# Efficient Propagation of Uncertainty thru Nonlinear Dynamical Systems

Ensuring the safety of the human is usually the most critical requirement during human-machine interactions. Given a dynamical model for a machine and a model of uncertainty for the operation of the machine by a human, one can analyze the safety and many other properties of the human-machine interaction by propagating the model of uncertainty through the machine dynamics. Our group has developed convex optimization tools to address this problem and is currently investigating techniques to improve the speed and scalability of these methods.

### References

- R. Vasudevan, “Numerical Advection of Probability Densities for High Dimensional Systems,” in
*SIAM Conference on Applications of Dynamical Systems*, 2015. - V. Shia, Y. Gao, R. Vasudevan, K. Campbell, T. Lin, F. Borrelli and R. Bajcsy, “Semiautonomous Vehicular Control Using Driver Modeling,”
*IEEE Transactions on Intelligent Transportation Systems*, vol. 15, no. 6, pp. 2696-2709, November 2014. [url] - V. Shia, R. Vasudevan, R. Bajcsy and R. Tedrake, “Convex Computation of the Reachable Set for Controlled Polynomial Hybrid Systems,” in
*IEEE Conference on Decision and Control*, 2014. [pdf] - R. Vasudevan, V. Shia, Y. Gao, R. Cervera-Navarro, R. Bajcsy and F. Borrelli, “Safe semi-autonomous control with enhanced driver modeling,” in
*American Control Conference*, pp. 2896-2903, 2012. [pdf] - A. Majumdar, R. Vasudevan, M. M. Tobenkin and R. Tedrake, “Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures,”
*International Journal of Robotics Research*, vol. 33, pp. 1209-1230, August 2014. [url]