Pade Approximation Approach Research Articles

Distributed adaptive event‐triggered consensus of switched nonlinear multi‐agent systems with state and input delays

SummaryIn this article, for switched nonlinear time‐delay multi‐agent systems (MASs) under directed graphs, an adaptive event‐triggered (ET) consensus problem is investigated. Each agent's switching signal is allowed to be arbitrary and asynchronous. To save communication resources, an adaptive ET consensus strategy is designed. In addition, the Pade approximation approach is introduced to transform the system into an input delay‐free system. A Lyapunov–Krasovskii functional is employed to analyze the effect of time‐varying delays on system stability. It is proved that the consensus errors of switched NMASs are bounded, and the Zeno behavior does not exist. Finally, the presented strategy's effectiveness is verified by simulation results.

Command filter‐based adaptive robust prescribed performance formation control for nonlinear multi‐agent systems

SummaryThis paper investigates an observer‐based adaptive robust fuzzy formation tracking control method for nonlinear multi‐agent systems (MAS) with input delay. The considered nonlinear MAS contains the unknown nonlinear functions, that is, unmeasured states. The fuzzy logic systems (FLS) are used to approximate the unknown nonlinear functions, and then a fuzzy adaptive state observer is designed to estimate the unmeasured states. The Pade approximation approach is introduced to solve the input delay issue. By combining command filtering and backstepping recursive control techniques, a robust adaptive prescribed performance formation output feedback tracking controller is designed. Moreover, the proposed controller can avoid the “explosion of complexity” and “singularity” problems in the backstepping design framework. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (SGUUB), and the formation tracking errors do not exceed the prescribed performance bounds. Finally, the feasibility of the proposed control approach can be further verified through numerical and practical examples.

Fuzzy finite-time consensus control for uncertain nonlinear multi-agent systems with input delay

A fuzzy finite-time consensus control method for a class of uncertain nonlinear multi-agent systems (MASs) with input delay is developed. The Pade approximation approach and Laplace transform technology are employed to eliminate the effect of input delay. Then, the fuzzy logic systems are applied to deal with the uncertain nonlinear terms. Furthermore, a relative threshold event-triggered control scheme is established to alleviate the communication burden of the control network. Meanwhile, to ensure MASs can synchronize in finite time, an adaptive consensus control method is developed. With the proposed method, even if the MASs suffer from input delay, all followers in the MASs reach finite-time synchronization and track the virtual leader. Finally, the validity of the proposed method is illustrated by the theoretical analysis and simulation examples.

Thermal distribution through a moving longitudinal trapezoidal fin with variable temperature-dependent thermal properties using DTM-Pade approximant

The present inspection elaborates the thermal distribution through a convective-radiative longitudinal trapezoidal moving fin with an internal heat source by considering the linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient. The non-dimensionalization of the energy equation is carried out using dimensionless terms, and the resulting nonlinear ordinary differential equation (ODE) is solved analytically using the differential transform method (DTM) with Pade approximant approach. Furthermore, the consequence of several non-dimensional parameters, namely thermal conductivity parameter, convection-conduction parameter, Peclet number, radiation-conduction parameter, fin taper ratio, temperature ratio parameter, and internal heat generation parameter on temperature gradient and fin efficiency is explained with the help of graphs. The significant primary results of the investigation illustrate that the thermal distribution through the fin gradually decreases as the magnitude of the convection-conduction parameter, temperature ratio parameter, and radiation-conduction parameter rise. In contrast, it upsurges for heat generation and thermal conductivity parameters.

Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders * *Supported by the Chongqing Graduate Research and Innovation Foundation (ydstd1912, CYB21045), the National Natural Science Foundation of China (11625520, 12047564) and the Fundamental Research Funds for the Central Universities (2020CQJQY-Z003)

In this study, we investigate in detail the generalized Crewther Relation (GCR) between the Adler function (D) and the Gross-Llewellyn Smith sum rules coefficient ( ) using the newly proposed single-scale approach of the principle of maximum conformality (PMC). The resultant GCR is scheme-independent, with the residual scale dependence due to unknown higher-order terms highly suppressed. Thus, a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data. Moreover, a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented. Additionally, for the first time, the Pade approximation approach has been adopted for estimating the unknown -loop contributions from the known four-loop perturbative series.

Order Diminution of LTI Systems Using Modified Big Bang Big Crunch Algorithm and Pade Approximation with Fractional Order Controller Design

In this paper, a novel approach is proposed for the reduced order modelling of linear time invariant (LTI) systems. The proposed approach is a combination of modified Big bang big crunch (BBBC) optimization algorithm and Pade approximation technique. The beauty of the proposed approach is that the selection of solution space for BBBC algorithm is not entirely random, but structured via the use of Pade approximation approach. Hence, two principal criticisms of soft computing algorithms, i.e., random choice of solution space and larger simulation time are averted in the proposed technique. The proposed technique is substantiated via four different numerical examples from literature and compared with existing model order reduction (MOR) techniques. The concept of controller design is introduced via application of fractional order internal model control technique for load frequency control of power systems. Further, BBBC algorithm is employed to tune a boiler loop in power station. The results convey the efficiency and powerfulness of the proposed technique.

Practical fixed-time adaptive consensus control for a class of multi-agent systems with full state constraints and input delay

This paper concentrates on a fixed-time consensus issue for nonstrict nonlinear uncertain multi-agent systems (MASs) with state constraints and input delay. In comparison with previous works, the topic of full state constraints and input delay is first embodied in nonstrict MASs in a fixed time. A semi-global practical fixed-time stability (SPFTS) is employed to handle the consensus problem in this note. The radial basis function neural networks (RBFNNs) are developed to counteract unknown items in each agent. Pade approximation approach is introduced to cope with input delay. By using the backstepping technique, adaptive virtual controllers, adaption laws and the actual consensus controller are devised. And the rest followers can converge to a specified trajectory built by the leader in fixed time. Finally, a practical example is employed to test the correctness for the proposed control protocol.

