Set Based Computing Methods in Optimization and Control
Boris Houska
ShanghaiTech University
Tuesday, June 22, 2021, 9:00
online via Zoom
https://uni-freiburg.zoom.us/j/62791737415
Meeting-ID: 627 9173 7415
Password: syscop2021
This talk is about numerical methods for robust worst-case optimization and control of nonlinear dynamic systems. In the first part, we review set-based computing methods using intervals, ellipsoids, polytopes, zonotopes, or more general polynomial sets. We discuss the advantages and disadvantages of these sets from a computational perspective as well as their applications in the field of set-valued integration of dynamic systems. The second part of the talk starts with an overview of robust model predictive control (MPC) methods. In detail, we explain how the above set-based computing methods can be used to synthesize Tube MPC controllers. In contrast to many existing Tube MPC implementations, we propose a framework that does not involve discretizing the control policy and therefore the conservatism of the predicted tube depends solely on the accuracy of the set parameterization. The talk concludes with a personal view of the open problems and challenges that Tube MPC has been facing during the last decade and we will share a research vision for the coming years.
References
1. Villanueva et.al. A set-theoretic generalization of dissipativity with applications in Tube MPC. Automatica, 2020.
2. Houska, Villanueva. Robust optimization for MPC. Handbook of MPC, Springer, 2019.
3. Hu et.al. Real-time tube MPC applied to a 10-state quadrotor model. ACC, 2018.
4. Villanueva et.al. Robust MPC via min-max differential inequalities. Automatica, 2017.
5. Rajyaguru et.al. Chebyshev models arithmetic for factorable functions. Journal of Global Optimization, 2017.
6. Houska et.al. Stable set-valued integration of nonlinear dynamic systems using affine set parameterizations. SIAM Journal on Numerical Analysis, 2015.
7. Villanueva et.al. Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs. Journal of Global Optimization, 2015.