Optimal control of lumped parameter systems via shifted Legendre polynomial approximation
Shifted Legendre polynomial functions are employed to solve the linear- quadratic optimal control problem for a lumped parameter system. Using the characteristics of the shifted Legendre polynomials, the system equations and the adjoint equations of the optimal control problem are reduced to functional ordinary differential equations. The solution of the functional differential equations are obtained in a series of the shifted Legendre functions. The operational matrix for the integration of the shifted Legendre polynomial functions is also introduced in the simulation step in order to simplify the computational procedure. An illustrative example of an optimal control problem is given, and the computational results are compared with those of the exact solution. The proposed method is effective and accurate.
scientific article; zbMATH DE number 3852900
scientific article