MULTIPLE-CRITERION CONTROL - A CONVEX-PROGRAMMING APPROACH

The performance of linear dynamic systems with respect to a non-linear increasing value function that aggregates convex functionals is investigated within a convex programming framework. The methodology developed in this paper combines fundamental properties of convex sets in order to decompose the multicriterion control problem into a two-level structure. The upper level of this structure comprises only decision-making aspects of the problem, and involves the solution of a relaxed and static multicriterion problem. The lower level of the structure comprises, in turn, only optimal control aspects of the problem. The overall procedure is easily implemented. The solution of the aggregated problem is obtained as the limit of a sequence of optimal control problems that preserve their original solution properties. Relationships between the approach adopted here and existing solution techniques are discussed. The solutions of the classical minimax and Salukvadze problems are obtained as special cases of the proposed approach.