**Structure-preserving model reduction of controlled systems**

Model reduction is a major issue for control, optimization and simulation of large-scale systems. Common spatial decomposition methods such as Proper Orthogonal Decomposition or the Principal Component Analysis aim at identifying a subspace of “high-energy” modes onto which the dynamics is projected. These modes, however, may not be relevant for the dynamics. Moreover these methods tacitly assume that all degrees of freedom can be observed or measured. An alternative procedure for stable input-output systems is the method of balanced truncation. Unlike the aforementioned approaches balanced truncation accounts for incomplete observability. It consists in finding a coordinate transformation such that modes which are least sensitive to an external perturbation (controllability) also give the least output (observability) and therefore can be neglected. In this project we study balanced truncation in the context of singularly perturbed control system, both deterministic and stochastic.

The project is funded through MATHEON project A15.

**Selected Publications**

- C. Hartmann, V.-M. Vulcanov, Ch. Schütte (2010), Balanced truncation of linear second-order systems: A Hamiltonian approach, Multiscale Model. Simul. 8, No. 4, pp. 1348 – 1367

- C. Hartmann, A. Zueva and B. Schäfer-Bung (2010), Balanced model reduction of bilinear systems with applications to positive systems, submitted to SIAM J. Control Optim

**Head:**

C. Hartmann

Project researchers

Carsten Hartmann, Boris Schäfer-Bung,

Burkhard Schmidt, Valentina Vulcanov, Christof Schütte