We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of s...We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of stochastic model errors. By utilizing spectral factorization to minimize the performance index, we derive an optimal controller design method and further study best performance in the presence of stochastic perturbation. The results can be used to evaluate optimal performance in practical control system designs.展开更多
The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the unde...The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.展开更多
Accurate prediction of magmatic intrusion into a coal bed is illustrated using the method of seismic spectral decomposition.The characteristics of coal seismic reflections are first analyzed and the effect of variable...Accurate prediction of magmatic intrusion into a coal bed is illustrated using the method of seismic spectral decomposition.The characteristics of coal seismic reflections are first analyzed and the effect of variable time windows and domain frequencies on the spectral decomposition are examined.The higher domain frequency of coal bed reflections using the narrower STFT time window,or the smaller ST scale factor,are acceptable.When magmatic rock intrudes from the bottom of the coal bed the domain frequency of the reflections is decreased slightly,the frequency bandwidth is narrowed correspondingly,and the response from spectral decomposition is significantly reduced.Intrusion by a very thin magmatic rock gives a spectral decomposition response that is just slightly less than what is seen from a normal coal bed.Results from an actual mining area were used to validate the method.Predicting the boundary of magmatic intrusions with the method discussed herein was highly accurate and has been validated by observations from underground mining.展开更多
This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square...This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square criterion of the tracking error and the plant input energy over a class of additive model errors is defined. Then, utilizing spectral factorization to minimize the performance index, we obtain an optimal controller design method, and furthermore study optimal tracking performance under plant uncertainty and control energy constraint. The results can be used to evaluate optimal average tracking performance and control energy in designing practical control systems.展开更多
A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confi...A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confined within linear response theory. The calculating experience suggests that the proposed technique is simple and efficient in implementation, and the comparison with stochastic simulation shows that the first three orders of susceptibilities calculated by the proposed technique have high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and another observed phenomenon of stochastic resonance in the systems induced by the location of a single periodic orbit is disclosed and explained.展开更多
The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which ref...The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which reflects the spectrum rigidity of the Hamiltonian.In this work,we explore the general properties of SFF in open quantum systems.We find that in open systems the SFF first decays exponentially,followed by a linear increase at some intermediate time scale,and finally decreases to a saturated plateau value.We derive general relations between(i)the early-time decay exponent and Lindblad operators;(ii)the long-time plateau value and the number of steady states.We also explain the effective field theory perspective of general behaviors.We verify our theoretical predictions by numerically simulating the Sachdev−Ye−Kitaev(SYK)model,random matrix theory(RMT),and the Bose−Hubbard model.展开更多
We propose an efficient colocated multiple-input multiple-output radar waveform-design method based on two-step optimizations in the spatial and spectral domains. First, a minimum integrated side-lobe level strategy i...We propose an efficient colocated multiple-input multiple-output radar waveform-design method based on two-step optimizations in the spatial and spectral domains. First, a minimum integrated side-lobe level strategy is adopted to obtain the desired beam pattern with spatial nulling. By recovering the hidden convexity of the resulting fractional quadratically constrained quadratic programming non-convex problem, the global optimal solution can be achieved in polynomial time through a semi- definite relaxation followed by spectral factorization. Second, with the transmit waveforms obtained via spatial optimization, a phase changing diagonal matrix is introduced and optimized via power method-like iterations. Without influencing the shape of the optimized beam pattern, the transmit waveforms are further optimized in the spectral domain, and the desired spectral nulling is formed to avoid radar interference on the overlaid licensed radiators. Finally, the superior performance of the proposed method is demonstrated via numerical results and comparisons with other approaches to waveform design.展开更多
The visible infrared radiometer(VIRR)is the first instrument with longest measurements equipped on the Fengyun(FY)polar-orbiting satellites.Through re-processing of the historic VIRR measurements,long-term(over 20 yr)...The visible infrared radiometer(VIRR)is the first instrument with longest measurements equipped on the Fengyun(FY)polar-orbiting satellites.Through re-processing of the historic VIRR measurements,long-term(over 20 yr)global data can be integrated from multiple participating VIRRs on a consistent radiometric scale,which are valuable to climate and climate change studies.Due to lack of an onboard calibration system for VIRR,the reflective solar bands must be vicariously calibrated.This study applied the multi-site vicarious approach for consistent calibration of the VIRR visible(VIS)and near-infrared(NIR)data,and produced calibration coefficients for five VIRRs on FY-1 C/D and FY-3 A/B/C.The data quality was then evaluated with observations.The reflectance predicted by using the radiative transfer model over multiple invariant desert and ocean targets was used to derive the calibration slope via a weighted fitting scheme,in which the weights are the inverse of the variance from a radiative transfer simulation evaluated with reference to Aqua moderate resolution imaging spectroradiometer(MODIS).The sensor-specific calibration coefficients were derived on a daily basis by using piecewise polynomials.The calibration reference of the VIRR solar band record was further traced to the Aqua MODIS Collection 6.1 reference calibration with a systematic correction derived from the Libya4 desert.The VIRR record was compared with the Aqua MODIS C6.1 calibration over the polar region based on simultaneous nadir overpass observations.The lifetime relative difference for each sensor are within 3.3%and 4.5%for channels 1 and 2.Invariant deserts were also employed to evaluate the stability and consistency of the VIRR record.In general,the means of the directional and spectral corrected reflectance for each sensor are within 1%of the 20-yr average,implying that the VIRR reflectance of the invariant targets is consistent to within 1%among the sensors for channels 1 and 2.The VIRR data thus derived are reliable.展开更多
基金the National High-Technology Research and Development Program of China(Grant No.2003AA517020)
文摘We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of stochastic model errors. By utilizing spectral factorization to minimize the performance index, we derive an optimal controller design method and further study best performance in the presence of stochastic perturbation. The results can be used to evaluate optimal performance in practical control system designs.
