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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.

This paper presents the optimization principle and law of classic scaling fractal fractance approximation circuits (FACs). The scaling extension of FACs with negative half-order operational performance can facilitate the design of scaling fractal FACs with arbitrary-order fractional operators. This report summarizes the operational performance and mathematics describing of typical scaling fractal FACs. The scaling iteration algorithm was used to numerically calculate the impedance–admittance function of arbitrary real-order scaling fractal FACs, the features and defects of frequency-domain curves of the scaling fractal FACs were analyzed. Moreover, the methods of optimizing arbitrary-order scaling fractal FACs were analyzed theoretically, and symmetrical resistor–capacitor T-sections with certain universality were developed for FAC optimization. By comparing the approximation performances of FACs before and after optimization, the functions and indices for quantitatively analyzing the effects of circuit optimization were obtained and verified using examples. Fractance devices and active devices such as operational amplifiers can be combined to develop active fractional-order circuits and systems. Moreover, -0.2-order FACs before and after optimization were selected to construct fractional-order operational circuits and to obtain the results of the fractional-order differentiation and integration of a periodic square wave. The experimental simulation results agreed with the theoretical analysis. The test results prove that the FAC optimization proposed herein is theoretically correct, and that the circuit optimization methods are universal; these methods provide valuable references for solving the problem of FAC optimization.

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the$GI/GI/K$queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

In order to study the approximation performance of general regression neural networks, the structure and algorithm of general regression neural networks are first introduced. Then general regression neural networks and back propagation neural networks improved by Levenberg-Marquardt algorithm are established through programming using MATLAB language. A certain nonlinear function is taken as an example to be approximated by the two kinds of neural networks. The simulation results indicate that compared with back propagation neural networks, general regression neural networks has better approximation precision and faster convergence speed, which means it has much better approximation ability than back propagation neural networks. Therefore, for more complex function approximation, general regression neural networks is recommended. It can reduce the complexity of neural networks and it is also easier to design.

Among all improved BP neural network algorithms, the one improved by heuristic approach is studied in this paper. Firstly, three types of improved heuristic algorithms of BP neural network are programmed in the environment of MATLAB7.0. Then network training and simulation test are conducted taking a nonlinear function as an example. The approximation performances of BP neural networks improved by different numerical optimization approaches are compared to aid the selection of proper numerical optimization approach.

When approximating nonlinear functions, standard BP algorithms and traditional improved BP algorithms have low convergence rate and tend to be stuck in local minimums. In this paper, standard BP algorithm is improved by numerical optimization algorithm. Firstly, the principle of Levenberg-Marquardt algorithm is introduced. Secondly, to test its approximation performance, LMBP neural network is programmed via MATLAB7.0 taking specific nonlinear function as an example. Thirdly, its approximation result is compared with those of standard BP algorithm and adaptive learning rate algorithm. Simulation results indicate that compared with standard BP algorithm and adaptive learning rate algorithm, LMBP algorithm overcomes deficiencies ranging from poor convergence ability, prolonged convergence time, increasing iteration steps to nonconvergence. Thus with its good approximation ability, LMBP algorithm is the most suitable for medium-sized networks.

The authors consider an integrated service system, where real-time (RT) calls of multiple rate requirements and non-real-time (NRT) calls share the total system capacity. Typically, RT calls are given strict priority over NRT calls; therefore NRT performance is dependent on the RT process. When RT call arrivals do not follow a Poisson process, the effect of the RT traffic burstiness on the NRT performance has not been investigated. In this study, the authors investigate this effect and provide computationally efficient approximations and bounds for the NRT performance evaluation in the integrated service system with multi-rate non-Poisson RT traffic. With known first and second moments of the RT call arrival processes, the authors propose to consider the multi-rate non-Poisson RT traffic streams as an equivalent single-rate Poisson traffic stream. Then, the authors evaluate the NRT performance by converting the original system to a system offered with the equivalent RT traffic and the NRT traffic. The authors’ approximations and bounds are validated by extensive numerical examples.

Supply chain network designing and programming is a momentous issue that many practitioners have focused on and contributed numerous novelties for this prompt. This paper puts forward a fuzzy multi-agent system according to which compatible with the decision makers’ interests and environmental survey, identifies the parameters of the mathematical model. An embedded optimization party including evolutionary-based optimizer intelligent agents, obtains non-dominated potential solutions. The output of these optimizer agents during the calibration process is an underpinning for evaluating the performance of the party. The system makes the policy of optimization complying with the results evaluation as well as the decision makers’ elaborated desires. Afterwards, in step with this policy, it sets a pool from obtained Pareto Fronts and aggregates them to extract a set of the best individuals. It interactively represents this set to the decision makers and catches their desired circumstance amongst these optional solutions. Proposing the network graph and program—which its generic morphography is determined—for decision makers is contrived as the system last stage. The main competencies of this system could be contemplated regarding the facts that it interactively fulfills the decision makers’ utilities relying on its robustness in optimization, self-tuning, training loop, ambient intelligence and consciousness toward the changes in environment.

We consider the packet routing problem in store-and-forward networks whose topologies are either paths, trees, or rings. We are interested by the quality of the solution produced, with respect to a global optimal solution, if each link uses a (fixed) local policy to schedule the packets which go through it. The quality of the derived solutions is measured using the worst case analysis for two global optimality criteria, namely the maximum arrival date of a packet at its destination (or makespan) and the average arrival date of the packets at their destinations. We consider the setting where n packets, each one having a size (or length) and a destination, are released from the same source. In the case of rings, there exist two paths between the source and a destination. Each packet is owned by a user which chooses a path to its destination. We assume that users are rational: knowing the local policy used by the links and the state of the network, a user chooses the path which minimizes the arrival date of its packet at its destination. We are then interested by the quality of the Nash equilibria obtained.

Recently, 2-band interpolating wavelet transform has attracted much attention. It has the following several features: (i) The wavelet series transform coefficients of a signal in the multiresolution subspace are exactly consistent with its discrete wavelet transform coefficients; (ii) good approximation performance; (iii) efficiency in computation. However orthogonal 2-band compactly supported interpolating wavelet transform is only the first order. In order to overcome this shortcoming, the orthogonal M-band compactly supported interpolating wavelet basis is established. First, the unitary interpolating scaling filters of the lengthL =MK are characterized. Second, a scheme is given to design high-order unitary interpolating scaling filters. Third, a parameterization of the unitary interpolating scaling filters of the lengthL = 4M is made. Fourth, the orthogonal 2-order and 3-order three-band compactly supported interpolating scaling functions are constructed. Finally, the properties of the orthogonal M-band compactly supported interpolating wavelets and the approximation performance of the Mallat projection are discussed. For the smooth signal inL2(ℝ), the asymptotic formula of the approximation enor of the Mallat projection is obtained, and for the band-limited signal, the quantitative estimate of its upper bounds is given. The results show that the Mallat projection has the same approximation order as the orthogonal projection, and particularly for the orthogonal even number-order M-band compactly supported interpolating scaling function, they have the same approximation performance. The quantitative result also shows that the selection of the initial scale depends on the distribution of the signal frequency and the regularity order of the scaling function. For the given scaling function and signal, using these results one can determine the initial scale and at the same time estimate the initial scaling coefficients without prefiltering according to the error requirement