Continuous Input Function Research Articles

Mathematical model written by ordinary differential equations for hysteresis games

In game theory, the hysteresis effect manifests itself in the fact that small differences in one or more parameters lead two systems to opposite stable equilibrium. The mathematical model (called smooth model) of hysteresis game writing by ordinary differential equations with the great parameter K is studied. Estimations of closeness of output functions for smooth and classical models through the continuity module of continuous input function are received. This error can be controlled by increasing the parameter K to a sufficiently large value. The result was conducted by studying of mathematical model and using programs Mathematica, Matlab or Maple. Experiments were carried out, and the obtained results were summarized and presented through evaluations and graphical interpretation.

Gas path parameter prediction of aero-engine based on an autoregressive discrete convolution sum process neural network

In order to improve the approximation ability of neural network to functional and improve the prediction accuracy of time series data, this paper proposes an autoregressive discrete convolution sum process neural network prediction model and applies it to the prediction of aero-engine gas path performance parameters. Coupling threshold wavelet de-noising method is applied to the preprocessing of engine gas path parameters, which can effectively remove the noise in the time series data. Process neurons are applied to artificial neural networks to expand the computational functions of artificial neurons. The process neuron can not only realize the spatial aggregation operation of discrete input data and the connection weight, but also realize the time aggregation operation of the product integral of the continuous input function and the connection weight function. The output of discrete time series is affected by the current input/output, and also by the historical input/output value. Therefore, an autoregressive feedback link is added to the network topology, and the value of the network's output node is used as the input to adjust the network connection weight. The convolution sum operation of discrete time series data can realize the time accumulation effect, so the discrete convolution sum operator is used to replace the integral operator to realize the time aggregation function of the process neuron. Since the integral operation of the continuous function is avoided, the weight training process of the process neural network is effectively simplified, and the accuracy loss in the continuous-time function fitting process of discrete input samples is effectively avoided. Bayesian regularization network weight learning algorithm is used to solve the problems of slow convergence speed and easy to fall into local optimum of back propagation learning algorithm, and improve the generalization ability of neural network. It can be seen from the prediction simulation results of the two engines that the average relative error and root mean square error of the engine gas path parameter prediction based on the autoregressive discrete convolution sum process neural network model can be reduced to 0.67% and 0.35 respectively. The stable and high-precision prediction results show that the network model and weight learning algorithm proposed in this paper have better robustness in functional approximation, and have higher accuracy in time series data prediction.

Canonical form of ordered weighted averaging operators

Discrete Ordered Weighted Averaging (OWA) operators as one of the most representative proposals of Yager (1988) have been widely used and studied in both theoretical and application areas. However, there are no effective and systematic corresponding methods for continuous input functions. In this study, using the language of measure (capacity) space we propose a Canonical Form of OWA operators which yield some common properties like Monotonicity and Idempotency and thus serve as a generalization of Discrete OWA operators. We provide also a representation of the Canonical Form by means of asymmetric Choquet integrals. The Canonical Form of OWA operators can effectively handle some input functions defined on ordered sets.

An optimized non-linear input shaper for payload oscillation suppression of crane point-to-point maneuvers

Payload oscillation suppression in point-to-point maneuvers is a challenging problem in the design and control process of overhead crane systems. To address this issue, this article proposes an input shaping control method coupled with a genetic algorithm strategy to tune the jib input acceleration. A polynomial function is defined as the input for the jib acceleration to move the payload on a specific track that satisfies the system constraints, while the desired final conditions are achieved. All three phases of a crane maneuver, including filling the ladle, moving the payload to a new position, and eventually unloading the ladle, are captured by the optimization algorithm. The proposed method is evaluated for both constant and variable hoisting cable length cases. The numerical results indicate that the introduced method enables the crane to safely perform an accurate controlled maneuver by constraining the payload angular motion within a certain range, which is critical in handling sensitive loads. In compared with the existing techniques, the new input shaper also provides a faster system response owing to the fact that it is driven by a continuous input function. A sensitivity study is performed and a non-sensitive optimized input polynomial function is obtained for the variable hoisting length case.

Learning data discretization via convex optimization

Discretization of continuous input functions into piecewise constant or piecewise linear approximations is needed in many mathematical modeling problems. It has been shown that choosing the length of the piecewise segments adaptively based on data samples leads to improved accuracy of the subsequent processing such as classification. Traditional approaches are often tied to a particular classification model which results in local greedy optimization of a criterion function. This paper proposes a technique for learning the discretization parameters along with the parameters of a decision function in a convex optimization of the true objective. The general formulation is applicable to a wide range of learning problems. Empirical evaluation demonstrates that the proposed convex algorithms yield models with fewer number of parameters with comparable or better accuracy than the existing methods.

