TY - JOUR
T1 - Robust observer-based controller design for state constrained uncertain systems
T2 - attractive ellipsoid method
AU - Mera, Manuel
AU - Salgado, Ivan
AU - Chairez, Isaac
N1 - Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2020/6/2
Y1 - 2020/6/2
N2 - This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers.
AB - This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers.
KW - Barrier Lyapunov functions
KW - Constrained linear systems
KW - attractive ellipsoid method
UR - http://www.scopus.com/inward/record.url?scp=85052321729&partnerID=8YFLogxK
U2 - 10.1080/00207179.2018.1508853
DO - 10.1080/00207179.2018.1508853
M3 - Artículo
SN - 0020-7179
VL - 93
SP - 1397
EP - 1407
JO - International Journal of Control
JF - International Journal of Control
IS - 6
ER -