Data-driven estimation of the algebraic Riccati equation for the discrete-time inverse linear quadratic regulator problem
Mathematics - Optimization and Control
Electrical Engineering and Systems Science - Systems and Control
DOI:
10.1007/s42452-024-05931-0
Publication Date:
2024-05-20T07:01:46Z
AUTHORS (5)
ABSTRACT
AbstractIn this paper, we propose a method for estimating the algebraic Riccati equation (ARE) with respect to an unknown discrete-time system from the system state and input observation. The inverse optimal control (IOC) problem asks, “What objective function is optimized by a given control system?” The inverse linear quadratic regulator (ILQR) problem is an IOC problem that assumes a linear system and quadratic objective function. The ILQR problem can be solved by solving a linear matrix inequality that contains the ARE. However, the system model is required to obtain the ARE, and it is often unknown in fields in which the IOC problem occurs, for example, biological system analysis. Our method directly estimates the ARE from the observation data without identifying the system. This feature enables us to economize the observation data using prior information about the objective function. We provide a data condition that is sufficient for our method to estimate the ARE. We conducted a numerical experiment to demonstrate that our method can estimate the ARE with less data than system identification if the prior information is sufficient.
SUPPLEMENTAL MATERIAL
Coming soon ....
REFERENCES (21)
CITATIONS (0)
EXTERNAL LINKS
PlumX Metrics
RECOMMENDATIONS
FAIR ASSESSMENT
Coming soon ....
JUPYTER LAB
Coming soon ....