Showing papers by "Michel Gevers published in 1992"

Quantifying the error in estimated transfer functions with application to model order selection

Abstract: Previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics. This prior information took the form of parameterized bounding functions or parameterized probability density functions, in the time or frequency domain with known parameters. It is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique. This significantly reduces the prior information required to estimate transfer function error bounds. The authors illustrate the usefulness of the method with a number of simulation examples. How the obtained error bounds can be used for intelligent model-order selection that takes into account both measurement noise and under-modeling is shown. Another simulation study compares the method to Akaike's well-known FPE and AIC criteria. >

Optimal FWL design of state-space digital systems with weighted sensitivity minimization and sparseness consideration

Abstract: The optimal finite word length (FWL) state-space digital system problem is investigated. Instead of the unusual sensitivity measure, it is argued that it may be desirable to minimize a frequency weighted sensitivity measure over all similarity transformations. The set of optimal realizations minimizing this weighted sensitivity is completely characterized, and an algorithm is proposed to find the optimal solution set. It is shown that a subset of the optimal realization set consists of sparse Schur realizations, whose actual sensitivity (taking into account the zero elements) is even smaller than the theoretical minimal sensitivity. Some properties of the Schur realizations are discussed. A numerical example that confirms the theoretical results is given. >

Disturbance Rejection: on-line refinement of controllers by closed loop modelling

Abstract: Many practical applications of control system design based on input-output measurements permit the repeated application of a system identification procedure operating on closed loop data together with successive refinement of the designed controller. Recently several iterative schemes for mutually enhanced plant identification and robust control design have been proposed [l]-[3]. In this paper we shall analyze the methodology of [1] from the viewpoint of closed loop signal conditioning and investigate the effect of the noise modelling error and plant modelling error on the closed loop performance.

Difference and differential Riccati equations: a note on the convergence to the strong solution

Abstract: The convergence of the solutions of the differential difference Riccati equations to the strong solution of the corresponding algebraic Riccati equation (ARE) is addressed. Detectability only is required in the analysis, and no assumption is made on the eigenvalues on the real imaginary axis (on the unit circle, in the discrete-time case). In particular, from the results, it follows that under the sole assumption of detectability, a positive definite initial condition guarantees convergence to the strong solution, even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle. >

Identification of linearly overparametrized nonlinear systems

Abstract: Often, a dynamical model is nonlinear in the unknown parameters, but it can be transformed into an overparametrized linear regression model, where the components of the overparametrization vector are nonlinear functions of the smaller number of unknown parameters. An algorithm that directly identifies the unknown parameters is presented, and the authors characterize the convergence domains under two different sets of assumptions on the excitation of the signals. The corresponding convergence rates are computed. >

Stabilizable by a stable and by an inverse stable but not by a stable and inverse stable

Abstract: The authors disprove conjectures on simultaneous stabilizability conditions by showing that, unlike the case of two plants, the existence of a simultaneous stabilizing controller for more than two plants is not guaranteed by the existence of a controller such that the closed loops have no real unstable poles. An example of a plant which has the even interlacing property but which is not stabilizable by a bistable controller is presented. >

Data filtering, reparametrization, and the numerical accuracy of parameter estimators

Abstract: It is established that a reparametrization of a discrete transfer function in terms of polynomials other than the classical powers of the shift operator z is equivalent to a filtering of the data. In adaptive parameter estimation problems, such reparametrization can yield significantly better accuracy for the estimate and convergence speed for the parameter estimator. One such generalized parametrization is presented. It yields good numerical results independently of the spectral properties of the data that enter into the unknown system. >

Estimated Transfer Functions with Application to Model Order Selection

Abstract: Previous results on estimating errors or error bounds on identified transfer functions have relied upon prior assumptions about the noise and the unmodeled dynamics. This prior information took the form of parameterized bounding functions or parameterized probability density functions, in the time or frequency domain with known parameters. Here we show that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique. This significantly reduces the prior infor- mation required to estimate transfer function error bounds. We illustrate the usefulness of the method with a number of simula- tion examples. The paper concludes by showing how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under-model- ing. Another simulation study compares our method to Akaike's well-known FPE and AIC criteria.