scholarly journals Hysteretic Control Lyapunov Functions with Application to Global Asymptotic Tracking for Underwater Vehicles

Author(s):  
Erlend A. Basso ◽  
Henrik M. Schmidt-Didlaukies ◽  
Kristin Y. Pettersen
Author(s):  
Fre´de´ric Mazenc ◽  
Marcio de Queiroz ◽  
Michael Malisoff

We prove global uniform asymptotic stability of adaptively controlled dynamics by constructing explicit global strict Lyapunov functions. We assume a persistency of excitation condition that implies both asymptotic tracking and parameter identification. We also construct input-to-state stable Lyapunov functions under an added growth assumption on the regressor, assuming that the unknown parameter vector is subject to suitably bounded time-varying uncertainties. This quantifies the effects of uncertainties on the tracking and parameter estimation. We demonstrate our results using the Ro¨ssler system.


Author(s):  
Zhigang Deng ◽  
Mohammed Tousif Zaman ◽  
Zhenzhong Chu

Unmanned underwater vehicles (UUVs) move in dynamic environments and need to avoid other non-cooperative obstacles while executing a task, such as tracking a target or a special trajectory. It is a challenge to avoid collisions with moving obstacles in the tracking process. The present paper describes the implementation of horizonplane adaptive cruise control, which follows a given desired trajectory using control Lyapunov functions while satisfying constraints specified by a control barrier function to avoid collision with obstacles. The Lyapunov function is treated as a soft constraint, and the barrier function as hard constraint for the UUV; both are satisfied simultaneously using quadratic programming. Finally, the present paper describes a simulation of avoiding moving obstacles while tracking a target, with the results showing this as effective and feasible.


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