The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results a...The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.展开更多
In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ...In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.展开更多
In this work, temperature dependences of small-signal model parameters in the SiGe HBT HICUM model are presented. Electrical elements in the small-signal equivalent circuit are first extracted at each temperature, the...In this work, temperature dependences of small-signal model parameters in the SiGe HBT HICUM model are presented. Electrical elements in the small-signal equivalent circuit are first extracted at each temperature, then the temperature dependences are determined by the series of extracted temperature coefficients, based on the established temperature for- mulas for corresponding model parameters. The proposed method is validated by a 1x 0.2 x 16 μm2 SiGe HBT over a wide temperature range (from 218 K to 473 K), and good matching is obtained between the extracted and modeled resuits. Therefore, we believe that the proposed extraction flow of model parameter temperature dependence is reliable for characterizing the transistor performance and guiding the circuit design over a wide temperature range.展开更多
Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow...Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting(CC)molds with narrow widths for the production of automobile exposed panels.Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process.The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold.Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone.The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min^−1 and casting speed of 1.7 m·min^−1.Under the present experimental conditions,the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.展开更多
The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier c...The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.展开更多
This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of t...This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, solutions either grow or decay exponentially in the distance from the finite end of the cylinder. In the case of decay, the effect of perturbing the equation parameters is also investigated.展开更多
This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identificat...This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.展开更多
The relationships between the surface quality of a single crystal copper ingot and the process parameters of heated mould continuous casting method were studied experimentally using our own design of horizontal heated...The relationships between the surface quality of a single crystal copper ingot and the process parameters of heated mould continuous casting method were studied experimentally using our own design of horizontal heated mould continuous casting apparatus, and the mechanism by which process parameters affect the surface quality of a single crystal copper ingot is analyzed in the present paper. The results show that the process parameters affect the surface quality of a pure copper ingot by affecting the position of the liquid-solid interface in the mould. The position of the liquid-solid interface in the mould must be controlled carefully within an appropriate range, which is determined through a series of experiments, in order to gain a single crystal copper ingot with good surface quality.展开更多
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorial...A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.展开更多
Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this...Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydro-cracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.展开更多
The finite strip controlling equation of pinned curve box was deduced on basis of Novozhilov theory and with flexibility method, and the problem of continuous curve box was resolved. Dynamic Bayesian error function of...The finite strip controlling equation of pinned curve box was deduced on basis of Novozhilov theory and with flexibility method, and the problem of continuous curve box was resolved. Dynamic Bayesian error function of displacement parameters of continuous curve box was found. The corresponding formulas of dynamic Bayesian expectation and variance were derived. After the method of solving the automatic search of step length was put forward, the optimization estimation computing formulas were also obtained by adapting conjugate gradient method. Then the steps of dynamic Bayesian estimation were given in detail. Through analysis of a Classic example, the criterion of judging the precision of the known information is gained as well as some other important conclusions about dynamic Bayesian stochastic estimation of displacement parameters of continuous curve box.展开更多
According to turbulent theory and characteristics of beam blank continuous casting, 3-D model to represent the flow of beam blank mould is established. The predicted results indicate that the exit obliquity of up 15...According to turbulent theory and characteristics of beam blank continuous casting, 3-D model to represent the flow of beam blank mould is established. The predicted results indicate that the exit obliquity of up 15°(+15°) should be adopted, which will benefit the floatation of non-metallic inclusion and purification of the molten steel. When the nozzle angle is 120°, the flow pattern is reasonable. Proper nozzle depth can be 200mm. Turbulent kinetic of meniscus can be reduced by adopting the square nozzle and suitable area of side outlet when casting speed increases. The results are consistent with those of water model experiment, so the model is exact and reasonable. The model can provide important information for design of SEN and defining of immersion depth.展开更多
We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bi...We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bivariate normal case this dependence takes the form of a parameter (here the “expected value”) of one probability density depending continuously (here linearly) on realizations of the other random variable. The point is, that such a pattern does not need to be restricted to that classical case of the bivariate normal. We show that this paradigm can be generalized and viewed in ways that allows one to extend it far beyond the bivariate or multivariate normal probability distributions class.展开更多
A novel integrated water treatment facility, inner-recycling continuous sand filter, is discussed. The theory of micro-flocculation is applied in the sand-washing circulation system with continuous filtration and back...A novel integrated water treatment facility, inner-recycling continuous sand filter, is discussed. The theory of micro-flocculation is applied in the sand-washing circulation system with continuous filtration and backwashing. The design and operation parameters, which affect the performance of the filter, are discussed. The key design parameters are provided as follows: diameter of filter material is 0.7 to 1.0 mm, depth of filter bed is 0.6 m, filtration velocity is less than 12 m/h, ratio of gas to water is 9:11 and sand recycling rate is 2 to 4 mm/min.展开更多
