Novel Ways in Control and Computation: Predictive and Analog
Final Report Abstract
The main goal of the project was to combine and integrate control and computation in order to understand and to develop solutions for problems where both aspects, control and computation, play a crucial role. Specifically, the research was focused on model predictive control algorithms and continuous-time optimization algorithms. Hereby, the general research approach of the project was a bidirectional view on control and computation in the sense of applying optimization algorithms to control problems as well as applying system theoretic ideas to optimization problems. As a result of this research approach, the novel concept of relaxed barrier function based model predictive control was introduced and highly efficient model predictive control algorithms were developed. Further, a novel theory of extremum seeking control based on Lie bracket approximations was introduced and a general design and analysis framework for extremum seeking problems was developed. On a more fundamental level and beyond model predictive control and extremum seeking algorithms, basic exploratory research were carried out and a system-theoretic paradigm for designing and analyzing optimization algorithms was initiated.
Publications
- On a class of smooth optimization algorithms with applications in control. In Proc. of the 4th IFAC NMPC Conference 2012, Leeuwenhorst, Netherlands, pages 291–298, 2012
H.B. Dürr and C. Ebenbauer
(See online at https://doi.org/10.3182/20120823-5-NL-3013.00027) - Lie Bracket Approximation of Extremum Seeking Systems. Automatica, 49:1538–1552, June 2013
H. B. Dürr, M. S. Stanković , C. Ebenbauer, and K. H. Johansson
(See online at https://doi.org/10.1016/j.automatica.2013.02.016) - Continuous-time linear MPC algorithms based on relaxed logarithmic barrier functions. In Proc. of the 19th IFAC World Congress, Cape Town, South Africa, pages 2482–2488, 2014
C. Feller and C. Ebenbauer
(See online at https://doi.org/10.3182/20140824-6-ZA-1003.01022) - Extremum seeking on submanifolds in Euclidean spaces. Automatica, 50:2591–2596, October 2014
H. B. Dürr, M. S. Stanković , K. H. Johansson, and C. Ebenbauer
(See online at https://doi.org/10.1016/j.automatica.2014.08.019) - A Hessenberg-Jacobi isospectral flow. Nonlinear Differential Equations and Applications, 22:87–103, 2015
A. Arsie and C. Ebenbauer
(See online at https://doi.org/10.1007/s00030-014-0276-z) - Singularly perturbed Lie bracket approximation. IEEE Transactions on Automatic Control, 60:3287–3292, December 2015
H.B. Dürr, M. Krstic, A. Scheinker, and C. Ebenbauer
(See online at https://doi.org/10.1109/TAC.2015.2416925) - A stabilizing iteration scheme for model predictive control based on relaxed barrier functions. Automatica, 80:328–339, June 2017
C. Feller and C. Ebenbauer
(See online at https://doi.org/10.1016/j.automatica.2017.02.001) - Convergence properties of an isospectral saddle-point dynamics. In Proc. of the 20th IFAC World Congress, Toulouse, France, pages 8790–8794, 2017
B. Gharesifard and C. Ebenbauer
(See online at https://doi.org/10.1016/j.ifacol.2017.08.813) - Relaxed logarithmic barrier function based model predictive control of linear systems. IEEE Transactions on Automatic Control, 62:1223–1238, March 2017
C. Feller and C. Ebenbauer
(See online at https://doi.org/10.1109/TAC.2016.2582040) - On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties. Automatica, 94:151–160, August 2018
V. Grushkovskaya, A. Zuyev, and C. Ebenbauer
(See online at https://doi.org/10.1016/j.automatica.2018.04.024) - Sparsity-exploiting anytime algorithms for model predictive control: A relaxed barrier approach. IEEE Transactions on Control Systems Technology, pages 1–11, December 2018
C. Feller and C. Ebenbauer
(See online at https://doi.org/10.1109/TCST.2018.2880142)
