Identification of Non-linear Nonautonomous State Space Systems from Input-Output Measurements

This paper presents a method to determine a nonlinear state-space model from a finite number of measurements of the inputs and outputs. The method is based on embedding theory for nonlinear systems, and can be viewed as an extension of the subspace identification method for linear systems. The paper describes the underlying theory and provides some guidelines for using the method in practice. To illustrate the use of the identification method, it was applied to a second-order nonlinear system

Optimal and Robust Feedback Controller Estimation for a Vibrating Plate using Subspace Model Identification

This paper presents a method to estimate the H2 optimal and a robust feedback controller by means of Subspace Model Identification using the internal model control (IMC) approach. Using IMC an equivalent feed forward control problem is obtained, which is solved by the Causal Wiener filter for the H2 optimal controller. The robust variant, called the Cautious Wiener filter, optimizes the average performance w.r.t. probabilistic model errors. The identification of the Causal and Cautious Wiener filters are control-relevant. The method is illustrated by experiments on a 4-inputs 4-outputs vibrating plate with additional mass variation

Blind multivariable ARMA subspace identification

In this paper, we study the deterministic blind identification of multiple channel state-space models having a common unknown input using measured output signals that are perturbed by additive white noise sequences. Different from traditional blind identification problems, the considered system is an autoregressive system rather than an FIR system; hence, the concerned identification problem is more challenging but possibly having a wider scope of application. Two blind identification methods are presented for multi-channel autoregressive systems. A cross-relation identification method is developed by exploiting the mutual references among different channels. It requires at least three channel systems with square and stably invertible transfer matrices. Moreover, a general subspace identification method is developed for which two channel systems are sufficient for the blind identification; however, it requires the additive noises to have identical variances and the transfer matrices having no transmission zeros. Finally, numerical simulations are carried out to demonstrate the performance of the proposed identification algorithms

Bilinear State Space Systems for Nonlinear Dynamical Modelling

We discuss the identification of multiple input, multiple output, discrete-time bilinear state space systems. We consider two identification problems. In the first case, the input to the system is a measurable white noise sequence. We show that it is possible to identify the system by solving a nonlinear optimization problem. The number of parameters in this optimization problem can be reduced by exploiting the principle of separable least squares. A subspace-based algorithm can be used to generate initial estimates for this nonlinear identification procedure. In the second case, the input to the system is not measurable. This makes it a much more difficult identification problem than the case with known inputs. At present, we can only solve this problem for a certain class of single input, single output bilinear state space systems, namely bilinear systems in phase variable form

H∞ output feedback control for linear discrete time-varying systems via the bounded real lemma

In this paper we develop a solution to the discrete-time H∞ output feedback control problem for Linear Time-Varying (LTV) systems. The solution is developed along the strategy set up in [Doyle et. al. 1989] and the main ingredient in its derivation is the extension of the well-known bounded real lemma to a (discrete) time-varying context, developed in [van der Veen and Verhaegen 1995]. This approach contributes to the conceptual simplicity, and hence to the accessibility, of the solution. Apart from that, we treat the infinite-horizon case for LTV system of non-uniform state dimension, and varying input and output dimension. Both situations can easily occur in practice, e.g. in multirate sampled data control systems. The algorithm that can be derived from the solution presented is then applied to the H∞ output feedback of a dynamical system changing from one operation point in its operation envelope to another