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Seminarium naukowe: „Stabilization and Motion Planning of Nonlinear Control Systems: A Gradient Flow Approximation”

W dniu 13.05.2025 r. (wtorek) o godz. 10:15 w sali 25 WI2 odbędzie się seminarium naukowe podczas którego prof. Alexander Zuyev z Instytutu Maxa Plancka przedstawi zagadnienie:

„Stabilization and Motion Planning of Nonlinear Control Systems:  A Gradient Flow Approximation”.

This talk focuses on nonlinear control-affine systems governed by ordinary differential equations with time-varying vector fields. We introduce a unified control design framework employing oscillatory inputs to address both trajectory tracking and stabilization problems, assuming the system satisfies a bracket-generating condition. Our core idea is to approximate gradient-like dynamics by the trajectories of a suitably designed closed-loop system. As an intermediate result, we describe the asymptotic behavior of solutions to this class of nonlinear systems with oscillating inputs, under quite general conditions on the underlying potential function. The proposed approach is further applied to trajectory tracking and obstacle avoidance problems for mathematical models of mobile robots.