Fuzzy Adaptive Inverse Compensation Method to Tracking Control of Uncertain Nonlinear Systems With Generalized Actuator Dead Zone

This paper solves the problem of adaptive fuzzy inverse compensation control for an uncertain nonlinear system whose actuator is subjected to generalized dead-zone nonlinearity. By defining a continuous connection function and combining with the mean-value theorem, the generalized dead zone is first decomposed into a nominal asymmetric dead zone multiplying an uncertain continuous input function. Afterward, a smooth inversion and its parameterization are further proposed such that a new expression of adaptive asymmetric dead-zone compensation error is established in Theorems 1 and 2. With such an expression, the fuzzy systems can be successfully embedded into a compensation structure to indirectly handle uncertain input dynamics. In addition, a separation scheme is developed to construct two online estimators. Based on the above design procedure, an adaptive inverse compensator for generalized dead zone is built eventually. With the backstepping iteration design of compensator input, an adaptive fuzzy controller is developed to establish the closed-loop system stability. Finally, two simulations are conducted to illustrate the effectiveness and applicability of the proposed control scheme.

Approximation of nonlinear differential functional equations

We have investigated the approximation of an element with delay in $ {{\mathbb{R}}^n} $ for the case of a continuous input function. We have constructed and substantiated a scheme of the approximation of solutions of an initial-value problem for a nonlinear differential functional equation by the solutions of the Cauchy problem for a system of ordinary differential equations. Calculations for the model example based on the proposed scheme of approximation are in good agreement with well-known results in the literature.

Approximation with the output of linear control systems

In this paper we give a new proof that for controllable and observable linear systems every L 2 [ 0 , T ] function can be approximated in the L 2 [ 0 , T ] sense with an output function generated by an L 2 [ 0 , T ] input function. We also give a new characterization of how continuous functions on [ 0 , T ] are uniformly approximated by an output generated by a continuous input function. The relative degree of the transfer function of the system determines those functions that can be approximated. We further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions.

Digital Robust Control of Nonlinear Mechanical Systems

Various continuous-time robust control methods have been proposed for nonlinear systems. However the implementation of these methods usually requires digital control systems. A digital implementation of a control algorithm based on a continuous-time theory often leads to chattering, even when a continuous input function is used, and makes the control error larger than the theoretically guaranteed control error limits. In this paper we propose a robust control scheme of nonlinear mechanical systems, on the premise of using the digital control. This scheme gives the admissible control error taking the sampling period into consideration, and introduces the weighting function for the input gain in order to reduce the chattering. Then it is shown that the proposed control scheme is effective by numerical simulations.

Segmentally Continuous input Functions in Linear Multicompartment Systems

The convolutions of segmentally continuous zero- and first-order input functions with the general form of pharmacokinetic multicom-partmental disposition functions can be used to analyze and simulate the time course of drug invasion into the central compartment of mammillary models and certain physiologically relevant recirculating systems. The generalized model equations may be used to assess the reliability and intercorrelations of parameter estimates directly, since partial derivatives with respect to all model constants can be computed explicitly. In combination with curve-fitting algorithms, input functions identical to those of the point-area deconvolution can be obtained, although at the expense of significantly longer computing times. On the other hand, the range of potential applications goes far beyond the reconstruction of the time course of drug absorption.

Two-Port Analysis of SC Networks with Continuous Input Signals

Switched-capacitor (SC) networks are comprised of capacitors interconnected by an array of periodically operated switches. Such networks are particularly attractive in light of the high circuit density possible with MOS circuit technology and hybrid integrated circuits using thin-film and silicon technology. Their implementation and analysis have received increasing attention over the last years, and economical designs find applications in communication and electronic equipment. Previous publications by the author and G. S. Moschytz have shown that SC networks can be analyzed as time-variant sampled-data networks by using nodal charge equations. This led to four-port equivalent circuits in the Z domain, thus modeling the SC network with a time-invariant network. The four-port equivalent circuit was reduced to a two-port, and a two-port transfer function for the entire SC network was derived. This previous work assumed that the network is fed by a staircase input function. In this paper, we show how the theory can be extended to continuous input functions. The results obtained are similar to those obtained by Liou and Kuo, but, since we use traditional two-port theory, the derivation is different. This derivation makes it simple and more intuitively accessible. The interpretation of the analytical expression leads to a bypass circuit that has the properties of a classical ring modulator added to the two-port equivalent circuit mentioned above. We present examples.