Nonlinear control systems analysis

Project members: J.M.A. Scherpen, W.S. Gray (Virginia, USA), K. Fujimoto (Kyoto, Japan)

Sponsored by: NWO

This research focuses on extensions of linear realization theory to nonlinear control systems. The relation between input-output systems, Hankel operators, state-space realizations, minimality, and balanced realizations is considered. These considerations are important for applications to model and controller reduction, numerical efficiency, nonlinear black box identification and order estimation, sensor and actuator placements, etc. A sequence of papers in this direction has been published.

The study towards the relation of Hankel operators, its factorization in an observability and controllability part, and their state-space realizations, has given rise to a generalization of the notion of Hilbert adjoint systems to the nonlinear case. This topic uses concepts from physical systems, namely, Hamiltonian systems and their extensions, Legendre transformations, etc. Based on these methods, a procedure towards a new balancing method for nonlinear system is defined, resulting in a procedure for model reduction that is part of the on-going research. So far, a constructive algorithm is part of the procedure, which aims at the development of implementation tools.