Research on optimal control problem based on composite pseudospectral method
YE Shijin
LI Taifang
Abstract：This paper presents a composite pseudospectral method for solving a class of optimal control problems with piecewise smooth differential equations and inequality constraints.The system's operating interval to be optimized is divided into multiple sub-intervals with unequal spacing based on the non-smooth time points of the function.Within each sub-interval,segmented interpolation polynomials are constructed through transformed Legendre-Gauss-Radau nodes.The weak differential representation method is used to derive the corresponding derivative operation matrix.The Legendre-Gauss quadrature formula and the obtained derivative operation matrix are used to discretize the optimal control problem into a nonlinear programming problem,where the non-smooth points of the state function and control function are unknown parameters.The obtained discretized nonlinear programming problem can be solved using Matlab nonlinear solver.Due to the fact that the elements and structures in the derivative operation matrix establish connections between adjacent sub-interval systems states,this method can be used to handle optimal control problems for non-smooth ordinary differential equations.Numerical examples have verified the effectiveness of the proposed method.
Keywords：optimal controlpseudospectral methodpiecewise smooth functionweak differentiation method
Publication Date：2025-09-15
Online Publishing Date：2025-12-22(First online date of this platform, not the publication date of the document)
Pages：7( 200-206 )