Title :
Set-Membership Error-in-Variables Identification Through Convex Relaxation Techniques
Author :
Cerone, Vito ; Piga, Dario ; Regruto, Diego
Author_Institution :
Dipt. di Autom. e Inf., Politec. di Torino, Torino, Italy
Abstract :
In this technical note, the set membership error-in-variables identification problem is considered, that is the identification of linear dynamic systems when both output and input measurements are corrupted by bounded noise. A new approach for the computation of parameter uncertainty intervals is presented. First, the identification problem is formulated in terms of nonconvex optimization. Then, relaxation techniques based on linear matrix inequalities are employed to evaluate parameter bounds by means of convex optimization. The inherent structured sparsity of the original identification problems is exploited to reduce the computational complexity of the relaxed problems. Finally, convergence properties and complexity of the proposed procedure are discussed. Advantages of the presented technique with respect to previously published results are discussed and shown by means of two simulated examples.
Keywords :
computational complexity; concave programming; identification; linear matrix inequalities; linear systems; set theory; uncertain systems; variable structure systems; computational com¬ plexity; convergence properties; convex relaxation techniques; input measurements; linear dynamic systems; linear matrix inequalities; nonconvex optimization; output measurements; parameter uncertainty intervals; set-membership error-in-variables identification; Indexes; Noise; Optimization; Polynomials; Strontium; Uncertain systems; Uncertainty; Errors-in-variables (EIV); linear matrix inequality (LMI) relaxation; set-membership identification; sparse polynomial optimization;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2168073