The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied.The reaction boundary conditions for the temperature T and the salt concentra...The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied.The reaction boundary conditions for the temperature T and the salt concentration were imposed.With the aid of some useful a priori bounds,we were able to demonstrate the continuous dependence result for the Forchheimer coefficient λ.展开更多
In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the...In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the continuous dependence on the density <i><span style="white-space:nowrap;"><i>ρ</i></span></i> and the coefficient of thermal conductivity <i>K</i>. These results show that small changes for these coefficients can’t cause tremendous changes for the solutions.展开更多
In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An ...In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.展开更多
In this paper,we consider the initial-boundary value problem for the large scale three-dimensional(3D)viscous primitive equations under random force.Assuming that the random force and the heat source satisfy the some ...In this paper,we consider the initial-boundary value problem for the large scale three-dimensional(3D)viscous primitive equations under random force.Assuming that the random force and the heat source satisfy the some assumptions,we firstly establish rigorous a priori bounds with coefficients which depend only on boundary data,initial data and the geometry of the problem,and then with the aid of these a priori bounds,the continuous dependence of the solution on changes in the heat source is obtained.展开更多
The design of robust H∞ filtering problem of polytopic uncertain linear time-delay systems is addressed. The uncertain parameters are supposed to reside in a polytope. A parameter-dependent Lyapunov function approach...The design of robust H∞ filtering problem of polytopic uncertain linear time-delay systems is addressed. The uncertain parameters are supposed to reside in a polytope. A parameter-dependent Lyapunov function approach is proposed for the design of filters that ensure a prescribed H∞performance level for al ad-missible uncertain parameters, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty do-main. This idea is realized by careful y selecting the structure of the matrices involved in the products with system matrices. An extended H∞ sufficient condition for the existence of robust esti-mators is formulated in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms.展开更多
An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integratio...An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integration,an equivalent discrete identification model which is parameterized with continuous-time model parameters is developed,and the parameters can be estimated by the least-squares (LS) algorithm.Even with white noises in input and output measurement data,the LS estimate is biased,and the bias is determined by the variances of noises.According to the asymptotic analysis,the relationship between bias and noise variances is derived.One equation relating to the measurement noise variances is derived through the analysis of the LS errors.Increasing the degree of denominator of the system transfer function by one,an extended model is constructed.By comparing the true value and LS estimates of the parameters between original and extended model,another equation with input and output noise variances is formulated.So,the noise variances are resolved by the set of equations,the LS bias is eliminated and the unbiased estimates of system parameters are obtained.A simulation example by comparing the standard LS with bias eliminating LS algorithm indicates that the proposed algorithm is an efficient method with noisy input and output measurements.展开更多
基金The NSF (10271095) of China and NWNU-KJCXGC-212.
文摘The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.
文摘In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.
基金supported partially by the Important National Science&Technology Specific Projects,China(Grant No.2013ZX02503003)
文摘In this work, temperature dependences of small-signal model parameters in the SiGe HBT HICUM model are presented. Electrical elements in the small-signal equivalent circuit are first extracted at each temperature, then the temperature dependences are determined by the series of extracted temperature coefficients, based on the established temperature for- mulas for corresponding model parameters. The proposed method is validated by a 1x 0.2 x 16 μm2 SiGe HBT over a wide temperature range (from 218 K to 473 K), and good matching is obtained between the extracted and modeled resuits. Therefore, we believe that the proposed extraction flow of model parameter temperature dependence is reliable for characterizing the transistor performance and guiding the circuit design over a wide temperature range.
基金This work was financially supported by the Hunan Valin Lianyuan Iron&Steel Co.,Ltd.,China(No.18H00582).The authors are grateful to Hunan Valin Lianyuan Iron&Steel Co.,Ltd.,China for their assistance with the industrial measurement of velocities near the mold surface.
文摘Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting(CC)molds with narrow widths for the production of automobile exposed panels.Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process.The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold.Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone.The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min^−1 and casting speed of 1.7 m·min^−1.Under the present experimental conditions,the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.
文摘The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.
基金supported by the National Research Foundation of Korea (NRF) (No.2010-0012215)
文摘This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, solutions either grow or decay exponentially in the distance from the finite end of the cylinder. In the case of decay, the effect of perturbing the equation parameters is also investigated.
基金funded by the National Natural Science Foundation of China(No.61773182)the 111 Project(B12018).
文摘This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.
文摘The relationships between the surface quality of a single crystal copper ingot and the process parameters of heated mould continuous casting method were studied experimentally using our own design of horizontal heated mould continuous casting apparatus, and the mechanism by which process parameters affect the surface quality of a single crystal copper ingot is analyzed in the present paper. The results show that the process parameters affect the surface quality of a pure copper ingot by affecting the position of the liquid-solid interface in the mould. The position of the liquid-solid interface in the mould must be controlled carefully within an appropriate range, which is determined through a series of experiments, in order to gain a single crystal copper ingot with good surface quality.
文摘A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.
文摘Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydro-cracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.
