Methods and Tools

What am I researching? Generally speaking, I develop machine learning algorithms to model dynamical systems. Here are some “buzzwords” and tools that I use and that you might have come across already:

…and now my actual research:

Machine Learning with Nonlinear State Space Models

Dr.-Ing. Max Schüssler
Automatic Control – Mechatronics
University of Siegen


  • Field of interest: System identification (data driven modeling) for nonlinear dynamic systems*.
  • Motivation: Need for accurate dynamic models in many fields of engineering. Especially nonlinear dynamic modeling is becoming increasingly important to be able to model complex, nonlinear systems (for example for model predictive control).
  • Challenge: Well-known approaches such as the nonlinear autoregressive with exogeneous input (NARX) models or nonlinear finite impulse response (NFIR) models do not capture internal dynamics well.
  • Approach: Use local model state space networks (LMSSN) and deep recurrent neural networks (DRNN) for the identification of nonlinear dynamic systems.

*the time dependence is indicated by the discrete time variable \(k\)

Local Model State Space Networks

  • Architecture: Use local model networks for the approximation of the nonlinear functions \(\underline f_s(\cdot,\cdot)\) and \(g_s(\cdot,\cdot)\)
  • Procedure: Apply the local linear model tree (LOLIMOT) or hierarchical local model tree (HILOMOT) algorithm to incrementally increase the model complexity until a satisfactory performance level is achieved.
  • Performance: Comparable performance as state-of-the-art system identification algorithms on benchmark systems.
  • Implementation: Constantly evolving LMSSN Matlab®  Toolbox

Deep Recurrent Neural Networks

  • Architecture: Use (series-connected) recurrent layers (with affine cells, long short-term memory (LSTM) cells, … to approximate \(\underline f(\cdot,\cdot)\) and fully-connected layers to approximate \(g(\cdot)\) .
  • Procedure: Use stochastic gradient descent with mini batches and decreasing learning rate over time for  optimization.
  • Performance: Acceptable performance on benchmark problem.
  • Implementation: PythonTM code using tensorflow and keras machine learning libraries

Doctoral Thesis

Journal Papers

  • M. Schüssler and O. Nelles, “Optimization Approaches for Nonlinear State Space Models”, IEEE Control Systems Letters, vol. 5, no. 4, Art. no. 4, 2021, doi: 10.1109/LCSYS.2020.3037682.
  • T. J. Peter*, M. Schüssler*, and O. Nelles, “Identification of a potable water system”,  at – Automatisierungstechnik, vol. 69, no. 10, Art. no. 10, 2021, doi: 10.1515/auto-2021-0022*equal contributions

Conference Papers (peer-reviewed)

  • V. Smits, M. Schüssler, G. Kampmann, C. Illg, T. Decker and O. Nelles, “Modeling Benchmark on NOx Emissions of a Diesel Engine excited by an APRBS inside a Non-Convex Hull”, IEEE Conference on Control Technology and Applications 2022, 2022. (accepted for publication)
  • M. Schüssler and O. Nelles, “Extrapolation Behavior Comparison of Nonlinear State Space Models”, 19h IFAC Symposium on System Identification (SYSID 2021), 2021, doi: 10.1016/j.ifacol.2021.08.407.
  • T. Münker, G. Kampmann, M. Schüssler, and O. Nelles, “System Identification and Control of a Polymer Reactor”, 21th World Congress of the International Federation of Automatic Control, 2020, doi: 10.1016/j.ifacol.2020.12.212.
  • M. Schüssler, T. Münker, and O. Nelles, “Local Model Networks for the Identification of Nonlinear State Space Models”, in 2019 IEEE 58th Conference on Decision and Control (CDC), Dec. 2019, pp. 6437–6442, doi: 10.1109/CDC40024.2019.9028945.
  • M. Schüssler, T. Münker, and O. Nelles, “Deep Recurrent Neural Networks for Nonlinear System Identification”, in 2019 IEEE Symposium Series on Computational Intelligence (SSCI), Dec. 2019, pp. 448–454, doi: 10.1109/SSCI44817.2019.9003133.

Abstracts (non-peer-reviewed)

  • T. Decker, H. Patel, M. Schüssler, and O. Nelles, “Neural Networks with different Dynamics Realizations for the Bouc-Wen Benchmark Problem”, in Nonlinear System Identification Benchmarks Workshop, Eindhoven, Netherlands, Apr. 2021.
  • M. Schüssler and O. Nelles, “Comparison of Extrapolation Behavior between Different State Space Models”, in Proceedings – 29th Workshop Computational Intelligence, Dortmund, Germany, Nov. 2019, doi: 10.5445/KSP/1000098736.
  • M. Schüssler, T. O. Heinz, and O. Nelles, “Local Model State Space Networks for Hysteresis Identification”, in Nonlinear System Identification Benchmarks Workshop, Eindhoven, Netherlands, Apr. 2019.