Computationally simulating complex physical systems in engineering design has become a common practice. Yet most of today's simulations rely on extensive numerical computations. Nonlinear physical systems can exhibit extremely complex behaviors that defy human analysis and pure numerical simulations. The analysis and design for these systems are limited by the available computational power and the system complexities. This research project will develop powerful computer simulation technologies for the analysis and design of nonlinear control systems. Programmable primitives will be developed for constructing simulations and synthesizing high-performance controllers. Hybrid computation will be for integrating symbolic and numerical methods with AI reasoning and representation techniques in (1) manipulating and visualizing the dynamics of physical systems based on a phase-space representation, and (2) guiding the execution of numerical computations. The expected results of this is to expand the scope of what current numerical simulation programs or state-of-the-art knowledge-based systems can do solving pressing scientific and engineering problems.
