ISSN:
1573-2878
Keywords:
Minimax problems
;
minimax function
;
minimax function depending on the state
;
minimax function depending on the control
;
optimal control
;
minimax optimal control
;
numerical methods
;
computing methods
;
transformation techniques
;
gradient-restoration algorithms
;
sequential gradient-restoration algorithms
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In a previous paper (Part 1), we presented general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We considered two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). In this paper, the transformation techniques presented in Part 1 are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Both the single-subarc approach and the multiple-subarc approach are employed. Three test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation techniques and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the analytical solutions from the point of view of the minimax performance index. The relative differences between the numerical values and the analytical values of the minimax performance index are of order 10−3 if the single-subarc approach is employed. These relative differences are of order 10−4 or better if the multiple-subarc approach is employed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934326
