Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements
Access Status
Authors
Date
2019Type
Metadata
Show full item recordCitation
Source Title
ISSN
School
Funding and Sponsorship
Collection
Abstract
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.
Related items
Showing items related by title, author, creator and subject.
-
Chai, Qinqin (2013)In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem ...
-
Yuan, J.; Zhang, X.; Liu, Chongyang; Chang, L.; Xie, J.; Feng, E.; Yin, H.; Xiu, Z. (2016)Time-delay dynamical systems, which depend on both the current state of the system and the state at delayed times, have been an active area of research in many real-world applications. In this paper, we consider a nonlinear ...
-
Liu, C.; Gong, Z.; Teo, Kok Lay (2018)In this paper, we consider estimation problems involving a class of nonlinear systems characterized by two non-standard attributes: (i) such systems evolve over multiple stages; and (ii) the dynamics in each stage involve ...