A. Miele

Sequential gradient-restoration algorithm for optimal control problems

AbstractThis paper considers the problem of minimizing a functionalI which depends on the statex(t), the controlu(t), and the parameter π. Here,I is a scalar,x ann-vector,u anm-vector, and π ap-vector. At the initial point, the state is prescribed. At the final point, the statex and the parameter π are required to satisfyq scalar relations. Along the interval of integration, the state, the control, and the parameter are required to satisfyn scalar differential equations. Asequential algorithm composed of the alternate succession of gradient phases and restoration phases is presented. This sequential algorithm is contructed in such a way that the differential equations and boundary conditions are satisfied at the end of each iteration, that is, at the end of a complete gradient-restoration phase; hence, the value of the functional at the end of one iteration is comparable with the value of the functional at the end of any other iteration.In thegradient phase, nominal functionsx(t),u(t), π satisfying all the differential equations and boundary conditions are assumed. Variations Δx(t), Δu(t), Δπ leading to varied functions

General technique for solving nonlinear, two-point boundary-value problems via the method of particular solutions

\tilde x

Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions

(t),ũ(t),

Optimal take-off trajectories in the presence of windshear

\tilde \pi

Study on a memory gradient method for the minimization of functions

are determined so that the value of the functional is decreased. These variations are obtained by minimizing the first-order change of the functional subject to the linearized differential equations, the linearized boundary conditions, and a quadratic constraint on the variations of the control and the parameter.Since the constraints are satisfied only to first order during the gradient phase, the functions