THE OBJECTIVE OF THE PRESENT PROPOSAL IS THE DEVELOPMENT OF SOME MATHEMATICAL AND COMPUTATIONAL TOOLS THAT ARE APPROPRIATE TO THE NEXT GENERATION OF CAD (COMPUTER-AIDED DESIGN) ENVIRONMENTS.

THE OBJECTIVE OF THE PRESENT PROPOSAL IS THE DEVELOPMENT OF SOME MATHEMATICAL AND COMPUTATIONAL TOOLS THAT ARE APPROPRIATE TO THE NEXT GENERATION OF CAD (COMPUTER-AIDED DESIGN) ENVIRONMENTS. THESE CAD PACKAGES WILL BE RADICALLY DIFFERENT THAN THE PRESENT ANALYSIS PACKAGES IN THAT THEY WILL TRULY BE ABLE TO PERFORM CONTROL SYSTEM SYNTHESIS. IN ORDER FOR THIS IDEAL SITUATION TO COME ABOUT, IT IS NECES-SARY FIRST TO SOLVE SOME IMPORTANT PROBLEMS IN THE MATHEMATICS OF CONTROL SYSTEMS AS WELL AS IN COMPUTATIONAL TECHNIQUES. PHASE I OF THE PROPOSED RESEARCH PROGRAM IS ADDRESSED TO STUDYING THE FEASIBILITY OF SOLVING SOME OF THE PROBLEMS. AMONG THE PROBLEMS WE PROPOSE TO STUDY ARE THE FOLLOWING: (I) NEW APPROACHES TO THE SIMULTANEOUS STABILIZATION PROBLEM, (II) UNCERTAINTY MODELLING, (III) NUMERICAL TECHNIQUES FOR CONSTRAINED OPTIMIZATION PROBLEMS, AND (IV) STABILITY OF REDUCED ORDER ADAPTIVE CONTROL. THESE PROBLEMS ARE INTIMATELY CONNECTED, EACH PROBLEM BEING AN ESSENTIAL TASK IN A TYPICAL INTERACTIVE CAD PROCEDURE.