A Taylor series expansion(TSE) based design for minimum mean-square error(MMSE) and QR decomposition(QRD) of multi-input and multi-output(MIMO) systems is proposed based on application specific instruction set process...A Taylor series expansion(TSE) based design for minimum mean-square error(MMSE) and QR decomposition(QRD) of multi-input and multi-output(MIMO) systems is proposed based on application specific instruction set processor(ASIP), which uses TSE algorithm instead of resource-consuming reciprocal and reciprocal square root(RSR) operations.The aim is to give a high performance implementation for MMSE and QRD in one programmable platform simultaneously.Furthermore, instruction set architecture(ISA) and the allocation of data paths in single instruction multiple data-very long instruction word(SIMD-VLIW) architecture are provided, offering more data parallelism and instruction parallelism for different dimension matrices and operation types.Meanwhile, multiple level numerical precision can be achieved with flexible table size and expansion order in TSE ISA.The ASIP has been implemented to a 28 nm CMOS process and frequency reaches 800 MHz.Experimental results show that the proposed design provides perfect numerical precision within the fixed bit-width of the ASIP, higher matrix processing rate better than the requirements of 5G system and more rate-area efficiency comparable with ASIC implementations.展开更多
As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial h...As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.展开更多
<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines ...<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. <strong>Objective:</strong> Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable <em>t</em> ∈ (<em>t<sub>m</sub></em>, +∞) and<em> t<sub>m</sub></em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t<sub>m</sub></em> <span style="white-space:nowrap;">≫</span> 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.展开更多
The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-o...The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.展开更多
The Taylor model arithmetic is introduced to deal with uncertainty.The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model(TM).Thus,time domai...The Taylor model arithmetic is introduced to deal with uncertainty.The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model(TM).Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential equations.In this paper,the Taylor series method is employed to compute differential equations;moreover,power system time domain simulation under uncertainty based on Taylor model method is presented.This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation.It is computationally fast compared with the Monte Carlo method,which is another technique for uncertainty analysis.The proposed method has been tested on the 39-bus New England system.The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.展开更多
The article proposes a nonlinear optimal(H-infinity)control approach for the model of a tracked robotic vehicle.The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of t...The article proposes a nonlinear optimal(H-infinity)control approach for the model of a tracked robotic vehicle.The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the ground.To solve the related control problem,the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the vehicle.For the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is designed.To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control,that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.展开更多
For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Ta...For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations recursively.Furthermore,the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition.Once a generating function is found,it can be used to generate a family of optimal control for different boundary conditions.Since the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method.It is useful to online optimal trajectory generation problems.Numerical examples illustrate the effectiveness of the proposed algorithm.展开更多
Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-...Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-infinity)control approach is developed for this control problem.The dynamic model of the satellite's attitude dynamics undergoesfirst approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude dynamics.For the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is designed.To compute the controller's feedback gains,an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.展开更多
基金Supported by the Industrial Internet Innovation and Development Project of Ministry of Industry and Information Technology (No.GHBJ2004)。
文摘A Taylor series expansion(TSE) based design for minimum mean-square error(MMSE) and QR decomposition(QRD) of multi-input and multi-output(MIMO) systems is proposed based on application specific instruction set processor(ASIP), which uses TSE algorithm instead of resource-consuming reciprocal and reciprocal square root(RSR) operations.The aim is to give a high performance implementation for MMSE and QRD in one programmable platform simultaneously.Furthermore, instruction set architecture(ISA) and the allocation of data paths in single instruction multiple data-very long instruction word(SIMD-VLIW) architecture are provided, offering more data parallelism and instruction parallelism for different dimension matrices and operation types.Meanwhile, multiple level numerical precision can be achieved with flexible table size and expansion order in TSE ISA.The ASIP has been implemented to a 28 nm CMOS process and frequency reaches 800 MHz.Experimental results show that the proposed design provides perfect numerical precision within the fixed bit-width of the ASIP, higher matrix processing rate better than the requirements of 5G system and more rate-area efficiency comparable with ASIC implementations.
