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Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

The optimal control on reassembly (remanufacturing assembly) error is one of the key technologies to guarantee the assembly precision of remanufactured product. However, because of the uncertainty existing in remanufactured parts, it is difficult to control assembly error during reassembly process. Based on the state space model, this paper aims to propose the optimal control method on reassembly precision to solve this problem.

Initially, to ensure the assembly precision of a remanufactured car engine, this paper puts forward an optimal control method on assembly precision for a remanufactured car engine based on the state space model. This method takes assembly workstation operation and remanufactured part attribute as the input vector reassembly status as the state vector and assembly precision as the output vector. Then, the compensation function of reassembly workstation operation input vector is calculated to direct the optimization of the reassembly process. Finally, a case study of a certain remanufactured car engine crankshaft is constructed to verify the feasibility and effectiveness of the method proposed.

The optimal control method on reassembly precision is an effective technology in improving the quality of the remanufactured crankshaft. The average qualified rate of the remanufactured crankshaft increased from 83.05 to 90.97 per cent as shown in the case study.

The optimal control method on the reassembly precision based on the state space model is available to control the assembly precision, thus enhancing the core competitiveness of the remanufacturing enterprises.

The purpose of this paper is to present the Galerkin method for analysis of steady-state processes in periodically time-varying circuits.

A converter circuit working on a time-varying load is often controlled by different signals. In the case of incommensurable frequencies, one can find a steady-state process only via calculation of a transient process. As the obtained results will not be periodical, one must repeat this procedure to calculate the steady-state process on a different time interval. The proposed methodology is based on the expansion of ordinary differential equations with one time variable into a domain of two independent variables of time. In this case, the steady-state process will be periodical. This process is calculated by the use of the Galerkin method with bases and weight functions in the form of the double Fourier series.

Expansion of differential equations and use of the Galerkin method enable discovery of the steady-state processes in converter circuits. Steady-state processes in the circuits of buck and boost converters are calculated and results are compared with numerical and generalized state-space averaging methods.

The Galerkin method is used to find a steady-state process in a converter circuit with a time-varying load. Processes in such a load depend on two incommensurable signals. The state-space averaging method is generalized for extended differential equations. A balance of active power for extended equations is shown.

This study aims to provide a new method of multiscale directional Lyapunov exponents (MSDLE) calculated based on the state space reconstruction for the nonstationary time series, which can be applied to detect the small target covered by sea clutter.

Reconstructed state space is divided into non-overlapping submatrices whose columns are equal to a predetermined scale. The authors compute eigenvalues and eigenvectors of the covariance matrix of each submatrix and extract the principal components σ_ip and their corresponding eigenvectors. Then, the angles ψ_ip of eigenvectors between two successive submatrices were calculated. The curves of (σ_ip, ψ_ip) reflect the nonlinear dynamics both in kinetic and directional and form a spectrum with multiscale. The fluctuations of (σ_ip, ψ_ip), which are sensitive to the differences of backscatter between sea wave and target, are taken out as the features for the target detection.

The proposed method can reflect the local dynamics of sea clutter and the small target within sea clutter is easily detected. The test on the ice multiparameter imaging X-ban radar data and the comparison to K distribution based method illustrate the effectiveness of the proposed method.

The detection of a small target in sea clutter is a compelling issue, as the conventional statistical models cannot well describe the sea clutter on a larger timescale, and the methods based on statistics usually require the stationary sea clutter. It has been proven that sea clutter is nonlinear, nonstationary or cyclostationary and chaotic. The new method of MSDLE proposed in the paper can effectively and efficiently detect the small target covered by sea clutter, which can be also introduced and applied to military, aerospace and maritime fields.

The state space method (SSM) is good at analyzing the interfacial physical quantities in laminated materials, while it has difficulty in calculating the mechanical quantities of interior points, which can be easily evaluated by the boundary element method (BEM). However, the material has to be divided into many subdomains when the traditional BEM is applied to analyze the functionally graded material (FGM), so that the computational amount will be increased enormously. This study aims to couple these two methods to strengthen their advantages and overcome their disadvantages.

Herein, a state space BEM in which the SSM is coupled by the BEM is proposed to analyze the elasticity of FGMs, where one BEM domain is set and the others belong to SSM domains. The discretized elements occur only on the boundary of the BEM domain and at the interfaces between different SSM domains. In SSM domains, the horizontal interfaces of FGMs are discretized by linear elements and the variables along the vertical direction are yielded by the precise integration method.

The accuracy of the proposed method is verified by comparing the present results with the ones from the finite element method (FEM). It is found that the present method can provide accurate displacements and stresses in the FGMs by fewer freedom degrees in comparison with the FEM. In addition, the present method can provide continuous interfacial stresses at the interfaces between different material domains, while the interfacial stresses by the FEM are discontinuous.

