Mechanical and Civil Engineering Seminar
Mechanical and Civil Engineering Seminar Series
Title: "Nonholonomic Stabilization and Pursuit-Evasion: Not-so-hard After All"
Abstract: In the polar coordinates, the unicycle/Dubins vehicle passes Brockett's condition. Hence, stabilization - even global - by static feedback is achievable. I present feedback designs for several categories of problems. For steering-controlled, constant-velocity unicycles, finite-time stable parking is achieved. Shifting the attention from static targets and ground vehicles to moving-target interception, a kinematically inferior evader is captured, in spite of the evader's arbitrarily vigorous maneuvering. In the language of control, ISS with an asymptotic gain = 0 is achieved in pursuit-evasion games. The new ideas are (a) treating the distance-to-target as time in the feedback design and (b) converting the vehicle's inability to slow down from a challenge into an asset. For parking and spacecraft docking, with direction-reversible velocity control on top of steering, global STRICT CLFs are sought - a problem open for 42 years - and found using integrator forwarding and backstepping. Thanks to the DRIFTLESS nature of the unicycle, the strict CLFs then yield (1) optimality without solving HJB PDEs and (2) infinite gain margins. The problem of strict CLF construction for nonholonomic systems was open for 40+ years.
Bio: Miroslav Krstic is Distinguished Professor; founding director of UC San Diego's Center for Control Systems and Dynamics (CCSD) and the US Navy-funded Naval Innovation, Science, and Engineering Center (NISEC); and Senior Associate Vice Chancellor for Research. He has received the IEEE Brockett Control Systems (Field) Award, Bellman Award, Bode Lecture Prize, SIAM Reid Prize, ASME Oldenburger Medal, ASME Nyquist Lecture Prize and Paynter Award, Ragazzini Education Award, and several IFAC awards (Chestnut Textbook Prize, Nonlinear Control Systems Award, Ruth Curtain Distributed Parameter Systems Award, Adaptive and Learning Systems Award, Time-Delay Lifetime Achievement Award). Krstic is Fellow of IEEE, AIAA, IFAC, ASME, SIAM, AAAS, IET, and Serbian Academy of Sciences and Arts. Krstic has coauthored nineteen books on adaptive/nonlinear control, extremum seeking, and PDE control. His industrial transitions have been in chip photolithography and advanced arresting gear on carriers.