A Unified KKL-Based Interval Observer for Nonlinear Discrete-Time Systems
- Resource Type
- Periodical
- Authors
- Dinh, T.N.; Quoc Bao Tran, G.
- Source
- IEEE Control Systems Letters IEEE Control Syst. Lett. Control Systems Letters, IEEE. 8:430-435 2024
- Subject
- Robotics and Control Systems
Computing and Processing
Components, Circuits, Devices and Systems
Observers
Vectors
Discrete-time systems
Nonlinear dynamical systems
Stability
Monitoring
Jacobian matrices
Interval observer
KKL observer
uncertain system
nonlinear systems
discrete-time systems
- Language
- ISSN
- 2475-1456
This letter proposes an interval observer design for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm. Our design extends to generic nonlinear systems without any assumption on the structure of its dynamics and output maps. Relying on a transformation putting the system into a target form where an interval observer can be directly designed, we then propose a method to reconstruct the bounds in the original coordinates using the bounds in the target coordinates, thanks to the Lipschitz injectivity of this transformation achieved under Lipschitz distinguishability when the target dynamics have a high enough dimension and are pushed sufficiently fast. An academic example serves to illustrate our methods.