Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements

Abstract

• A distributionally robust parameter identification model is proposed for time-delay systems. • The problem is transformed to a single-level optimization problem. • A gradient-based optimization method is developed to solve the transformed problem. 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.