ALOP Colloquium with Timm Faulwasser

On Monday, December 2 2019 at 9:00 c.t.  Prof. Dr. -Ing. Timm Faulwasser, TU Dortmund will present his recent work entitled

Dissipativity and Turnpike Properties in Optimal Control – Insights and Open Problems

In many engineering disciplines and beyond (economics, physics, …) performance optimization under explicit consideration of dynamics and operational constraints, i.e. optimal control, plays a pivotal role. The last 60 years have seen tremendous progress in terms of optimality conditions and PMP formulations, and in terms of powerful computational tools. In other words, as such optimal control theory of finite dimensional systems is a mature subject.

Inspired by physical notions of dissipative and passive systems, Jan Willems introduced a formal dissipativity notion in 1972, which can be regarded as an extension of Lyapunov stability notions to systems with inputs [6,7]. Yet, triggered by recent developments on so-called economic Model Predictive Control (MPC) [1,2], a system-theoretic notion of dissipativity of Optimal Control Problems (OCPs) has been subject to considerable recent research interest [3,4,5].

Parallel to Willems´ work, the 1970s also saw manifold contributions, especially in economics, to what is commonly called turnpike theorems of OCPs [8]. The term turnpike was coined in a seminal contribution by Dorfman, Samuelson and Solow in 1958 [9]. It refers to a phenomenon of parametric OCPs, whereby for varying initial conditions and horizon length, the time the optimal solutions spend outside of a neighborhood of the turnpike steady state is bounded independent of the horizon length. Early observations of this phenomenon can be traced back to works of John von Neumann from the 1930s/40s. Recently, turnpike properties have also been studied in time-varying and infinite-dimensional settings [10,11].

The main focus of this seminar is to provide insights into the link between turnpike and dissipativity properties of OCPs. Motivated by examples we will propose a formal definition of turnpike properties, which enables the derivation of converse turnpike results.  To this end, we recap the dissipativity notion of Willems and show how it can be applied to OCPs. Moreover, we will also provide insights into different viewpoints on turnpikes (primal vs. primal-dual), which link the phenomenon with the stability of a specific equilibrium of the Hamiltonian optimality system. Finally, we will provide an outlook on time-varying and periodic turnpikes and on turnpikes in mixed-integer problems

References

1. Angeli, David, Rishi Amrit, and James B. Rawlings. “On average performance and stability of economic model predictive control.” IEEE transactions on automatic control 57.7 (2011): 1615-1626.
2. Faulwasser, Timm, Lars Grüne, and Matthias A. Müller. “Economic nonlinear model predictive control.” Foundations and Trends® in Systems and Control 5.1 (2018): 1-98.
3. Faulwasser, T., Korda, M., Jones, C. N., & Bonvin, D. (2017). On turnpike and dissipativity properties of continuous-time optimal control problems. Automatica, 81, 297-304.
4. Müller, Matthias A., David Angeli, and Frank Allgöwer. “On necessity and robustness of dissipativity in economic model predictive control.” IEEE Transactions on Automatic Control 60.6 (2014): 1671-1676.
5. Grüne, Lars, and Matthias A. Müller. “On the relation between strict dissipativity and turnpike properties.” Systems & Control Letters 90 (2016): 45-53.
6. Willems, Jan C. “Dissipative dynamical systems part I: General theory.” Archive for rational mechanics and analysis 45.5 (1972): 321-351.
7. Willems, Jan C. “Dissipative dynamical systems.” European Journal of Control 13.2-3 (2007): 134-151.
8. McKenzie, Lionel W. “Turnpike theory.” Econometrica: Journal of the Econometric Society (1976): 841-865.
9. Dorfman, R., Samuelson, P. A., and RM Solow. Linear Programming and Economic Analysis (1958).
10. Gugat, M., Trélat, E., & Zuazua, E. (2016). Optimal Neumann control for the 1D wave equation: Finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Systems & Control Letters, 90, 61-70.
11. Grüne, L., Pirkelmann, S., & Stieler, M. (2018). Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. In Control Systems and Mathematical Methods in Economics (pp. 195-218). Springer, Cham.

Bio Sketch

Timm Faulwasser has studied Engineering Cybernetics at the University Stuttgart, with majors in systems and control and philosophy. He completed his PhD at the Otto-von-Guericke University Magdeburg, Germany, where he was also a member of the International Max Planck Research School for Analysis, Design and Optimization in Chemical and Biochemical Process Engineering Magdeburg. 2013-2016 he was with the Laboratoire d’Automatique, École Polytechnique Fédérale de Lausanne, Switzerland. During 2015-2019 he led the Optimization and Control Group at the Institute for Automation and Applied Informatics, Karlsruhe Institute for Technology. Since November 2019 he holds the Chair for Energy Efficiency at the Department of Electrical Engineering and Information Technology of TU Dortmund.

His main research interests are optimization-based and predictive control of networks of nonlinear systems with applications in energy systems, process systems engineering and climate economics.

The presentation will take place in E 51.  Coffee will be served.