TY - GEN
T1 - Nonlinear Data-Driven Control for Stabilizing Periodic Orbits
AU - Cetinkaya, Ahmet
AU - Kishida, Masako
N1 - Funding Information:
Ahmet Cetinkaya and Masako Kishida, National Institute of Informatics, Tokyo, 101-8430, Japan. cetinkaya@nii.ac.jp, kishida@nii.ac.jp This work was supported by JST ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603) and by JSPS KAKENHI Grant Number 20K14771.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - In this paper, we propose a data-driven control framework for locally stabilizing unstable periodic orbits of discrete-time nonlinear systems. Specifically, we explore the scenarios where the locations of the orbits are not precisely known. In our framework, we use a Pyragas-type delayed feedback controller. This controller uses the difference between the current state and a delayed version of the state as feedback to the system. We show that the system under our controller can be described by another nonlinear system with a particular structure. The periodic orbit stabilization problem for the original system is then characterized as an equilibrium stabilization problem for the new system. For this new system, we investigate local exponential stabilization while paying special attention to situations where neither the location of the equilibrium nor the linearized dynamics around that equilibrium are precisely known. To handle such cases, we develop a data-driven framework that accounts for the scenarios where the difference between the state and the equilibrium is not observable. In our framework, we design the gain of a stabilizing controller by using the data generated through a nonlinear projection of the state.
AB - In this paper, we propose a data-driven control framework for locally stabilizing unstable periodic orbits of discrete-time nonlinear systems. Specifically, we explore the scenarios where the locations of the orbits are not precisely known. In our framework, we use a Pyragas-type delayed feedback controller. This controller uses the difference between the current state and a delayed version of the state as feedback to the system. We show that the system under our controller can be described by another nonlinear system with a particular structure. The periodic orbit stabilization problem for the original system is then characterized as an equilibrium stabilization problem for the new system. For this new system, we investigate local exponential stabilization while paying special attention to situations where neither the location of the equilibrium nor the linearized dynamics around that equilibrium are precisely known. To handle such cases, we develop a data-driven framework that accounts for the scenarios where the difference between the state and the equilibrium is not observable. In our framework, we design the gain of a stabilizing controller by using the data generated through a nonlinear projection of the state.
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U2 - 10.1109/CDC45484.2021.9683587
DO - 10.1109/CDC45484.2021.9683587
M3 - Conference contribution
AN - SCOPUS:85126019256
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4326
EP - 4331
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -