A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identifica...A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.展开更多
From the basic properties of skein systems, we build a generalized tangle algebra (GTA). The elements of GTA are four basic tangles. There are three operations, which are connection, splicing and scalar multiplication...From the basic properties of skein systems, we build a generalized tangle algebra (GTA). The elements of GTA are four basic tangles. There are three operations, which are connection, splicing and scalar multiplication. From GTA we derive two generalized recursion formulae (GRF) and prove the existence of a generalized skein relation which satisfies GRF. The obtained generalized skein relation epitomizes all generalizations from the Jones polynomial and thus forms a unified model. Two important topological parameters, twisting measure and loop values, appear explicitly in the expressions of the unified model, and this fact greatly simplifies the operations.展开更多
The motion＇s generation consists in finding an analytic expression of a motion according to time. A Map road type planner or Cell decomposition provide to the motion generator some possible free crossing points of co...The motion＇s generation consists in finding an analytic expression of a motion according to time. A Map road type planner or Cell decomposition provide to the motion generator some possible free crossing points of collision. The global trajectory＇s interpolation by a polynomial is generally not possible, because the degree of the polynomial increases with the number of crossing points which can generate vibrations or loops of the. trajectory. The solution consists in using polynomials in an inferior degree and to build the motion in pieces. The theoretical developments concern the motion＇s generation, the modeling of the vehicle, then the management of its redundancy steam-power. All these methods contribute to improve the robot precision （accuracy）. The authors are presenting the motion＇s generator which constructs into lines a continuous trajectory C2 while enabling the transformation of the crossing points into lines. The generator presented here as part of omnidirectional robot is adaptable to any kind of vehicle.展开更多
In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by ter...In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.展开更多
Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of el...Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.展开更多
Hong's theorem for Grobner bases under polynomial composition is generalized to module case with more general cosideration. Similar generalization is also considered when the coefficient field is replaced by a Ded...Hong's theorem for Grobner bases under polynomial composition is generalized to module case with more general cosideration. Similar generalization is also considered when the coefficient field is replaced by a Dedekind domain.展开更多
基金Support by China 973 Project (No. 2002CB312200).
文摘A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
文摘From the basic properties of skein systems, we build a generalized tangle algebra (GTA). The elements of GTA are four basic tangles. There are three operations, which are connection, splicing and scalar multiplication. From GTA we derive two generalized recursion formulae (GRF) and prove the existence of a generalized skein relation which satisfies GRF. The obtained generalized skein relation epitomizes all generalizations from the Jones polynomial and thus forms a unified model. Two important topological parameters, twisting measure and loop values, appear explicitly in the expressions of the unified model, and this fact greatly simplifies the operations.
文摘The motion＇s generation consists in finding an analytic expression of a motion according to time. A Map road type planner or Cell decomposition provide to the motion generator some possible free crossing points of collision. The global trajectory＇s interpolation by a polynomial is generally not possible, because the degree of the polynomial increases with the number of crossing points which can generate vibrations or loops of the. trajectory. The solution consists in using polynomials in an inferior degree and to build the motion in pieces. The theoretical developments concern the motion＇s generation, the modeling of the vehicle, then the management of its redundancy steam-power. All these methods contribute to improve the robot precision （accuracy）. The authors are presenting the motion＇s generator which constructs into lines a continuous trajectory C2 while enabling the transformation of the crossing points into lines. The generator presented here as part of omnidirectional robot is adaptable to any kind of vehicle.
基金supported by the National Natural Science Foundation of China under Grant No.11171051the Major Research plan of the National Natural Science Foundation of China under Grant No.91230103the Fundamental Research Funds for the Central Universities under Grant No.DUT14RC(3)023
文摘In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.
文摘Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.
基金This research is supported by 973 Project(1998030600).
文摘Hong's theorem for Grobner bases under polynomial composition is generalized to module case with more general cosideration. Similar generalization is also considered when the coefficient field is replaced by a Dedekind domain.
