Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some struct...Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some structural parameters. Consequently, Cl substitution positions were taken as theoretical descriptors to establish a novel QSPR model for predicting –lgSw of all PCB congeners. The model achieved in this work contains four variables, of which r^2 = 0.9527, q^2 = 0.9490 and SD = 0.25 with large t values. In addition, the variation inflation factors （VIFs） of variables in this model are all less than 5.0, suggesting high accuracy of the –lgSw predicting model. And the results of cross-validation test and method validation also show that the model exhibits optimum stability and better predictive capability than that from the AM1 method.展开更多
In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）...In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）. The Legendre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto （CGL） collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.展开更多
On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is ...On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their property.As a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic forces.Further,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general solutions.Benefiting from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general form.Specifically,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms involved.Unlike what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)method.As a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.展开更多
基金This work was supported by the 973 National Basic Research Program of China (2003CB415002)the China Postdoctoral Science Foundation (No. 2003033486)
文摘Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some structural parameters. Consequently, Cl substitution positions were taken as theoretical descriptors to establish a novel QSPR model for predicting –lgSw of all PCB congeners. The model achieved in this work contains four variables, of which r^2 = 0.9527, q^2 = 0.9490 and SD = 0.25 with large t values. In addition, the variation inflation factors （VIFs） of variables in this model are all less than 5.0, suggesting high accuracy of the –lgSw predicting model. And the results of cross-validation test and method validation also show that the model exhibits optimum stability and better predictive capability than that from the AM1 method.
基金supported by the National Natural Science Foundation of China (Grant Nos.10471089,60874039)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）. The Legendre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto （CGL） collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.
文摘On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their property.As a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic forces.Further,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general solutions.Benefiting from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general form.Specifically,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms involved.Unlike what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)method.As a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.
