TY - JOUR
T1 - Guaranteed State Estimation via Direct Polytopic Set Computation for Nonlinear Discrete-Time Systems
AU - Khajenejad, Mohammad
AU - Shoaib, Fatima
AU - Yong, Sze Zheng
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2022
Y1 - 2022
N2 - This letter introduces a set-theoretic state estimation approach for bounded-error nonlinear discrete-time systems, subject to nonlinear observations or constraints, when polytope-valued uncertainties are assumed. Our approach relies on finding a polytopic enclosure to the true range of nonlinear mappings via the direct use of hyperplane and vertex representations of polytopes. In particular, we derive a tractable enclosure of the set-product of an interval and a polytope, which is then used in a two-step state estimation approach consisting of (i) state propagation (prediction) using the nonlinear system dynamics and (ii) measurement update (refinement) based on nonlinear observations. Moreover, we analyze the computational complexity of our proposed technique and derive sufficient conditions for stability of the estimation errors. Finally, we compare the effectiveness of our approach with existing polytopic and interval observers in the literature.
AB - This letter introduces a set-theoretic state estimation approach for bounded-error nonlinear discrete-time systems, subject to nonlinear observations or constraints, when polytope-valued uncertainties are assumed. Our approach relies on finding a polytopic enclosure to the true range of nonlinear mappings via the direct use of hyperplane and vertex representations of polytopes. In particular, we derive a tractable enclosure of the set-product of an interval and a polytope, which is then used in a two-step state estimation approach consisting of (i) state propagation (prediction) using the nonlinear system dynamics and (ii) measurement update (refinement) based on nonlinear observations. Moreover, we analyze the computational complexity of our proposed technique and derive sufficient conditions for stability of the estimation errors. Finally, we compare the effectiveness of our approach with existing polytopic and interval observers in the literature.
KW - Estimation
KW - observers for nonlinear systems
KW - polytope-valued observers
KW - uncertain systems
UR - http://www.scopus.com/inward/record.url?scp=85122092741&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85122092741&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2021.3138355
DO - 10.1109/LCSYS.2021.3138355
M3 - Article
AN - SCOPUS:85122092741
SN - 2475-1456
VL - 6
SP - 2060
EP - 2065
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
ER -