A GRADIENT ALGORITHM FOR MINIMAX DESIGN.
Abstract
The minimax design of dynamic systems containing variable parameters is considered. The parameters fall into two categories: those which can be selected by the designer, x, and the parameters which can neither be preset nor precisely measured, y. For a given dynamic system the merits of the various parameter values are assumed to be summarized by a scalar performance index, J(x,y). Designs based on the minimax or worst case approach consist of selecting an x such that the maximum value of J(x,y) with respect to y is minimized. A gradient algorithm is presented for solving minimax problems. The term gradient is used here to denote the direction of steepest descent and is usually not a vector or partial derivatives evaluated at a point (x,y). The algorithm is shown to converge to local solutions which satisfy the necessary conditions for a minimax solution. As the proofs of convergence do not restrict the solution to be a saddle point, the algorithm can be applied to both saddle point and non-saddle point solutions. In addition to convexity requirements on the function J(x,y) are necessary. Both the theoretical and the numerical aspects of the algorithm are discussed. Two examples are presented and the results of the examples illustrate the usefulness and simplicity of the procedure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0685875
Entities
People
- James Ernest Heller
Organizations
- University of Illinois Urbana–Champaign