The Vdot function does not satisfy negative definite condition

YaChienChang / Neural-Lyapunov-Control

Learning Lyapunov functions and control policies of nonlinear dynamical systems

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The Vdot function does not satisfy negative definite condition #5

Closed kimukook closed 3 years ago

kimukook commented 3 years ago

Hi Ya-Chien,

I tried to run your inverted pendulum case on my own laptop and plot the Lyapunov function and its Lie derivative as shown below: NNLF_V NNLF_Vdot2

There are some regions that Lie derivative of V is positive. Also I found it is pretty weird but I am not sure which part I did it incorrectly, running the same code from Jupiter notebook on my laptop does not show Lyapunov conditions are satisfied from CheckLyapunov using dReal. Any suggestion on this? Thank you!

YaChienChang commented 3 years ago

Hi Muhan Zhao, Some regions of LieV are positive because the candidate Lyapunov function is not a valid Lyapunov function (it doesn’t pass the verification from dReal). I run the inverted pendulum jupyter notebook with dReal: v4.19.02.1 and Pytorch: 1.2.0. The candidate can pass and the LieV plot shown as below: Lie The different versions of the tool might need to use different parameters and iteration to pass the verification. Thank you :)