOD FOR A CLASS OF LINEAR PERIODIC INITIAL VALUE PROBLEMS

This paper presents a two-step explicit method of order four for solving aclass of linear periodic initial value problems. At each computational step, only tworight function evaluations and one derivative evaluation are employed. Basing on aspecial vector operation, the method can be extended to the vector-applicable in multi-dimensional space.

Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning

Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach.

Admissible Periodic Bouncing Solutions for A Class of Semi-linear and Non-conservative Impact Oscillators

In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.

Toward Optimal Periodic Crowd Tracking via Unmanned Aerial Vehicle

Crowd management and analysis(CMA)systems have gained a lot of interest in the vulgarization of unmanned aerial vehicles(UAVs)use.Crowd tracking using UAVs is among the most important services provided by a CMA.In this paper,we studied the periodic crowd-tracking(PCT)problem.It consists in usingUAVs to follow-up crowds,during the life-cycle of an open crowded area(OCA).Two criteria were considered for this purpose.The first is related to the CMA initial investment,while the second is to guarantee the quality of service(QoS).The existing works focus on very specified assumptions that are highly committed to CMAs applications context.This study outlined a new binary linear programming(BLP)model to optimally solve the PCT motivated by a real-world application study taking into consideration the high level of abstraction.To closely approach different real-world contexts,we carefully defined and investigated a set of parameters related to the OCA characteristics,behaviors,and theCMAinitial infrastructure investment(e.g.,UAVs,charging stations(CSs)).In order to periodically update theUAVs/crowds andUAVs/CSs assignments,the proposed BLP was integrated into a linear algorithm called PCTs solver.Our main objective was to study the PCT problem fromboth theoretical and numerical viewpoints.To prove the PCTs solver effectiveness,we generated a diversified set of PCTs instances with different scenarios for simulation purposes.The empirical results analysis enabled us to validate the BLPmodel and the PCTs solver,and to point out a set of new challenges for future research directions.

Periodic Solution for Stochastic Predator-Prey Systems with Nonlinear Harvesting and Impulses

In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.