基金the National Natural Science Foundation of China under Grant No.60574016
文摘The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.
基金provided by the National Natural Science Foundation of China (Nos. 40804026 and 40874054)the Postdoctoral Science Foundation of China (No. 20100471003)+2 种基金the Postdoctoral Science Foundation of Jiangsu Province (No.1002023B)the Open Projects of State Key Laboratory of Coal Resources and Mine Safety (No. 10KF05)the Youth Foundation of CUMT,are gratefully acknowledged
文摘Accurate prediction of magmatic intrusion into a coal bed is illustrated using the method of seismic spectral decomposition.The characteristics of coal seismic reflections are first analyzed and the effect of variable time windows and domain frequencies on the spectral decomposition are examined.The higher domain frequency of coal bed reflections using the narrower STFT time window,or the smaller ST scale factor,are acceptable.When magmatic rock intrudes from the bottom of the coal bed the domain frequency of the reflections is decreased slightly,the frequency bandwidth is narrowed correspondingly,and the response from spectral decomposition is significantly reduced.Intrusion by a very thin magmatic rock gives a spectral decomposition response that is just slightly less than what is seen from a normal coal bed.Results from an actual mining area were used to validate the method.Predicting the boundary of magmatic intrusions with the method discussed herein was highly accurate and has been validated by observations from underground mining.
基金High Technology Research and Development (863) Program(No.2003AA517020)
文摘This paper has investigated best tracking performance for linear feedback control systems in the case that plant uncertainty and control effort need to be considered simultaneously. Firstly, an average integral square criterion of the tracking error and the plant input energy over a class of additive model errors is defined. Then, utilizing spectral factorization to minimize the performance index, we obtain an optimal controller design method, and furthermore study optimal tracking performance under plant uncertainty and control energy constraint. The results can be used to evaluate optimal average tracking performance and control energy in designing practical control systems.
基金Project supported by BH foundation of XJTU and the major program of the National Natural Science Foundation of China（Grant No 10432010）.
文摘A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confined within linear response theory. The calculating experience suggests that the proposed technique is simple and efficient in implementation, and the comparison with stochastic simulation shows that the first three orders of susceptibilities calculated by the proposed technique have high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and another observed phenomenon of stochastic resonance in the systems induced by the location of a single periodic orbit is disclosed and explained.
文摘The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which reflects the spectrum rigidity of the Hamiltonian.In this work,we explore the general properties of SFF in open quantum systems.We find that in open systems the SFF first decays exponentially,followed by a linear increase at some intermediate time scale,and finally decreases to a saturated plateau value.We derive general relations between(i)the early-time decay exponent and Lindblad operators;(ii)the long-time plateau value and the number of steady states.We also explain the effective field theory perspective of general behaviors.We verify our theoretical predictions by numerically simulating the Sachdev−Ye−Kitaev(SYK)model,random matrix theory(RMT),and the Bose−Hubbard model.
基金the National Natural Science Foundation of China （No. 61302153）
文摘We propose an efficient colocated multiple-input multiple-output radar waveform-design method based on two-step optimizations in the spatial and spectral domains. First, a minimum integrated side-lobe level strategy is adopted to obtain the desired beam pattern with spatial nulling. By recovering the hidden convexity of the resulting fractional quadratically constrained quadratic programming non-convex problem, the global optimal solution can be achieved in polynomial time through a semi- definite relaxation followed by spectral factorization. Second, with the transmit waveforms obtained via spatial optimization, a phase changing diagonal matrix is introduced and optimized via power method-like iterations. Without influencing the shape of the optimized beam pattern, the transmit waveforms are further optimized in the spectral domain, and the desired spectral nulling is formed to avoid radar interference on the overlaid licensed radiators. Finally, the superior performance of the proposed method is demonstrated via numerical results and comparisons with other approaches to waveform design.
基金Supported by the National Key Research and Development Program of China(2018YFB0504905 and 2018YFB0504900)。
文摘The visible infrared radiometer(VIRR)is the first instrument with longest measurements equipped on the Fengyun(FY)polar-orbiting satellites.Through re-processing of the historic VIRR measurements,long-term(over 20 yr)global data can be integrated from multiple participating VIRRs on a consistent radiometric scale,which are valuable to climate and climate change studies.Due to lack of an onboard calibration system for VIRR,the reflective solar bands must be vicariously calibrated.This study applied the multi-site vicarious approach for consistent calibration of the VIRR visible(VIS)and near-infrared(NIR)data,and produced calibration coefficients for five VIRRs on FY-1 C/D and FY-3 A/B/C.The data quality was then evaluated with observations.The reflectance predicted by using the radiative transfer model over multiple invariant desert and ocean targets was used to derive the calibration slope via a weighted fitting scheme,in which the weights are the inverse of the variance from a radiative transfer simulation evaluated with reference to Aqua moderate resolution imaging spectroradiometer(MODIS).The sensor-specific calibration coefficients were derived on a daily basis by using piecewise polynomials.The calibration reference of the VIRR solar band record was further traced to the Aqua MODIS Collection 6.1 reference calibration with a systematic correction derived from the Libya4 desert.The VIRR record was compared with the Aqua MODIS C6.1 calibration over the polar region based on simultaneous nadir overpass observations.The lifetime relative difference for each sensor are within 3.3%and 4.5%for channels 1 and 2.Invariant deserts were also employed to evaluate the stability and consistency of the VIRR record.In general,the means of the directional and spectral corrected reflectance for each sensor are within 1%of the 20-yr average,implying that the VIRR reflectance of the invariant targets is consistent to within 1%among the sensors for channels 1 and 2.The VIRR data thus derived are reliable.
