CAREER: System Design Under Risk Constraints

9984260 Lagoa The 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. ***