Many phenomena arising in real-world applications are inherently nonlinear. In our research, we develop tools and methods that can be used for the analysis, estimation and control of such nonlinear systems. Examples of our past and current research in this area include the following topics:
- Systems theoretic properties of nonlinear systems with inputs and outputs, such as input-to-state stability or dissipativity as well as their connection to optimal control.
- Controllability properties of nonlinear systems.
- State estimation for nonlinear systems. Here, we in particular focus on optimization-based state estimation, where the current system state is computed by solving an optimization problem using past input and observed output sequences.
SELECTED PUBLICATIONS
- S. Knüfer and M. A. Müller: Robust global exponential stability for moving horizon estimation. In Proc. of the 57th IEEE Conference on Decision and Control, pp. 3477-3482, 2018.
- M. A. Müller: Nonlinear moving horizon estimation in the presence of bounded disturbances. Automatica, vol. 79, pp. 306-314, 2017.
- L. Grüne and M. A. Müller: On the relation between strict dissipativity and turnpike properties. Systems & Control Letters, vol. 90, pp. 45-53, 2016.
- M. A. Müller, D. Liberzon, and F. Allgöwer: Norm-controllability of nonlinear systems. IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1825-1840, 2015.
- M. A. Müller, D. Liberzon, and F. Allgöwer: Norm-controllability, or how a nonlinear system responds to large inputs. In Proc. of the 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS), Toulouse, France, 2013, pp.104-109. Semi-plenary paper.
- M. A. Müller, and D. Liberzon: Input/output-to-state stability and state-norm estimators for switched nonlinear systems. Automatica, vol. 48, no. 9, pp. 2029-2039, 2012.
