CAREER: System Design Under Risk Constraints

本提案的研究目标是为存在参数不确定性的风险约束下的系统设计提供一个全面的框架。PI的目的是为已知不确定参数分布的情况和不知道分布的情况开发有效的设计程序。概率稳健性这一新兴领域的最新研究成果提供了风险评估的框架，即使不确定参数的分布是未知的，但它的一些特征是可用的。人们可能会问的一个问题是：为什么在设计系统时考虑风险约束？虽然在许多情况下希望满足允许不确定性的每个可能值的性能规范，但在某些情况下，人们愿意在违反规范的小风险和系统的复杂性之间进行权衡。此外，有几个问题自然而然地导致了涉及风险规范的表述。一个例子与紧急系统处理有关。在这种情况下，人们愿意容忍系统发生故障的一些风险，以换取性能的改善，从而有更好的机会处理手头的紧急情况。因此，希望能够设计一种在系统故障风险较小且定义良好的情况下最大化性能的控制系统。到目前为止，在风险约束下的系统设计成果有限。它们使用随机搜索来确定系统增益，并且只处理不确定参数分布可用的情况。这项研究的目的是在已知不确定参数的分布和已知其部分特征的情况下，为风险规范下的系统设计开发有效的确定性程序。其目的是将首席调查员当前的研究与课程内容联系起来，并使学生更接近控制科学的最新发展。至于本科教育，重点将放在改进控制高级课程的内容上，引入本科课程通常不会涉及的概念，如系统不确定性。这还将包括开发实验室实验，为学生提供系统设计的实践经验。该协会还计划开设两个研究生课程。第一门课程的初步题目是“离散随机系统”，重点是离散随机系统的分析和控制器设计。本课程将被设计为一门多学科的课程，不仅针对控制领域的学生，也针对其他领域的学生，即通信领域的学生。第二门课程将致力于研究多变量控制的最新发展。本课程将与机械工程系合作开发。*

9984260LagoaThe research objective of this proposal is to provide a comprehensive framework for system design under risk constrains in the presence of parametric uncertainty. The PI aims at developing efficient design procedures for both the case when the distribution of the uncertain parameters is known and for the case when the distribution is not available. Recent results in the emergent area of Probabilistic Robustness provide the main motivation for the proposed research since they provide a framework for risk assessment even if the distribution of the uncertain parameters is not known, only some of its characteristics are available.One question that one might ask is: Why consider risk constraints when designing a system? Although in many cases it is desirable to satisfy the performance specifications for every possible value of the admissible uncertainties, there are cases in which one is willing to have a tradeoff between a small risk of violation of the specifications and complexity of the system. Also, there are several problems that naturally lead to a formulation involving risk specifications. One example relates to emergency system handling. In this case, one is willing to tolerate some risk of failure of the system in exchange for an improvement on the performance and, therefore, a better chance of handling the emergency at hand. Hence, it would be desirable to be able to design a control system that maximizes the performance under a small well defined risk of system failure. Results to date on system design under risk constraints are limited. They use random search to determine the system gains and only address the case where the distribution of the uncertain parameters is available. The research proposed aims at developing efficient deterministic procedures for system design under risk specifications when the distribution of the uncertain parameters is available and when only some of its characteristics are known.The education plan described in this proposal includes curriculum development of both undergraduate and graduate courses. The objective is to interconnect the Principal Investigator current research with the content of the courses and to "bring" the students closer to the latest developments in control science. As for undergraduate education, the emphasis will be put in the improvement of the content of senior courses in control, introducing concepts which are not usually covered in undergraduate courses such as system uncertainty. This will also include the development of laboratory experiments which will provide the students with a hands-on experience in system design. The PI also plans on developing two graduate courses. The first, whose preliminary title is "Discrete-Time Stochastic Systems", is a course whose emphasis will be in the analysis and controller design for discrete stochastic systems. This course will be designed as a multidisciplinary course, aimed not only at students in control but also at students in other areas, namely at those in the communications area. The second course will be dedicated to the study of the latest developments in multivariable control. This course is to be developed in collaboration with the Mechanical Engineering Department.***