Verifying Stability of Non-linear Systems with Gaussian Noise

Abstract:

We consider the problem of bounding the failure probability (defined as leaving a finite region of state space) over a finite time for stochastic nonlinear systems with continuous state. Our approach uses exponential barrier functions to prove bounds using a variant of the classic supermartingale result. We use a semi-definite relaxation to find barrier functions that give good upper bounds. We show the effectiveness of the approach on the rimless wheel, pendulum, and cart-and-pole systems.

Biography:

I'm an applied math major who became interested in robotics after participating in MASLAB as a programmer. I currently work in the Robot Locomotion Group under Russ Tedrake. In addition to robotics, I am interested in statistical machine learning and computational cognitive science. I believe that the advent of the computer, and the continual rise in computing power, is revolutionizing the way we do research, and that the interesting questions are about what we can compute efficiently, not what we can write down compactly. Two specific research programs I am interested in are statistical models of intuitive physics and verification-based learning algorithms for dynamical systems.