CAREER: Feedback Control Theory for Biological Pattern Generation

目的：这个职业计划的总体目标是探索在动物运动中发现的节奏模式的产生的反馈控制系统设计的纯跨学科主题，开发有效的教学方法，在系统和控制的背景下启发工科学生学习生物学知识。具体目标：1.开发一种由生物模式产生器建模产生的非线性系统的轨道轨迹分析方法。2.建立一种设计方法，实现具有前述振荡轮廓的模式生成的动力系统的设计。3.修改动力学和控制课程，通过神经科学的跨学科培训，提供更广泛的系统视野。4.将生物控制研究整合到包括K-12和大学本科生在内的广泛水平的科学和工程教育中。5.广泛传播拟议活动的结果。方法和步骤(根据具体目标)：1.用数学方法描述一个振荡分析问题，并利用鲁棒控制理论中的工具推导出解决方案。检验利用特定中央模式发生器(CPG)体系结构的生物学知识的保守性程度。II.以文[1]的分析结果为基础，利用线性矩阵不等式方法，为CPG的设计发展一般理论。通过引入神经元建模和模式生成机制，改进本科系统建模课程，测试设计条件的适用性。开发一门关于调节和生物振荡的稳健和非线性控制的新研究生课程。IV。通过多学科、团队合作、高级论文项目开发基于研究的教育工具。利用这些工具，通过一系列外展/教育活动，激发K-12和本科生对工程和科学的求知欲。v.利用会议报告、档案期刊上的出版物、特邀研讨会，以及可能在大型国际会议上举办的辅导工作坊。智力价值：反馈控制理论的中心主题是围绕动力系统平衡点的调节。相比之下，涉及周期性运动(或振荡)生成的控制规范尽管具有实际意义，但受到的关注要少得多。本提案中概述的基础研究将为新的控制范式提供初步的垫脚石，该范式专注于通过反馈动力学来自主生成模式。特别是，该项目将通过开发关于神经元振荡器的生物学知识，建立一种分析和设计模式类属的系统方法。广泛的影响：生物学和控制领域的跨学科研究活动被纳入各级教育活动。修订后的课程将为本科生和研究生提供更广阔的工程问题视角。高级论文项目将培养学生在多学科环境中以团队为导向的解决问题的能力。外展活动将有助于提高K-12学生的科学素养。

Objective: The overall goal of this career proposal is to explore the purely interdisciplinary subjectof 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 ofbiological knowledge in the context of systems and control.Specific Goals:I. Develop an orbital trajectory analysis method for a class of nonlinear systems arising frommodeling of biological pattern generators.II. Establish a method for designing a dynamical system that achieves pattern generation with aprescribed oscillation profile.III. Revise the dynamics and control curriculum to provide a broader view of systems throughcrossdisciplinary training in neuroscience.IV. Integrate the bio-control research into the science and engineering education at broad levelsincluding 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 toolsfrom robust control theory. Examine the degree of conservatism exploiting the biological knowl-edgeof 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 CPGsutilizing linear matrix inequality methods. Test the applicability of the design conditions againstthe CPGs known from biology.III. Improve an undergraduate course on systems modeling by introducing neuronal modelingand pattern generation mechanism. Develop a new graduate course on robust and nonlinear controlfor regulation and biological oscillation.IV. Develop research-based educational tools through multidisciplinary, teamworking, seniorthesis projects. Use the tools to stimulate K-12 and undergraduate students' intellectual curiosityinto engineering and science through a series of outreach/educational activities.V. Utilize conference presentations, publications in archival journals, invited seminars, andpossibly tutorial workshops in major international conferences.Intellectual Merit: The central theme of feedback control theory has been the regulation around anequilibrium point of a dynamical system. In contrast, much less attention has been paid to controlspecifications 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 anew control paradigm that focuses on autonomous pattern generation by feedback dynamics. Inparticular, the project will establish a systematic method for analysis and design of pattern genera-torsthrough the exploitation of biological knowledge on neuronal oscillators.Broader Impact: The crossdisciplinary research activities over biology and control fields are in-tegratedinto educational activities at all levels. The revised curriculum will provide undergraduateand graduate students with a broader perspective on engineering problems. The senior thesis projectwill 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.