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An improved prescribed performance control using a backstepping technique and adaptive fuzzy is proposed for a strict feedback nonlinear dynamic system. A new virtual variable was defined to generate the virtual control that forces the tracking errors to fall within prescribed boundaries, and an adaptive fuzzy system was used to obtain required approximation performances. A strict feedback controller and adaptive laws for estimating the unknown non-linear function were designed to avoid a singularity problem and calculation of the explosive number of terms generated by the error transformations of conventional error constraint method and the recursive steps of traditional backstepping control. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The prescribed error constraint performance of the proposed control scheme was validated by applying it to control the position of a second-order non-linear system and a robot manipulator.

Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the c-differential uniformity of power functions over finite fields of odd characteristic. Based on some known almost perfect nonlinear functions, we present several classes of power functions f(x)=xd with cΔf≤3 . Especially, two new classes of perfect c-nonlinear power functions are proposed.

有限域 F2n 上的几乎完全非线性 (APN) 函数是差分均匀度最优的函数, 即具有最强的抵抗差分攻击的能力. APN 函数及其广义 APN 函数在编码理论、序列设计、有限几何等领域也有很重要的应用. 本文就 APN 函数及其广义 APN 函数成果做如下两方面的综述. 一方面是从偶特征有限域 F2n、奇特征有限域 Fpn 和整数环 Zn 上的 APN 函数分别总结研究成果; 另一方面是关于有限域上的广义 APN 函数, 从 GAPN 函数、APcN 函数和局部 APN 函数三方面分别综述研究结果. 最后提出 APN 函数及广义 APN 函数方面值得探索和研究的问题.

In this article, nonlocal two-point boundary value problem for a system of two impulse systems of differential equations with a nonlinear function under the differential sign and with maxima is investigated. Each system of differential equations contains a product of two nonlinear vector functions, for each of which the Lipschitz condition is satisfied. The existence, uniqueness and continuous dependence of the solution on the given functions are proved. The problem is reduced to a system of nonlinear functional integral equations in a Banach space. The method of successive approximations in combination with the method of contraction mappings is applied in proving the existence and uniqueness of a solution to nonlinear systems of functional integral equations with maxima.

This article methodically develops an improved self-regulating fuzzy-adaptive Sliding Mode Controller (SMC) that strengthens the disturbance compensation capacity of the nonlinear rotary pendulum systems while effectively attenuating the chattering content and curbing the control energy consumption. The article contributes to augmenting the SMC with online adaptation tools to achieve the said objectives. It employs the conventional Gao’s power-rate reaching law as the baseline. The scaling gain and the power rate of the said reaching law are adaptively modulated via a pre-calibrated two-input state-error-driven fuzzy nonlinear function. Additionally, the sign function in the law is also replaced with an odd-symmetric nonlinear fuzzy function to address the hard limits imposed by the former. Finally, the membership functions of the fuzzy function are self-regulated using the Extended-Kalman-Filter to improve the compensator’s adaptability in handling the system’s rapidly changing control requirements under exogenous disturbances. The aforementioned propositions are verified by performing customized and reliable hardware-in-loop experiments on the Quanser single-link rotary pendulum platform. As compared to baseline SMC law, the proposed control procedure contributes a ∼45.2%, ∼48.5%, and ∼34.8% reduction in position-regulation errors, control energy consumption, and peak overshoots, respectively. The experimental assessment validates the proposed control system’s enhanced robustness and chattering-suppression capability.

The aim of this paper is to propose a quasi-invariant technique suitable for describing the transverse dynamics of electrons in a synchrotron and to exhibit that the methodology allows the emergence of resonances in phase space. The proposed technique is implemented by using symbolic computation software, which provides sets of coupled differential equations for functions participating in the nonlinear dynamics, numerically solved with periodic boundary conditions. This approach allows the construction of an approximate invariant in a vicinity of the phase space origin. That portion of phase space is used for holding a stable beam of charge particles in synchrotrons. The submitted approach capability for describing the phase space is tested by comparing numerical results obtained with this technique against tracking simulations performed with available software. Finally, the possibility of applying this technique to control resonances in the optimization of the fourth-generation synchrotron light sources magnetic lattices is discussed.

For any odd prime p≥5, some optimal p-ary cyclic codes with parameters [pm−1,pm−2m−2,4] are presented by using perfect nonlinear monomials and the inverse function over pm . In addition, almost perfect nonlinear monomials, and other monomials over 5m are used to construct optimal quinary cyclic codes with parameters [5m−1,5m−2m−2,4].

The main aim of the presented study is estimating the parameters of Weibull distribution by utilizing simulation to generated the samples size when n=10, 50,100. Considering in the current study the parameters estimator of Weibull membership function, then using the nonlinear membership function for Gaussian function to find the fuzzy number for these parameters estimator. After that utilizing the ranking function to transform the fuzzy number to crisp number.

The dynamic behaviour of many systems can be approximated by a static non-linearity in series with a linear dynamic part. Systems with static input or output non-linearities are very common in many engineering applications. Such models are known as block-oriented models in the existing literature. The Hammerstein model is a special kind of block-oriented model, where a non-linear block is followed by a linear system. This study investigates the identification of Hammerstein systems with asymmetric two-segment piecewise-linear non-linearities. The basic idea is to employ a key-term separation technique and a corresponding auxiliary model initially. Then, the identification problem of non-linear system is changed into a non-linear function optimisation problem over parameter space. Further, the estimates of all the parameters of the non-linear block, the linear subsystem and the noise part are obtained based on an improved particle swarm optimisation algorithm. Finally, simulation examples are included to demonstrate the effectiveness and robustness of the proposed identification scheme.

Range-based localisation and tracking methods use the time-of-arrival (TOA) between the mobile station and several base stations, but the multipath propagation of non-line-of-sight channels complicates the estimation and processing. For channel modelling, the Gaussian scatterer distribution model has been reported to have a reasonable match between its TOA probability density distribution (PDF) and measured TOA data. In this study, this TOA PDF is adapted, along with selection from multiple motion models of the mobile station, for a new location and tracking algorithm. Since the TOA PDF is non-Gaussian and is a non-linear function of the position of the mobile, particle filtering is used which increases the complexity of the algorithm. The focus is on the tracking performance, and this is evaluated by simulation using idealised statistical channels, allowing direct comparison between different location algorithms. In this context, the presented algorithm is more accurate than the benchmarks of extended Kalman filter tracking, and positioning using least squares.