Several real-world systems can be represented by nonlinear autoregressive exogenous (NARX) models. The dynamics of these models not only depend on the current and past inputs, but also on the past outputs through a nonlinear function. Thus, they can be seen as a nonlinear version of linear infinite impulse response (IIR) filter.

Traditionally, control problems are solved in two steps: first, a model is identified based on input/output data and then the desired controller is designed. In a data-driven paradigm, either these two steps are combined in a single step or the desired controller is designed without identifying the model.

Central among control problems are the stabilization problem and the output matching problem. Loosely speaking, stabilization problem is defined as designing a controller that makes the system stable and output matching problem refers to designing a controller that enforces the output to match a given reference output.

The goal of this thesis is to develop data-driven methods to solve these problems wherein the underlying system is assumed to be an NARX. First, we will learn prevalent data-driven methods for control of linear and nonlinear systems, see references [1-7], and then develop new methods in order to work with the problems at hand. A typical strategy to tackle these control problems is to first write down a data-driven (data-based) representation of the system and then employ it to deal with the problem at hand.

### References

- V. K. Mishra, I. Markovsky, and B. Grossmann. Data-driven tests for controllability. IEEE Control Systems Letters, 5:517-522, 2020.
- H. J. van Waarde, J. Eising, H. L. Trentelman, and M. K. Camlibel. Data informativity: a new perspective on data-driven analysis and control. IEEE Trans. Autom. Control, 2020.
- J. G. Rueda-Escobedo and J. Schiﬀer. Data-driven internal model control of second-order discrete volterra systems. arXiv preprint arXiv:2003.14158, 2020.
- P. Dreesen and I. Markovsky. Data-driven simulation using the nuclear norm heuristic. In In Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Brighton, UK, 2019.
- J. Berberich and F. Allgower. A trajectory-based framework for data- driven system analysis and control. arXiv preprint arXive: 1903.10723, 2019.
- C. De Persis and P. Tesi. Formulas for data-driven control: Stabilization, optimality, and robustness. IEEE Trans. Autom. Control, 65(3):909-924, 2019.
- I. Markovsky and P. Rapisarda. Data-driven simulation and control. Int. J. Control, 81(12):1946-1959, 2008.

2020