N. Linard

Iterative controller optimization for nonlinear systems

A data-driven model-free control design method has been proposed in Hjalmarsson et al. (1994). It is based on the minimization of a control criterion with respect to the controller parameters using an iterative gradient technique. In this paper, we extend this method to the case where both the plant and the controller can be nonlinear. It is shown that an estimate of the gradient can be constructed using only signal based information. It is also shown that by using open loop identification techniques, one can obtain a good approximation of the gradient of the control criterion while performing fewer experiments on the actual system.

Brief Identification of a nonlinear plant under nonlinear feedback using left coprime fractional based representations

It has been shown that the set of all nonlinear plants stabilised by a known linear controller, which also stabilises a linear nominal model of the plant, can be parametrised by a stable operator known as the Youla-Kucera parameter. By utilising this description it is possible to convert the closed-loop plant identification problem to one of open-loop identification. This paper extends previous work by allowing the model of the nominal plant and the controller in the above scenario to be nonlinear. The ideas rely on a concept of differential coprimeness for nonlinear fractional system descriptions.

Closed loop identification of nonlinear systems

Several new methods for the identification of approximate models of an open loop plant on the basis of closed loop data have been presented. In this paper, we extend two of these methods to the nonlinear case: we consider that both the plant and the controller can be nonlinear. The first method is a two-step procedure. The sensitivity function of the closed loop system is identified through a high order nonlinear model and it is used in the second step to simulate a noise free input signal for an open loop like identification of the plant. The second method identifies the right coprime factors of the plant through an open loop like identification of the filtered sensitivity and complementary sensitivity functions. For both methods, we assume that the measurement noise enters the system under a high S/N ratio assumption.

Technical Communique: Gradient expressions for a closed-loop identification scheme with a tailor-made parametrization

In this paper, we present gradient expressions for a closed-loop parametric identification scheme. The method is based on the minimization of a standard identification criterion and a parametrization that is tailored to the closed-loop configuration. It is shown that for both linear and nonlinear plants and controllers, the gradient signals can be computed exactly.

On closed-loop identification with a tailor-made parametrization

We present gradient expressions for a closed-loop parametric identification scheme. The method is based on the minimization of a standard identification criterion and a parametrization that is tailored to the closed-loop configuration. It is shown that for both linear and nonlinear plants and controllers, the gradient signals can be computed exactly.

Coprimeness properties of nonlinear fractional system realizations

In this paper, the relationship between the Bezout and the set-theoretic approaches to left coprimeness is studied. It is shown that left coprimeness in the set-theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relations between two left coprime realizations of the same system.

Identification of nonlinear plants under linear control using Youla-Kucera parametrizations

This paper treats the identification of a noise contaminated nonlinear plant operating in a closed-loop with a stabilizing controller. The a priori model of the plant is nonlinear, and its update is obtained via a Youla-Kucera parameter. The introduction of this parameter induces a nonstandard open-loop identification problem, which in a low noise situation can be formulated as a standard open-loop problem.

Implementation issues for a nonlinear version of the Hansen scheme

We propose a method for the identification of a nonlinear plant under possibly nonlinear feedback. This procedure is a nonlinear extension of a method known as the Hansen scheme in the literature. It is shown that using nonlinear left fractional descriptions one can convert a general nonlinear closed-loop identification problem to one of open-loop identification by parametrizing the model using a Youla-Kucera parameter. The open-loop problem can be implemented by parametrizing the nonlinear Youla parameter in terms of a model of the plant. We provide gradient expressions for implementation in a steepest descent algorithm.