Long Actuator Delays - Extending the Smith Predictor to Nonlinear

Miroslav KrsticHarold W. Sorenson Professor of Control SystemsDept. of Mechanical & Aerospace EngineeringUniversity of California at San DiegoAbstract: One would be hard pressed to find "long actuator delays" and "nonlinear control" co-existing in the same sentence in the existing control literature, which is due to the infinite dimensionality and the potential for finite escape time instability in the underlying problems. On the 50th anniversary of Otto Smith's invention of the "predictor" feedback for compensating long actuator delays for linear systems, a method that has since become one of the favorite tools in chemical process control and many other applications, I am pleased to present an approach for synthesizing a predictor feedback to go along with any stabilizing nominal nonlinear controller, with actuator delay of any length. Interestingly, Smith's idea was actually an elementary version of "infinite dimensional backstepping," which I have been developing over the last few years for PDE problems such as Navier-Stokes, MHD, Euler and Timoshenko beams, and other systems in mechanics. By employing the backstepping point of view to construct Lyapunov-Krasovskii functionals, it becomes possible to prove several forms of robustness of predictor feedbacks, including robustness to both underestimating and overestimating the length of the actuator delay. The latter is a particularly subtle result because it involves a non-standard dynamic perturbation - the controller (inadvertently) inserts an additional infinite-dimensional state to an already infinite-dimensional feedback loop.

Location: Seaver Science Library, Rm 150

Audiences: Everyone Is Invited

Contact: April Mundy