This award will support research collaboration between Dr. Robert L. Kosut, Integrated Systems, Inc. Palo Alto, California, and Dr. Karl J. Astrom, Lund Institute of Technology, Sweden. They plan to investigate issues related to the stability analysis of adaptive control systems. Such systems are more useful for dealing with uncertainty than are fixed model control systems. Adaptive control systems allow control functions to be implemented in real time and on-line, rather than off-line. A problem with adaptive control systems is their relative lack of robustness and stability. The intent of the proposed research is to develop theory and definitions of mathematical and computational tools to assist in the computer-aided-design for the next generation of computer-aided-design of adaptive control systems. Drs. Kosut and Astrom propose to investigate the transient behavior of adaptive control systems and the relation between the methods of system identification and robust control. They will try to develop a list of computational tools that will be useful for computer-aided-design of adaptive and nonlinear systems. They will also attempt to clarify model accuracy in system identification, which will aid in developing methods for robust on-line control tuning.