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dc.contributor.authorGong, Z.
dc.contributor.authorLiu, C.
dc.contributor.authorTeo, Kok Lay
dc.contributor.authorSun, Jie
dc.identifier.citationGong, Z. and Liu, C. and Teo, K.L. and Sun, J. 2019. Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements. Applied Mathematical Modelling. 69: pp. 685-695.

In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This problem is formulated as a distributionally robust parameter identification problem governed by a time-delay dynamical system. Using duality theory of linear optimization in a probability space, the distributionally robust parameter identification problem, which is a bi-level optimization problem, is transformed into a single-level optimization problem with a semi-infinite constraint. By applying problem transformation and smoothing techniques, the semi-infinite constraint is approximated by a smooth constraint and the convergence of the smooth approximation method is established. Then, the gradients of the cost and constraint functions with respect to time-delay and parameters are derived. On this basis, a gradient-based optimization method for solving the transformed problem is developed. Finally, we present an example, arising in practical fermentation process, to illustrate the applicability of the proposed method.

dc.titleDistributionally robust parameter identification of a time-delay dynamical system with stochastic measurements
dc.typeJournal Article
dcterms.source.titleApplied Mathematical Modelling
curtin.departmentSchool of Electrical Engineering, Computing and Mathematical Science (EECMS)
curtin.accessStatusOpen access

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