Applications oriented input design for closed-loop system identification: a graph-theory approach

Abstract

Applications oriented input design for closed-loop system identification: a graph-theory approach.In Abstract-A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.

Model Predictive Control oriented experiment design for system identification: A graph theoretical approach

“…The optimization problem (16) is independent of the controller structure, and hence the approach presented in this section can be also applied when the controller is known. Thus, the technique introduced in this article extends the results in Ebadat et al (2014b), where the controller law is assumed known, and an indirect method is employed to solve the identification problem.…”

“…However, many of these methods have difficulty in dealing with nonlinear and implicit feedback such as MPC. In Ebadat et al (2014b) a graph theoretical approach is explored, but a known controller is assumed and indirect identification is employed.…”

“…In this paper, which is an extension of the idea developed by Ebadat et al (2014b) to more general controllers with implicit control law, we present a new approach for MPC oriented experiment design in the presence of probabilistic constraints on input and output signals. The idea is to design the external excitation achieving the minimum experimental effort, while we are also taking care of the tracking performance of MPC.…”

Application-Oriented Input Spectrum Design in Closed-Loop Identification

“…The most common choice of the basis function is k e jω = e −jωk . A finite-dimensional parameterization is then acquired by substituting the spectrum Φ κ (ω) in (19) with the following approximation:…”

“…Therefore, the input design problem could be obtained by the signal spectrum approximation using the finite impulse response (FIR) process, where the optimal filter coefficients are computed by convex optimization [18]. Some interesting approaches to the problem of optimal input signal synthesis in the frequency domain for dedicated fields of applications have been published in recent years, and some of them have been presented in [19]. In the paper [20], a heuristic solution has been suggested to tune a bounded amplitude multisine control signal in a closed-loop setup.…”