an:04113390
Zbl 0679.49031
Agrawal, O. P.
General formulation for the numerical solution of optimal control problems
EN
Int. J. Control 50, No. 2, 627-638 (1989).
00155228
1989
j
49M29 49J15 33C45
variational virtual work approach; canonical equations; Lagrange multiplier technique; Orthogonal polynomials; time-invariant system; time-varying system; quadratic performance
Summary: A new improved computational method for a class of optimal control problems is presented. The state and the costate (adjoint) variables are approximated using a set of basis functions. A method, similar to a variational virtual work approach with weighing coefficients, is used to transform the canonical equations into a set of algebraic equations.
The method allows approximating functions that need not satisfy the initial conditions a priori. A Lagrange multiplier technique is used to enforce the terminal conditions. This enlarges the space from which the approximating functions can be chosen. Orthogonal polynomials are used to obtain a set of simultaneous equations with fewer nonzero entries. Such a sparse system results in substantial computational economy.
Two examples, a time-invariant system and a time-varying system with quadratic performance index, are solved using three different sets of orthogonal polynomials and the power series to demonstrate the feasibility and efficiency of this method.