TY - GEN
T1 - Discrete-Time Control of Nonlinear Control-Affine Systems with Uncertain Dynamics
AU - Dongare, Abhijit
AU - Sanyal, Amit K.
AU - Hamrah, Reza
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - A novel approach to data-enabled control of discrete nonlinear control-Affine systems with uncertain ('gray-box') dynamics is given here. The gray-box dynamics model accounts for known dynamics and lumps together the effects of disturbance inputs and poorly known dynamics into one time-varying unknown input, which is estimated in real time. This data-enabled approach leads to robust and stable real-Time tracking control of desired output trajectories in the presence of model uncertainties. The lumped unknown input is estimated by a Hölder-continuous robustly stable learning scheme, using input-output data in discrete time. This leads to finite-Time convergence of the estimation errors of the unknown dynamics to a bounded neighborhood of the zero vector, provided the system is Lipschitz-continuous with respect to states, inputs, outputs, and time. A Lyapunov analysis is carried out to show the nonlinear stability and robustness of the uncertainty observer and tracking control law. This results in simultaneous real-Time uncertainty estimation and tracking control. Numerical simulation results for an inverted pendulum with imperfectly known dynamics are carried out, which agree with the theoretical results on stability and robustness.
AB - A novel approach to data-enabled control of discrete nonlinear control-Affine systems with uncertain ('gray-box') dynamics is given here. The gray-box dynamics model accounts for known dynamics and lumps together the effects of disturbance inputs and poorly known dynamics into one time-varying unknown input, which is estimated in real time. This data-enabled approach leads to robust and stable real-Time tracking control of desired output trajectories in the presence of model uncertainties. The lumped unknown input is estimated by a Hölder-continuous robustly stable learning scheme, using input-output data in discrete time. This leads to finite-Time convergence of the estimation errors of the unknown dynamics to a bounded neighborhood of the zero vector, provided the system is Lipschitz-continuous with respect to states, inputs, outputs, and time. A Lyapunov analysis is carried out to show the nonlinear stability and robustness of the uncertainty observer and tracking control law. This results in simultaneous real-Time uncertainty estimation and tracking control. Numerical simulation results for an inverted pendulum with imperfectly known dynamics are carried out, which agree with the theoretical results on stability and robustness.
UR - http://www.scopus.com/inward/record.url?scp=85186958633&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85186958633&partnerID=8YFLogxK
U2 - 10.1109/ICC61519.2023.10442398
DO - 10.1109/ICC61519.2023.10442398
M3 - Conference contribution
AN - SCOPUS:85186958633
T3 - 2023 9th Indian Control Conference, ICC 2023 - Proceedings
SP - 389
EP - 394
BT - 2023 9th Indian Control Conference, ICC 2023 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 9th Indian Control Conference, ICC 2023
Y2 - 18 December 2023 through 20 December 2023
ER -