The overall goal of this career proposal is to explore the purely interdisciplinary subject of feedback control system design for generation of rhythmic patterns found in animal locomotion, and to develop effective pedagogical methods for inspiring engineering students with benefits of biological knowledge in the context of systems and control. Specific Goals: I. Develop an orbital trajectory analysis method for a class of nonlinear systems arising from modeling of biological pattern generators. II. Establish a method for designing a dynamical system that achieves pattern generation with a prescribed oscillation profile. III. Revise the dynamics and control curriculum to provide a broader view of systems through crossdisciplinary training in neuroscience. IV. Integrate the bio-control research into the science and engineering education at broad levels including K-12 and college undergraduate. V. Broadly disseminate the results of the proposed activities. Methods and Procedures (Keyed to the Specific Goals): I. Mathematically formulate an oscillation analysis problem and derive a solution using tools from robust control theory. Examine the degree of conservatism exploiting the biological knowl-edge of particular central pattern generator (CPG) architectures. II. Use the analysis result in I as a basis for developing a general theory for the design of CPGs utilizing linear matrix inequality methods. Test the applicability of the design conditions against the CPGs known from biology. III. Improve an undergraduate course on systems modeling by introducing neuronal modeling and pattern generation mechanism. Develop a new graduate course on robust and nonlinear control for regulation and biological oscillation. IV. Develop research-based educational tools through multidisciplinary, teamworking, senior thesis projects. Use the tools to stimulate K-12 and undergraduate students' intellectual curiosity into engineering and science through a series of outreach/educational activities. V. Utilize conference presentations, publications in archival journals, invited seminars, and possibly tutorial workshops in major international conferences. Intellectual Merit: The central theme of feedback control theory has been the regulation around an equilibrium point of a dynamical system. In contrast, much less attention has been paid to control specifications involving periodic motion (or oscillation) generation despite their practical impor-tance. The basic research outlined in this proposal will provide an initial stepping stone toward a new control paradigm that focuses on autonomous pattern generation by feedback dynamics. In particular, the project will establish a systematic method for analysis and design of pattern genera-tors through the exploitation of biological knowledge on neuronal oscillators. Broader Impact: The crossdisciplinary research activities over biology and control fields are in-tegrated into educational activities at all levels. The revised curriculum will provide undergraduate and graduate students with a broader perspective on engineering problems. The senior thesis project will develop students with team-oriented problem-solving skills in a multidisciplinary environment. The outreach activities will contribute to improve scientific literacy of K-12 students.
