Control Theory and Optimization

Distributed Optimization and Control

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Solving optimization problems using a group of agents, each capable of interchanging information over a communication network, has become an important area of research. Distributed optimization problems arise in many applications such as optimal power dispatch problems in Smart Grids, distributed Machine Learning or formation control of small mobile robots. Existing algorithms solving these problems often have quite limiting requirements on the problem class as well as the communication structure, e.g., consensus-type problems or undirected information flow. In our research we focus on the development of new approaches to distributed optimization, both in continuous- as well as discrete-time, which are applicable to a large class of constrained optimization problems under mild assumptions on the underlying communication network as well as the problem structure. In particular, we employ saddle-point (primal-dual) algorithms for centralized convex optimization and use Lie bracket approximation techniques to derive distributed approximations thereof.

  • Some publications:
  • S. Michalowksy, B. Gharesifard, C. Ebenbauer. A Lie bracket approximation approach to distributed optimization over directed graphs. To appear in Automatica 2019. (Preprint: https://arxiv.org/abs/1711.05486)
  • C. Ebenbauer, S. Michalowsky, V. Grushkovskaya, B. Gharesifard. Distributed Optimization over directed graphs with the help of Lie brackets. In Proc. of the 20th IFAC World Congress, Toulouse, France, 2017, pp. 15908-15913.
  • V. Grushkovskaya and C. Ebenbauer. Multi-agent coordination with Lagrangian measurements. In Proc. of the 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems, Tokyo, Japan, pages 115–120, 2016.
  • Cooperations:
  • Bahman Gharesifard, Queen's University, Kingston, ON, Canada.

System-theoretic Analysis and Design of Optimization Algorithms

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Optimization algorithms are often used to solve control and decision making problems. Control methods, however, are used much less in optimization, despite the facts that control is dedicated to the analysis and design of dynamical systems and that optimization algorithms are dynamical systems. Hence, our research idea is to analyze and design optimization algorithms employing methods from systems and control theory. In particular, we study continuous-time (models of) optimization algorithms and we employ robust control theory to analyze and design first-order optimization algorithms.

  • Some publications:
  • S. Michalowksy, C. Scherer, C. Ebenbauer. Robust and structure exploiting optimization algorithms: An integral quadratic constraint approach. (Preprint: https://arxiv.org/abs/1905.00279), 2019.
  • S. Michalowsky, C. Ebenbauer. The multidimensional n-th order heavy ball method and its application to extremum seeking. In Proc. of the 53rd IEEE Conf. Decision and Control (CDC), pp. 2660-2666, 2014.
  • H.B. Dürr, C. Ebenbauer. On a class of smooth optimization algorithms with applications in control. In Proc. of the 4th IFAC Conf. Nonlinear Model Predictive Control (NMPC), 2012.
  • C. Ebenbauer and A. Arsie. On an eigenflow equation and its Lie algebraic generalization. Communications in Information and Systems, 8:147–170, 2008.
  • Cooperations:
  • Carsten Scherer, University of Stuttgart, Germany.
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