The system equations of the state space BEM are built by combining the boundary integral equation with the state equations according to the continuity conditions at the interfaces. The mechanical parameters of any inner point can be evaluated by the boundary integral equation after the unknowns on the boundaries and interfaces are determined by the system equation.

We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single-factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state-space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.

The purpose of this paper is to propose an efficient and straightforward approach for system identification of a rotating single link flexible manipulator (RSLFM). Also, the achieved results are experimentally validated through identification procedure.

The proposed system identification approach is applied to a RSLFM with a tip mass. At first, the dynamic model of the system is derived using Lagrange method. Then, an efficient method is developed for identification of such a system. This method facilitates the nonlinear complicated identification problem of the RSLFM to a simplified root finding problem.

The main advantage of the developed method is to convert a complicated system identification process to a simple nonlinear equation solution. This approach uses small-size input/output data set and requires a short-time interval of data acquisition, which gives important advantages in lower computational load and lower execution time. The investigated approach is studied on experimental system identification of a single link flexible manipulator. To demonstrate this fact, the developed method is successfully applied in identification of two other mechanical systems; the inverted pendulum on a cart and the ball and beam apparatus.

In this work, the proposed identification approach has been originally applied to a RSLFM and two other mechanical examples. All obtained identification results show the performance and applicability of the developed method clearly. This approach is not restricted in using state space or transfer function. It has significant superiority in comparison with other known approaches including autoregressive with exogenous input (ARX) and Box-Jenkins (BJ).

Focuses on steady state modelling of basic unipolar non‐isolated PWM AC line matrix‐reactance choppers (MRC). Their single‐phase topologies are similar to well‐known basic DC/DC converter ones. The MRC are built up through the adaptation of DC/DC converter topologies, which are based on the substitution of self‐commutated unidirectional switches by bi‐directional ones.

Presents an approach to modelling of the MRC with averaging operator different to the one used in averaged modelling of the DC/DC converters. There is running averaging of each switching period in the proposed approach. Following this, there is a demonstration of the solutions convergence of the state space and averaged state space equations for infinitive switching frequency.

The running averaging of each switching period should be used if averaged state space method is applied to the analysis of presented choppers. A circuit averaged model build‐up procedure of the presented choppers is the same as for the DC/DC ones.

Presents a quantitative assessment of accuracy for the averaged models of the presented MRC for finite switching frequency.

The purpose of this paper is to present a neuro‐fuzzy system with a reinforcement learning algorithm (RL) for adaptive swarm behaviors acquisition. The basic idea is that each individual (agent) has the same internal model and the same learning procedure, and the adaptive behaviors are acquired only by the reward or punishment from the environment. The formation of the swarm is also designed by RL, e.g. temporal difference (TD)‐error learning algorithm, and it may bring out a faster exploration procedure comparing with the case of individual learning.

The internal model of each individual composes a part of input states classification by a fuzzy net, and a part of optimal behavior learning network which adopting a kind of RL methodology named actor‐critic method. The membership functions and fuzzy rules in the fuzzy net are adaptively formed online by the change of environment states observed in the trials of agent's behaviors. The weights of connections between the fuzzy net and the action‐value functions of actor which provides a stochastic policy of action selection, and critic which provides an evaluation to state transmission, are modified by TD‐error.

Simulation experiments of the proposed system with several goal‐directed navigation problems are accomplished and the results show that swarms are successfully formed and optimized routes are found by swarm learning faster than the case of individual learning.

Two techniques, i.e. fuzzy identification system and RL algorithm, are fused into an internal model of the individuals for swarm formation and adaptive behavior acquisition. The proposed model may be applied to multi‐agent systems, swarm robotics, metaheuristic optimization, and so on.

The purpose of this paper is to propose a mathematical model for voltage super-lift dc-dc power converter in continuous conduction mode (CCM). Using the presented mathematical model, the analysis of dynamics of power stage for voltage super-lift dc-dc power converter can be performed.

The proposed method is based on the average state space model using the state equations of the dc-dc power converter. In the proposed method, the converter is represented as a set of differential equations derived for each switching state of the power switch in terms of inductor current and capacitor voltage. The proposed method describes the dynamic behaviour of the system. The controller is designed to meet performance requirement of the system such as to maintain the dynamics such as stability, steady-state accuracy and the speed of response of the system. Using the obtained model, the analysis of dynamic response of the voltage super-lift dc-dc power converter can be performed.

The converter is modelled and verified using conventional circuit analysis method employing state-space averaging technique, and their corresponding transfer function is also derived. The dynamics of the converter is investigated using frequency response characteristics obtained using MATLAB programming environment. In addition, to improve the stability of the converter, proportional-integral controller is designed using Ziegler–Nichols tuning rules, and the effect of the compensator in the plant is also investigated.

The proposed method can be used for analysing the dynamics of power stage for voltage super-lift DC-DC power converter.