Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, ...Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.展开更多
Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addresse...Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.展开更多
Increasing the robustness to the unknown uncertainty and simultaneously enhancing the sensibility to the faults is one of the important issues considered in the fault detection development. Considering the L2-gain of ...Increasing the robustness to the unknown uncertainty and simultaneously enhancing the sensibility to the faults is one of the important issues considered in the fault detection development. Considering the L2-gain of residual system, this paper deals the observer-based fault detection problem. By using of H∞ control theory,an LMI approach to design fault detection observer is given. A numerical example is used to illustrate the effectiveness of the proposed approach.展开更多
This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov fun...This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach.For a given set of anti-windup compensation gains,we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances.Then,the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances.Furthermore,the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality(LMI) constraints.A numerical example is given to illustrate the effectiveness of the proposed design method.展开更多
The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L2-discrepancy.Based on the known formula,we present a new lower bound of wrap-around L2-discre...The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L2-discrepancy.Based on the known formula,we present a new lower bound of wrap-around L2-discrepancy for three-level U-type designs and compare it with those existing ones through figures,numerical simulation and illustrative examples.展开更多
How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of f...How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.展开更多
Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level ...Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level fractional factorials as the original designs,the general foldover plan and combined design under a foldover plan are defined,some theoretical properties of the defined foldover plans are obtained,a tight lower bound of the wrap-around L2-discrepancy of combined designs under a general foldover plan is also obtained,which can be used as a benchmark for searching optimal foldover plans.For illustration of the usage of our theoretical results,a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated,where 2≤ s ≤11.展开更多
The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two- and three-level design. A formulation of wrap-around...The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two- and three-level design. A formulation of wrap-around L2-discrepancy for the extended designs is developed. As a benchmark of obtaining （nearly） uniform asymmetrical extended designs, a lower bound to the wrap-around L2- discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.展开更多
A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The c...A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The characteristic finite difference methods for 2-dimensional enhanced oil recovery can be described as a coupled system of nonlinear partial differential equations. For a generic case of the cross interference and bounded region, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, and of calculus of variations, the theory of prior estimates and techniques. Optimal order estimates in L^2 norm are derived for the error in the approximate solutions. Thus we have thoroughly solved the well-known theoretical problem proposed by a famous scientist, J. Douglas, Jr.展开更多
This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall typ...This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.展开更多
The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in ...The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.展开更多
文摘Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.
基金supported by the National Natural Science Foundation of China (Nos. 60404001 and60774089)
文摘Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.
基金Supported by Shanghai postdoctoral found(2000478)
文摘Increasing the robustness to the unknown uncertainty and simultaneously enhancing the sensibility to the faults is one of the important issues considered in the fault detection development. Considering the L2-gain of residual system, this paper deals the observer-based fault detection problem. By using of H∞ control theory,an LMI approach to design fault detection observer is given. A numerical example is used to illustrate the effectiveness of the proposed approach.
基金supported by National Natural Science Foundation of China (Nos.61174073 and 90816028)
文摘This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach.For a given set of anti-windup compensation gains,we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances.Then,the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances.Furthermore,the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality(LMI) constraints.A numerical example is given to illustrate the effectiveness of the proposed design method.
基金Supported in part by the National Natural Science Foundation of China(Nos.11871237,11801576,11271147,11401596)the Fundamental Research Funds for the Central Universities(South-Central University for Nationalities(Nos.CZQ18017,CZQ19010))
文摘The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L2-discrepancy.Based on the known formula,we present a new lower bound of wrap-around L2-discrepancy for three-level U-type designs and compare it with those existing ones through figures,numerical simulation and illustrative examples.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135,11471136the UIC Grant R201409+1 种基金the Zhuhai Premier Discipline Grantthe Self-Determined Research Funds of CCNU from the Colleges Basic Research and Operation of MOE under Grant Nos.CCNU14A05041,CCNU16A02012
文摘How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.
基金supported by National Natural Science Foundation of China(Grant Nos.11201177 and 11271147)China Postdoctoral Science Foundation(Grant No.2013M531716)+2 种基金Scientific Research Plan Item of Hunan Provincial Department of Education(Grant No.12C0287)Jishou University Doctor Science Foundation(Grant No.jsdxxcfxbskyxm201113)Scientific Research Plan Item of Jishou University(Grant No.13JDY041)
文摘Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level fractional factorials as the original designs,the general foldover plan and combined design under a foldover plan are defined,some theoretical properties of the defined foldover plans are obtained,a tight lower bound of the wrap-around L2-discrepancy of combined designs under a general foldover plan is also obtained,which can be used as a benchmark for searching optimal foldover plans.For illustration of the usage of our theoretical results,a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated,where 2≤ s ≤11.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135,11471136support of Excellent Doctoral Dissertation to Cultivate Project of Central China Normal University under Grant No.2017YBZZ057
文摘The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two- and three-level design. A formulation of wrap-around L2-discrepancy for the extended designs is developed. As a benchmark of obtaining （nearly） uniform asymmetrical extended designs, a lower bound to the wrap-around L2- discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.
基金Project supported by the National Scaling Program and the National Eighth-Five-Year Tackling Key Problems Program
文摘A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The characteristic finite difference methods for 2-dimensional enhanced oil recovery can be described as a coupled system of nonlinear partial differential equations. For a generic case of the cross interference and bounded region, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, and of calculus of variations, the theory of prior estimates and techniques. Optimal order estimates in L^2 norm are derived for the error in the approximate solutions. Thus we have thoroughly solved the well-known theoretical problem proposed by a famous scientist, J. Douglas, Jr.
基金the National Natural Science Foundation of China (Grant Nos.10241005,10771001)Natural Science Foundation of Department of Education in Anhui Province (Grant No.KJ2008A025)
文摘This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.
基金Project supported by the National Scaling Program,the National Eighth-Five Year Tackling Key Problems Program and the Doctoral Found of the National Education Commission.
文摘The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.
