Nonlinear optimal control and optimal parameter selection by a modified reduced gradient method

An efficient method is described for handling the optimal control and optimal parameter selection problems of nonlinear dynamic systems involving equality and inequality algebraic constraints. The approximation of the optimal control problems is based on weighted residual approaches, but the residual equation is redefined based on the integral expression of the dynamic equations of the optimization problems. As a result, additional equality constraints for enforcing the continuity of the state variables at element boundaries are not required so that the approximate equations obtained by this collocation method can be unified into a compact expression. A modified reduced gradient method is then introduced toward determining the optimal solution of the approximate problem. The descent property of this partial feasible direction algorithm is proved in this study such that global convergence can be guaranteed.