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Center for Nonlinear Studies |
Partial differential equations are effective in modeling physical applications such as fluid flows, thermal dynamics, flexible wings, electrochemistry in batteries, or plasmas in lasers and tokamaks. In its early period PDE control focused on replicating linear control methods (pole placement, LQG, H-infinity, etc) in infinite dimension. Over the last 15 years, a continuum version of the "backstepping" method has given rise to control design tools for nonlinear PDEs and PDEs with unknown functional coefficients. Backstepping designs now exist for each of the major PDE classes (parabolic, hyperbolic, real- and complex-valued, and of various orders in time and space). As a special case, continuum backstepping compensates delays of arbitrary length and dependence on time in general nonlinear ODE control systems. I will present a few feedback design tools and several applications, including deep oil drilling (where a large parametric uncertainty occurs) and extruders in 3D printing (where a large delay is a nonlinear function of the value of the state).
Host: Anatoly Zlotnick