Discrete-Time Adaptive Control using a Retrospective Performance and Its Applications to Fluids and Structures

Adaptive control is an area of control theory focused on achieving control objectives when limited model information is available or models are highly uncertain. Most adaptive control techniques rely on restrictive plant assumptions, requiring, for example, that plants are minimum phase or open-loop stable, and have low relative degree. This seminar is focused on an adaptive control technique, namely, retrospective cost adaptive control, that can control plants that are minimum phase or non-minimum phase, open-loop stable or unstable, and have arbitrary relative degree. Retrospective cost adaptive controllers are designed by minimizing a retrospective performance function, which is a surrogate for a system’s true performance measurement. Retrospective cost adaptive control can be used for a variety of control objectives including stabilization, command following, and disturbance rejection. Notably, these adaptive controllers can follow deterministic commands and reject deterministic disturbances without knowledge of the command or disturbance spectrum.
This seminar will present the existing theory behind retrospective cost adaptive control. We’ll begin by presenting the adaptive law for single-input, single-output, minimum-phase systems. Next, we’ll extend the controller to handle nonminimum-phase zeros. Finally, we’ll cover the full multi-input, multi-output control problem for plants that are either minimum phase or nonminimum phase. Retrospective cost adaptive control has been demonstrated on applications including the Air Force’s deployable optical telescope testbed, flow control using computational fluid dynamics, and a testbed for flexible membrane control. The results of these applications will be shared.

Jesse Hoagg is currently a Postdoctoral Research Fellow in the Aerospace Engineering Department at the University of Michigan. His research interests include adaptive control with applications to flow control and structural control as well as system identification and robust control methods. Jesse received the Ph.D degree in aerospace engineering from the University of Michigan in 2006. After receiving the Ph.D, Jesse spent three years as a management consultant working for McKinsey & Company. Jesse also received the M.S.E. degree in aerospace engineering from the University of Michigan, the M.S. degree in mathematics from the University of Michigan, and the B.S.E. degree in civil and environmental engineering from Duke University.