Adaptive Dynamic Surface Control Design with Asymptotic Tracking Performance for a Class of Uncertain Input-Delayed Systems

In this paper, an adaptive tracking control problem is addressed for a class of uncertain nonlinear systems with input delay and perturbations. To design the desired adaptive controller, Pade approximation approach is introduced to handle the problem from the input delay. In addition, to avoid the problem from “explosion of complexity” existing in the conventional backstepping design, a dynamic surface control method is presented by employing a nonlinear filter. Then, a new adaptive controller with a simple structure is established. Under the proposed controller, all the closed-loop signals remain semiglobally bounded, and especially the system output can follow the given reference signal asymptotically. Some simulations are given to verify the effectiveness of the proposed control scheme.

Internal Model Control for Rank-Deficient System with Time Delays Based on Damped Pseudo-Inverse

It is a challenge to design a satisfactory controller for a complex multivariable industrial system with minimal offsetting and a slow response. An internal model control method is proposed for rank-deficient systems with a time delay based on a damped pseudo-inverse. An internal model control was designed to obtain the desired dynamic characteristics of the system by transforming the time-delay system into a system without a time delay, following the Pade approximation approach. By introducing a damping factor, the internal model controller was designed based on a damped pseudo-inverse, since the inverse matrix of the rank-deficient system does not exist. Furthermore, a singular value decomposition was used to analyze the steady-state performance of the system. The selection of the damping factor was also presented, and a μ analysis was made to evaluate the stability of the system. To demonstrate the effectiveness of the proposed method, a crude distillation process with five inputs and four outputs was considered as an example. The simulation results illustrate that not only can the proposed strategy guarantee the system’s stability, but it also has a relatively good dynamic performance.

Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes

Designing a random dynamical system requires the prediction of the statistics of the response, knowing the random model of the uncertain parameters. Direct Monte Carlo simulation (MCS) is the reference method for propagating uncertainties but its main drawback is the high numerical cost. A surrogate model based on a polynomial chaos expansion (PCE) can be built as an alternative to MCS. However, some previous studies have shown poor convergence properties around the deterministic eigenfrequencies. In this study, an extended Pade approximant approach is proposed not only to accelerate the convergence of the PCE but also to have a better representation of the exact frequency response, which is a rational function of the uncertain parameters. A second approach is based on the random mode expansion of the response, which is widely used for deterministic dynamical systems. A PCE approach is used to calculate the random modes. Both approaches are tested on an example to check their efficiency.

English

  In wireless communication the effect of multipath as well as shadowing takes place simultaneously over the channel and this phenomena leads to composite fading. G-distribution is frequently encountered distribution in wireless fading environment. Combination of multipath fading and shadowing model are used as composite fading model. This composite fading model is named as G-distribution. G-distribution is a combination of the Inverse-Gaussian distribution and the distribution. In this paper the Pade approximation approach is used to analyze the performance of composite multipath/shadowed fading channel. This distribution is used to approximate any system in form of closed form solution as well as for accurate approximation in several shadowing conditions. The Pade approximation is applied over the general expression that is given in terms of moment generating function and results are obtained by varying shadowing parameters as well as signal to noise power threshold ratio. Our study start by deriving the moment generating function of the G-distribution and approximate them by using the Pade approximation for the calculation of bit error rate and outage probability for different values of average Signal to noise ratio (SNR). All simulations are done using Maple-13 software tool and results are obtained for outage probability and bit error rate versus average SNR.   Key words: Pade’s approximation, G-distribution, moment generating function, inverse Gaussian distribution, Nakagami distribution and composite distributions, average signal to noise ratio, outage probability, bit error probability.

The Acoustic Properties of Expanded Clay Granulates

The purpose of this work is to characterise experimentally and theoretically the acoustic performance of mixes of loose expanded clay granulates. The surface acoustic impedance is obtained from measurements in the impedance tube and predicted using the Pade approximation approach. The random incidence absorption coefficient is measured using the ISO 345/85 method. Experimental data for the surface acoustic impedance are used to deduce the porosity, tortuosity and the statistical pore size distribution; these parameters are difficult to obtain directly, because of the relatively low density of the loose granulates and the fact that the granular base contains 5–30% of the closed, unconnected pores. Good agreement between the theory and the results is found; 50–100 mm layers of expanded clay granulates can be used efficiently for noise control over a broad frequency range.

Padé-approximant corrections to general variational expressions of scattering theory: Application to5σphotoionization of carbon monoxide

We discuss a method for systematically correcting results obtained using variational expressions in scattering theory. The approach taken is to compute a sequence of Pade approximants of the form [N/N] for the error in an initial variational estimate obtained using a basis-set expansion. The relationship between the Pade-approximant approach and the iterative Schwinger method for correcting variational estimates is also examined. We discuss a large class of general variational expressions to which the Pade-approximant approach can be applied. The variational expressions considered include those for the wave function, for photoionization transition matrix elements, as well as for scattering matrix (K-matrix) elements. We have applied this approach to the 5σ photoionization of CO using the frozen-core Hartree-Fock and fixed-nuclei approximations. We find that the Pade-approximant method converges rapidly and reliably. Both total photoionization cross sections and photoelectron angular distributions from threshold to 40 eV are presented and compared to previous experimental and theoretical results. We find major quantitative discrepancies between the present results for the total cross section and previous theoretical results.