Theory, Methods, and Applications of Nonlinear Control

The investigators developed new mathematical control methods and theory for nonlinear systems with time delays and uncertainty that included new controller designs and robustness analysis, adaptive control with parameter identification, and robust forward invariance that maintained state constraints under controller uncertainty and time delays. They also developed new optimal control and optimization theory for differential inclusions based on semiconcavity, state constraints, and systems on stratified domains. The investigators applied their theory to UAVs, planar vertical takeoff and landing aircraft, curve tracking using gyroscopic controls, and other important engineering models. The investigators authored 28 project-related archival publications that appeared or were accepted for publication or submitted during the project period. They supervised two project-related dissertations, one on Hamilton-Jacobi theory for stratified systems and a second on aerospace models with input constraints. The investigators also presented 53 conference or seminar talks. In recognition of their research, PI Malisoff was appointed as the Roy Paul Daniels Professor in the LSU College of Science, and PI Wolenski received a lifetime appointment as the Russell B. Long Professor of Mathematics.