Novel Ways in Control and Computation: Predictive and Analog

• Applicant: Professor Dr.-Ing. Christian Ebenbauer
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2009 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 80283926

• Final Report Year: 2019

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
  
• 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
  
• 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
  
• 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
  
• A Hessenberg-Jacobi isospectral flow. Nonlinear Differential Equations and Applications, 22:87–103, 2015
  A. Arsie and C. Ebenbauer
  
• 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
  
• A stabilizing iteration scheme for model predictive control based on relaxed barrier functions. Automatica, 80:328–339, June 2017
  C. Feller and C. Ebenbauer
  
• 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
  
• 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
  
• 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
  
• 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