Small-time local controllability and continuity of the optimal time function for linear systems

1987 ◽  
Vol 53 (2) ◽  
pp. 281-296 ◽  
Author(s):  
H. J. Sussmann
Keyword(s):  
Linear Systems ◽  
Small Time ◽  
Time Function ◽  
Local Controllability ◽  
Optimal Time

On the small-time controllability of discontinuous piece-wise linear systems

2013 ◽  
Vol 62 (2) ◽  
pp. 218-223 ◽  
Author(s):  
Mikhail Ivanov Krastanov ◽  
Marc Quincampoix
Keyword(s):  
Linear Systems ◽  
Small Time

A necessary condition for small-time local controllability

Automatica ◽  
2021 ◽  
Vol 124 ◽  
pp. 109258
Author(s):  
Mikhail Ivanov Krastanov ◽  
Margarita Nikolaeva Nikolova
Keyword(s):  
Small Time ◽  
Local Controllability ◽  
Necessary Condition

scholarly journals Stability and nonlinear controllability analysis of a quadrotor-like autonomous underwater vehicle considering variety of cases

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881940 ◽  
Author(s):  
Liwei Kou ◽  
Ji Xiang ◽  
Yanjun Li ◽  
Jingwei Bian
Keyword(s):  
Horizontal Plane ◽  
Autonomous Underwater Vehicle ◽  
Vertical Plane ◽  
Underwater Vehicle ◽  
Plane Motion ◽  
Small Time ◽  
Degree Of Freedom ◽  
Local Controllability ◽  
Actuation System ◽  
Nonlinear Controllability

A quadrotor-like autonomous underwater vehicle that is similar to, yet different from quadrotor unmanned aerial vehicles, has been reported recently. This article investigates the stability and nonlinear controllability properties of the vehicle. First, the 12-degree-of-freedom model of the vehicle deploying an X shape actuation system is developed. Then, a stability property is investigated showing that the vehicle cannot be stabilized by a time invariant smooth state feedback law. After that, by adopting a nonlinear controllability analysis tool in geometric control theory, the small-time local controllability of the vehicle is analyzed for a variety of cases, including the vertical plane motion, the horizontal plane motion, and the three-dimensional space motion. Finally, different small-time local controllability conditions for different cases are developed. The result shows that the small-time local controllability holds for vertical plane motion and horizontal plane motion. However, the full degree of freedom kinodynamics model (i.e. 12 states) of the vehicle does not satisfy the small-time local controllability from zero-velocity states.

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