Sequential gradientrestoration algorthim for optimal control problems with control inequality constraints and general boundary conditions
Abstract
The problem of minimizing a functional 1 subject to differential constraints, control inequality constraints, and terminal constraints is considered in this thesis. It consists of finding the state x(t), the control u(t), and the parameter pi so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. A sequential gradientrestoration algorithm is developed. It involves a sequence of twophase cycles, the gradient phase and the restoration phase. In the gradient phase, the value of the functional is decreased, while avoiding excessive constraint violation; in the restoration phase, the constraint error is decreased, while avoiding excessive change in the value of the functional. The variations delta x(t), delta u(t), delta pi are generated by requiring the first variation of the augmented functional J to be negative during the gradient phase; and by requiring the first variation of the constraint error P to be negative, while imposing a leastsquare criterion on the variations of the control, the parameter, and the initial state during the restoration phase.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1985
 Bibcode:
 1985PhDT........42C
 Keywords:

 Algorithms;
 Boundary Conditions;
 Boundary Value Problems;
 Constraints;
 Control Theory;
 Optimal Control;
 Independent Variables;
 Vectors (Mathematics);
 Fluid Mechanics and Heat Transfer