文摘The finite strip controlling equation of pinned curve box was deduced on basis of Novozhilov theory and with flexibility method, and the problem of continuous curve box was resolved. Dynamic Bayesian error function of displacement parameters of continuous curve box was found. The corresponding formulas of dynamic Bayesian expectation and variance were derived. After the method of solving the automatic search of step length was put forward, the optimization estimation computing formulas were also obtained by adapting conjugate gradient method. Then the steps of dynamic Bayesian estimation were given in detail. Through analysis of a Classic example, the criterion of judging the precision of the known information is gained as well as some other important conclusions about dynamic Bayesian stochastic estimation of displacement parameters of continuous curve box.
文摘According to turbulent theory and characteristics of beam blank continuous casting, 3-D model to represent the flow of beam blank mould is established. The predicted results indicate that the exit obliquity of up 15°(+15°) should be adopted, which will benefit the floatation of non-metallic inclusion and purification of the molten steel. When the nozzle angle is 120°, the flow pattern is reasonable. Proper nozzle depth can be 200mm. Turbulent kinetic of meniscus can be reduced by adopting the square nozzle and suitable area of side outlet when casting speed increases. The results are consistent with those of water model experiment, so the model is exact and reasonable. The model can provide important information for design of SEN and defining of immersion depth.
文摘We start with analyzing stochastic dependence in a classic bivariate normal density framework. We focus on the way the conditional density of one of the random variables depends on realizations of the other. In the bivariate normal case this dependence takes the form of a parameter (here the “expected value”) of one probability density depending continuously (here linearly) on realizations of the other random variable. The point is, that such a pattern does not need to be restricted to that classical case of the bivariate normal. We show that this paradigm can be generalized and viewed in ways that allows one to extend it far beyond the bivariate or multivariate normal probability distributions class.
文摘A novel integrated water treatment facility, inner-recycling continuous sand filter, is discussed. The theory of micro-flocculation is applied in the sand-washing circulation system with continuous filtration and backwashing. The design and operation parameters, which affect the performance of the filter, are discussed. The key design parameters are provided as follows: diameter of filter material is 0.7 to 1.0 mm, depth of filter bed is 0.6 m, filtration velocity is less than 12 m/h, ratio of gas to water is 9:11 and sand recycling rate is 2 to 4 mm/min.
基金Supported by National Natural Science Foundation of China(Grant No.11971123).
文摘The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied.The reaction boundary conditions for the temperature T and the salt concentration were imposed.With the aid of some useful a priori bounds,we were able to demonstrate the continuous dependence result for the Forchheimer coefficient λ.
文摘In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the continuous dependence on the density <i><span style="white-space:nowrap;"><i>ρ</i></span></i> and the coefficient of thermal conductivity <i>K</i>. These results show that small changes for these coefficients can’t cause tremendous changes for the solutions.
文摘In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.
基金Supported by Innovation Team Project of Humanities and Social Sciences in Colleges and Universities of Guangdong Province(Grant No.2020wcxtd008)Research Team Project Funding of Guangzhou Huashang college(Grant No.2021HSKT01).
文摘In this paper,we consider the initial-boundary value problem for the large scale three-dimensional(3D)viscous primitive equations under random force.Assuming that the random force and the heat source satisfy the some assumptions,we firstly establish rigorous a priori bounds with coefficients which depend only on boundary data,initial data and the geometry of the problem,and then with the aid of these a priori bounds,the continuous dependence of the solution on changes in the heat source is obtained.
基金supported by the Innovative Team Program of the National Natural Science Foundation of China(61021002)the Specialized Research Fund for the Doctoral Program of Higher Education(20122302120069)+3 种基金the Basic Research Plan in Shenzhen City(JC201105160564AJCYJ20120613135212389)the Fundamental Research Funds for the Central Universities(HIT.NSRIF.2009137)the Key Lab of Wind Power and Smart Grid in Shenzhen City(CXB201005250025A)
文摘The design of robust H∞ filtering problem of polytopic uncertain linear time-delay systems is addressed. The uncertain parameters are supposed to reside in a polytope. A parameter-dependent Lyapunov function approach is proposed for the design of filters that ensure a prescribed H∞performance level for al ad-missible uncertain parameters, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty do-main. This idea is realized by careful y selecting the structure of the matrices involved in the products with system matrices. An extended H∞ sufficient condition for the existence of robust esti-mators is formulated in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms.
基金Project(50875028) supported by the National Natural Science Foundation of China
文摘An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integration,an equivalent discrete identification model which is parameterized with continuous-time model parameters is developed,and the parameters can be estimated by the least-squares (LS) algorithm.Even with white noises in input and output measurement data,the LS estimate is biased,and the bias is determined by the variances of noises.According to the asymptotic analysis,the relationship between bias and noise variances is derived.One equation relating to the measurement noise variances is derived through the analysis of the LS errors.Increasing the degree of denominator of the system transfer function by one,an extended model is constructed.By comparing the true value and LS estimates of the parameters between original and extended model,another equation with input and output noise variances is formulated.So,the noise variances are resolved by the set of equations,the LS bias is eliminated and the unbiased estimates of system parameters are obtained.A simulation example by comparing the standard LS with bias eliminating LS algorithm indicates that the proposed algorithm is an efficient method with noisy input and output measurements.