Nonlinear and switched systems: Geometric motion planning, non-monotonic Lyapunov functions and input-to-state stability

Nonlinear systems;switched systems;motion planning;Lyapunov approach;input-to-state stability

Liu, Shenyu

关键词: Nonlinear systems;    switched systems;    motion planning;    Lyapunov approach;    input-to-state stability;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/107850/LIU-DISSERTATION-2020.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Both synthesis of control strategy for motion planning and analysis of stability of nonlinear and switched systems have been researched in this work. In terms of control strategy, we propose a novel approach to the long-standing problem of motion planning for non-holonomic systems. The admissible motion is obtained by properly assigning "length" to the motion trajectories which penalizes them in the inadmissible directions, and "deforming" them in order to minimize the "length" via solving a set of parabolic partial differential equations. Several variations of the fundamental motion planning problem are also considered in this work. In terms of stability analysis, we have studied two approaches related to non-monotonic Lyapunov functions. More explicitly, the techniques of "almost Lyapunov" functions and higher order derivatives of Lyapunov functions -- which were used to study the stability of autonomous nonlinear systems in the literature -- are generalized to nonlinear systems with inputs. Under some mild assumptions, the nonlinear systems can be proven to be input-to-state stable using these techniques of non-monotonic Lyapunov functions. In addition, the methodology used in the derivation can also be used to show the equivalence between several stability properties of state-dependent switched systems.