Statistics

Combinatorics

Physics

Astronomy

Mathematical analysis

Trajectory

Paleontology

Artificial intelligence

Nonlinear system

Set (abstract data type)

Invariant (physics)

Programming language

Controller (irrigation)

Control (management)

Extension (predicate logic)

Context (archaeology)

Mathematics

Mathematical physics

Computer science

Control theory (sociology)

Quantum mechanics

Agronomy

Linear system

State space

Kernel (algebra)

Biology

LTI system theory

The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven in the behavioral control framework, shows that a single measured trajectory can capture the full behavior of an LTI system and might therefore be used directly for system analysis and controller design, without explicitly identifying a model. In this paper, we translate the result from the behavioral context to the classical state-space control framework and we extend it to certain classes of nonlinear systems, which are linear in suitable input-output coordinates. Moreover, we show how this extension can be applied to the data-driven simulation problem, where we introduce kernel-methods to obtain a rich set of basis functions.

A trajectory-based framework for data-driven system analysis and control