基金This research was supported by the National Natural Science Foundation of China(41701499)the Sichuan Science and Technology Program(2018GZ0265)+3 种基金the Geomatics Technology and Application Key Laboratory of Qinghai Province,China(QHDX-2018-07)the Major Scientific and Technological Special Program of Sichuan Province,China(2018SZDZX0027)the Key Research and Development Program of Sichuan Province,China(2018SZ027,2019-YF09-00081-SN)Technology Planning Project of Guangdong Province(NO.2018B020207012)。
文摘As one of the key parameters for characterizing crop canopy structure, Leaf Area Index(LAI) has great significance in monitoring the crop growth and estimating the yield. However, due to the nonlinearity and spatial heterogeneity of LAI inversion model, there exists scale error in LAI inversion result, which limits the application of LAI product from different remote sensing data. Therefore, it is necessary to conduct studies on scale effect. This study was based on the Heihe Oasis, Zhangye city, Gansu province, China and the following works were carried out: Airborne hyperspectral CASI(Compact Airborne Spectrographic Imager) image and LAI statistic models were adopted in muti-scale LAI inversion. The overall difference of muti-scale LAI inversion was analyzed in an all-round way. This was based on two aspects, "first inversion and then integration" and "first integration and then inversion", and on scale difference characteristics of three scale transformation methods. The generation mechanism of scale effect was refined, and the optimal LAI inversion model was expanded by Taylor expansion. By doing so, it quantitatively analyzed the contribution of various inversion processes to scale effect. It was found that the cubic polynomial regression model based on NDVI(940.7 nm, 712 nm) was the optimal model, where its coefficient of determination R2 and the correlation coefficient of test samples R reached 0.72 and 0.936, respectively. Combined with Taylor expansion, it analyzed the scale error generated by LAI inversion model. After the scale effect correction of one-dimensional and twodimensional variables, the correlation coefficient of CCD-LAI(China Environment Satellite HJ/CCD images) and CASI-LAI products(Compact Airborne Spectro graphic Imager products) increased from 0.793 to 0.875 and 0.901, respectively. The mean value, standard deviation, and relative true value of the two went consistent. Compared with onedimensional variable correction method, the twodimensional method had a better correction result. This research used the effective information in hyperspectral data as sub-pixels and adopted Taylor expansion to correct the scale error in large-scale and low-resolution LAI product, achieving large-scale and high-precision LAI monitoring.
文摘<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. <strong>Objective:</strong> Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable <em>t</em> ∈ (<em>t<sub>m</sub></em>, +∞) and<em> t<sub>m</sub></em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t<sub>m</sub></em> <span style="white-space:nowrap;">≫</span> 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.
文摘The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.
基金supported by the National Natural Science Foundation of China (Grant No.50477035).
文摘The Taylor model arithmetic is introduced to deal with uncertainty.The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model(TM).Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential equations.In this paper,the Taylor series method is employed to compute differential equations;moreover,power system time domain simulation under uncertainty based on Taylor model method is presented.This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation.It is computationally fast compared with the Monte Carlo method,which is another technique for uncertainty analysis.The proposed method has been tested on the 39-bus New England system.The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.
基金supported by the Research“Advances in Applied Nonlinear Optimal Control”under Grant No.6065。
文摘The article proposes a nonlinear optimal(H-infinity)control approach for the model of a tracked robotic vehicle.The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the ground.To solve the related control problem,the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the vehicle.For the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is designed.To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control,that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.
基金supported by“the Fundamental Research Funds for the Central Universities”under Grant No.HIT.NSRIF.201620。
文摘For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper.This algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations recursively.Furthermore,the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition.Once a generating function is found,it can be used to generate a family of optimal control for different boundary conditions.Since the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method.It is useful to online optimal trajectory generation problems.Numerical examples illustrate the effectiveness of the proposed algorithm.
文摘Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-infinity)control approach is developed for this control problem.The dynamic model of the satellite's attitude dynamics undergoesfirst approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude dynamics.For the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is designed.To compute the controller's feedback gains,an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.
