Computational Sampled-Data Nonlinear Control

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

While researchers have made major breakthroughs in controlling nonlinear continuous time systems over the last two decades, more recently the research has started to focus on methods for controlling continuous time systems based on discrete time models and over digital networks, because of the need to control increas- ingly complex systems and because of the increasing computer power typically available. The proposed work aims to use previously developed nonlinear continuous time control methods as a springboard to develop new, high performance control algorithms for general nonlinear systems based on discrete-time models. The focus will be on developing algorithms that are robust, adaptive, and don't require full measurement of the system state. Applications of these results will include the development of optimal treatment schedules for HIV patients, leading to a non-progressive state where treatment is no longer needed. Other applica- tions will include control and calibration of automotive engines where state constraints, which are easy to incorporate into certain optimization-based control strategies but which often lead to non-robust control algorithms, play an important role. The proposed work also aims to give new, improved stability conditions for networked nonlinear control systems, especially those using protocols that don't necessarily guarantee transmission to every node of the communication network within a fixed amount of time. It is expected that these new stability conditions for networked control systems will give insight into the development of novel communication protocols which will, in turn, make networked control systems more successful and prevalent. Broader impact: The work in this proposal has the potential for broad impact via the role that control plays as an enabling technology. As suggested above, the ideas that we will investigate may help lead the way to efficient drug treatment schedules for HIV patients leading to a non-progressive state, thereby eliminating the need for further drug therapy. In general, it should make it more feasible to rely on optimization-based automation algorithms for a wide range of engineering tasks that impact all of society. The proposal will support graduate students who will present their findings at national and regional conferences. The results will be made available, promptly, on the web and will be immediately incorporated into graduate courses at the proposing institution. The work will help to further shape UCSB's Center for Control Engineering and Computation, which is one of the leading programs in control education in the nation. It will strengthen interactions with international partners, e.g., in Australia, France and Italy, will foster novel collaborative efforts with theoretical biologists at the Fred Hutchinson Cancer Research Center in Seattle, and will further collaborative efforts with researchers at Ford Motor Company.