2019/12/09 by Ivan Polekhin, Polekhin, Ivan
Engineering · Mathematics · #Adaptive Control of Nonlinear Systems #Control and Stability of Dynamical Systems #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1912.04027
openalex publication_date 2019/12/09 · arxiv created 2021/04/30 · arxiv updated 2021/05/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We consider a possible application of the Ważewski topological method to feedback control systems and to more general dynamical systems. We show how this method can be used to prove the impossibility of global stabilization in such problems. Moreover, we give sufficient conditions for the existence of a solution such that its trajectory never leaves a subset of the extended phase space of the system and does not tend asymptotically to a given equilibrium. We illustrate our result with various real-life systems including the Furuta pendulum and the wheeled inverted pendulum.