New Transformation Technique for Optimal Control Problems with Bounded State. Part I. Theory,
Abstract
The numerical solution of optimal control problems involving a state inequality constraint of the form L(x, theta) = or > 0 is considered. The approach employed is of the hybrid type, in an attempt to combine some of the best features of the indirect approach and the direct approach. While a predetermined number and sequence of subarcs are assumed (a feature of direct methods), enforcement of the state inequality constraint is obtained through a Valentine-type representation (a feature of indirect methods). A new transformation technique is developed by applying the Valentine-type representation to the kth derivative of the function L(x, theta), assumed to have a constant sign in each of the subarcs composing the extremal arc. The algorithm developed belongs to the class of sequential gradient-restoration algorithms. The principal property of the algorithm is that it produces a sequence of feasible suboptimal solutions: the functions x(t),u(t), pi obtained at the end of each cycle satisfy the constraints to a predetermined accuracy. Five numerical examples illustrating the theory are given in Part 2 (AD/A-004 334) and demonstrate the feasibility as well as the rapidity of convergence of the technique developed in this paper.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1974
- Accession Number
- ADA004333
Entities
People
- Angelo Miele
- J. R. Cloutier
Organizations
- Rice University