This proposal is for the continuation of research begun under Grant ECS-8505645 and is concerned with the development of theory and computer aided design algorithms for application of l1-optimization theory to the design of digital controllers for nonlinear systems. The current status of l1-optimal control is briefly reviewed and several areas of research are discussed in the context of control of a robotic manipulator. The problems discussed are of general interest and are not restricted to the particular device used for motivation.