Dr. Willem Esterhuizen
|Telephone:||+49 371 531-35820|
|Telefax:||+49 371 531-835820|
|Office hours:||by arrangement|
Set-based methods for control and analysis of nonlinear systems:
Reachable sets, reachable tubes, robustly invariant sets, viability kernels, etc. are fundamental to control theory, being closely associated with concepts such as controllability, stability and notions of performance. We are developing new methods for investigating the nature of these sets, and for constructing them (see for example , , ). We are also applying these sets to solve various problems, such as: guaranteeing transient stability in the electricity grid (part of the KONSENS project), and ensuring the "soft" landing of spacecraft on Mars during powered-descent. A strength of our methods is that they are applicable to very general nonlinear systems. High dimensionality is still a challenge for all methods that construct these sets. We are investigating ways to address this problem by considering "simpler" models (that may be lower-dimensional and/or linear) that are "consistently abstracted", in some sense, using ideas from differential geometry and topology as presented in, for example,  and .
 Esterhuizen, W., 2015. On barriers in constrained nonlinear systems with an application to hybrid systems (Ph.D. thesis), Mines ParisTech.
 Esterhuizen, W. and Lévine, J., 2016. Barriers and potentially safe sets in hybrid systems: Pendulum with non-rigid cable. Automatica, 73, pp.248-255.
 Esterhuizen, W., Aschenbruck, T. and Streif, S, 2018. On Maximal Robust Positively Invariant Sets in Constrained Nonlinear Systems, under review.
 Lévine, J., 2009. Analysis and Control of Nonlinear Systems: A Flatness-Based Approach. In Mathematical Engineering. Springer
 Tabuada, P. and Pappas, G. J., 2005. Quotients of Fully Nonlinear Control Systems. SIAM Journal on Control and Optimization 2005 43:5, 1844-1866
More information can be found here.
- Esterhuizen, W., Aschenbruck, T. and Streif, S, 2018. On Maximal Robust Positively Invariant Sets in Constrained Nonlinear Systems, under review.
- Esterhuizen, W., Wang, Q., 2018. Finite-Time Stability and Stabilisation with Polyhedral Domains for Linear Systems, International Journal of Control
- Esterhuizen, W., Wang, Q., 2017. Control Design with Guaranteed Transient Performance via Reachable Set Estimates, IFAC-PapersOnLine, 50, 2, 283-288
- Esterhuizen, W., Lévine, J. 2017. From Pure State and Input Constraints to Mixed Constraints in Nonlinear Systems, Feedback Stabilization of Controlled Dynamical Systems, 125-141, Springer International Publishing.
- Esterhuizen, W., Lévine, J., 2016. Barriers and potentially safe sets in hybrid systems: Pendulum with non-rigid cable. Automatica, 73, pp.248-255.
- Esterhuizen, W., 2015. On barriers in constrained nonlinear systems with an application to hybrid systems (Ph.D. thesis), Mines ParisTech.
- Esterhuizen, W., Lévine, J., 2015. Barriers in Nonlinear Control Systems with Mixed Constraints, arXiv preprint arXiv:1508.01708.
- Esterhuizen, W., Lévine, J., 2014. A preliminary study of barrier stopping points in constrained nonlinear systems, IFAC Proceedings Volumes, 47, 3, 11993-11997.
- Esterhuizen, W., Wang, H. O; Tanaka, K., Wang, X., 2013. Stability and stabilization conditions for Takagi-Sugeno fuzzy model via polyhedral Lyapunov functions, American Control Conference (ACC), 5637-5642.