Back to the Past: Retrospective Cost Adaptive Control for Plants with Uncertain Dynamics and Disturbance Spectra

Unlike most signal processing applications, feedback control entails real-time action with irrevocable real-world consequences. For example, an aircraft flies in response to wind gusts and control-surface deflections, and—-while there may be second chances if nothing drastic happens—we can't change the past. Suppose, however, that we *could* go back in time and replace the controls that were actually used with "retrospectively optimized" controls. Could these controls be used to guide the synthesis of a new controller that might provide better *future* performance? In this talk I will describe the ramifications of this simple idea, which originated in the lab and whose theoretical development is ongoing. In particular, this talk will show how online optimization of a retrospective cost function provides an easily implementable adaptive control algorithm that requires surprisingly little modeling information about the plant and command/disturbance spectra. To explain how RCAC works, I will describe recent theoretical developments based on virtual input reconstruction. Examples involving SISO and MIMO plants with possibly unknown nonminimum-phase zeros will be given along with nonlinear applications, where numerical results show promise but theory remains largely undeveloped. Finally, I will briefly describe applications of the same technique to adaptive state and input estimation for data assimilation.

Joint research with Anthony D'amato, Dogan Sumer, Jesse Hoagg, Mario Santillo, and Ravinder Venugopal.

Dennis Bernstein received his Ph.D. from the University of Michigan in 1982, where he has been a faculty member since 1991. He was previously employed by Harris Corporation and Lincoln Laboratory. He was editor-in-chief of the IEEE Control Systems Magazine from 2003 to 2011.