Chance-Constrained Model Predictive Control based on Deterministic Density Approximation and Homotopy Continuation
Final Report Abstract
We have completed a three-year project on stochastic optimal control under the consideration of chance constraints, i.e., constraints that have to be satisfied with a certain predefined probability. The key ideas of the project consisted in the use of a homotopy continuation technique to gradually introduce the constraints into an unconstrained problem, the use of deterministic sampling methods, and the application to MJLS. In the course of the project, we have developed a progressive chance-constrained control algorithm based on homotopy continuation methods as outlined in the proposal for both the cases of state and measurement feedback. The resulting algorithm is based on an affine control law that is obtained using LQG and serves as an initial solution. Then, the chance constraints are gradually introduced into the cost function using an exponential barrier. Our method was thoroughly evaluated in simulations and showed good convergence properties in our experiments. We also considered the use of deterministic sampling and provided results on the worst case behavior. Due to the limitations of this method, we investigated the use of sector and box approximations of polytopic chance constraints and presented two novel approaches that go beyond state-of-the-art methods such as ellipsoidal approximations. Furthermore, we investigated MJLS and presented several new fundamental results on control of MJLS without mode observations. Unlike many classical approaches, we did not attempt to estimate the mode of the system, but instead derived an optimal control law that is independent of the mode. We believe that the results obtained in the course of the project constitute a valuable contribution to the scientific research in the field of chance-constrained control and control of MJLS. Due to the widespread nature of these problem classes, many practical applications can benefit from the work performed in this project.
Publications
- Chance-constrained Model Predictive Control based on Box Approximations. In Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, December 2015
Maxim Dolgov, Gerhard Kurz, and Uwe D. Hanebeck
(See online at https://doi.org/10.1109/CDC.2015.7403353) - Finite-horizon Dynamic Compensation of Markov Jump Linear Systems without Mode Observation. In Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016), Las Vegas, Nevada, USA, December 2016
Maxim Dolgov, Gerhard Kurz, and Uwe D. Hanebeck
(See online at https://doi.org/10.1109/CDC.2016.7798679) - Progressive Closed-Loop Chance-Constrained Control. In Proceedings of the 19th International Conference on Information Fusion (Fusion 2016), Heidelberg, Germany, July 2016
Gerhard Kurz, Maxim Dolgov, and Uwe D. Hanebeck
- Linear Regression Kalman Filtering Based on Hyperspherical Deterministic Sampling. In Proceedings of the 56th IEEE Conference on Decision and Control (CDC 2017), Melbourne, Australia, December 2017
Gerhard Kurz and Uwe D. Hanebeck
(See online at https://doi.org/10.1109/CDC.2017.8263785) - Stochastic Optimal Control Using Local Sample-Based Value Function Approximation. In Proceedings of the 2018 American Control Conference (ACC 2018), Milwaukee, Wisconsin, USA, June 2018
Maxim Dolgov, Gerhard Kurz, Daniela Grimm, Uwe D. Hanebeck, and Florian Rosenthal
(See online at https://doi.org/10.23919/ACC.2018.8431584)
