TY - JOUR
T1 - Discrete-time data-driven control with Hölder-continuous real-time learning
AU - Sanyal, A. K.
N1 - Funding Information:
This work was supported by the National Science Foundation [grant number IIP 1938518]. The author acknowledges helpful discussions and support from his hosts at the Systems and Control (SysCon) Department at Indian Institute of Technology, Bombay, India, (IIT-B) during the summer of 2019, when commencing this work.
Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2022
Y1 - 2022
N2 - This work provides a framework for data-driven control of discrete-time systems with unknown dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control such that a feasible output trajectory can be tracked. This is made possible by Hölder-continuous real-time stable learning schemes that act as discrete-time stable uncertainty observers. These observers learn from prior input-output history and ensure finite-time stable convergence of estimation errors to a bounded neighborhood of the zero vector if the system is Lipschitz-continuous with respect to time, outputs, inputs, internal parameters and states. In combination with nonlinearly stable controllers, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. A numerical experiment on a second-order system demonstrates the performance of this nonlinear model-free control framework.
AB - This work provides a framework for data-driven control of discrete-time systems with unknown dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control such that a feasible output trajectory can be tracked. This is made possible by Hölder-continuous real-time stable learning schemes that act as discrete-time stable uncertainty observers. These observers learn from prior input-output history and ensure finite-time stable convergence of estimation errors to a bounded neighborhood of the zero vector if the system is Lipschitz-continuous with respect to time, outputs, inputs, internal parameters and states. In combination with nonlinearly stable controllers, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. A numerical experiment on a second-order system demonstrates the performance of this nonlinear model-free control framework.
KW - Data-driven control
KW - Hölder-continuous feedback
KW - finite-time stabilisation
KW - uncertainty observer
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U2 - 10.1080/00207179.2021.1901993
DO - 10.1080/00207179.2021.1901993
M3 - Article
AN - SCOPUS:85102922025
SN - 0020-7179
VL - 95
SP - 2175
EP - 2187
JO - International Journal of Control
JF - International Journal of Control
IS - 8
ER -