Constrained receding‐horizon experiment design and parameter estimation in the presence of poor initial conditions

Abstract

An optimal experiment design assumes the existence of an initial or nominal process model. The efficiency of this procedure depends on how the initial model is chosen. This creates a practical dilemma as estimating the model is precisely what the experiment tries to achieve. A novel approach to experiment design for identification of nonlinear systems is developed, with the purpose of reducing the influence of poor initial values. The experiment design and the parameter estimation are conducted iteratively under a receding-horizon framework. By taking steady-state prior knowledge into account, constraints on the parameters can be derived. Such constraints help reduce influence of poor initial models. The proposed algorithm is illustrated through examples to demonstrate its efficiency. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: [2808][2809][2810][2811][2812][2813][2814][2815][2816][2817][2818][2819][2820] 2011 Keywords: receding-horizon design, optimal experiment design, constrained EKF IntroductionOptimal experiment design aims at determining optimal experiment conditions to achieve a specific set of objectives. Experiment design is a broad subject that includes aspects such as input design, operating point design, and sampling time design. Although a significant amount of literature on optimal experiment design for linear systems has been published since the 1970s, 1,2 the optimal experiment design concerning nonlinear systems has remained largely unexplored.One significant challenge for nonlinear experiment design as well as parameters identification is that the sensitivity functions used to search for optimal conditions depend on the unknown model parameters. Three existing methods have been proposed to address this challenge: minimax experiment design, ED (expectation of determinant)/EID (expectation of the inverse of determinant)-optimal design, and adaptive experiment design.Minimax experiment design attempts to achieve robust experiment by minimizing the largest possible modeling error. This approach needs no prior information about parameter distributions. There are two recent representative publications on this topic. Rojas et al.3 developed a method of optimizing the worst case of modeling error over the parameter set, while a convex optimization algorithm is implemented on a linear system. In conjunction, Welsh and Rojas 4 proposed an algorithm to solve a robust optimal experiment design problem by scenario approach. To construct convex or semidefinite convex problems, both techniques formulate the identification problem in frequency domain, but neither of the methods can be used for identification in nonlinear system. Moreover, the optimality objective function for nonlinear identification is generally difficult to be formulated as a convex or semidefinite convex problem.Another group of methods (especially popular in bioscience fields) are experiment designs by optimizing over the expected determinant of a Fisher information matrix Correspondence concerning this article ...

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