CAREER: Feedback Control Theory for Biological Pattern Generation

目标：本职业建议的总体目标是探索纯粹跨学科的反馈控制系统设计，以产生动物运动中的节奏模式，并开发有效的教学方法，以激励工程专业的学生在系统和控制的背景下受益于生物学知识。具体目标:我。发展了一类由生物模式发生器建模而产生的非线性系统的轨道分析方法。建立一种动力系统的设计方法，使其能在规定的振荡廓形下实现模式生成。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阔的系统视野。将生物防治研究融入包括中小学和大学本科在内的广泛的理工科教育。广泛传播拟议活动的成果。方法和程序（与具体目标相关）：从数学上阐述一个振荡分析问题，并利用鲁棒控制理论的工具推导出一个解决方案。检查利用特定中央模式生成器（CPG）架构的生物知识优势的保守性程度。利用第1章的分析结果作为基础，提出了利用线性矩阵不等式方法设计cpg的一般理论。根据生物学已知的CPGs测试设计条件的适用性。通过引入神经元建模和模式生成机制来改进系统建模的本科课程。开设一门新的关于调节和生物振荡的鲁棒非线性控制的研究生课程。通过多学科、团队合作和高级论文项目开发以研究为基础的教育工具。通过一系列的推广/教育活动，利用这些工具激发K-12和本科生对工程和科学的求知欲。利用会议演讲，在档案期刊上发表文章，邀请研讨会，并可能在主要的国际会议上进行指导讲习班。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，尽管它们具有实际重要性，但对涉及周期运动（或振荡）产生的控制规范的关注要少得多。本提案中概述的基础研究将为新的控制范式提供一个初步的垫脚石，该范式侧重于通过反馈动力学产生自主模式。特别是，该项目将通过利用神经振荡器的生物学知识，建立一种分析和设计模式生成扭转的系统方法。更广泛的影响：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。毕业论文项目将培养学生在多学科环境中具有团队解决问题的能力。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.