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
Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spect...Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spectral accuracy. The numerical results coincide with those of the theoretical analysis. It is easy to generalize the proposed methods to multiple-dimensional prob- lems.展开更多
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.
基金the Chinese Key project on Basic Research (No.1999032804), and Shanghai Natural Science Foundation (No.00JC14D57).
文摘Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spectral accuracy. The numerical results coincide with those of the theoretical analysis. It is easy to generalize the proposed methods to multiple-dimensional prob- lems.
