103 research outputs found
A duality perspective on Loewner rational interpolation and state-space modelling of vector-exponential trajectories
No full textWe explore some connections between the Loewner approach to interpolation and realization, and that based on bilinear differential forms arising in the behavioral framework. We show that a crucial concept underlying both approaches is that of duality of trajectories, and that many known results can be interpreted in its ligh
Bilinear differential forms and the Loewner framework for rational interpolation
No full textThe Loewner approach, based on the factorization of a special-structure matrix derived from data generated by a dynamical system, has been applied successfully to realization, generalized interpolation, and model reduction. We examine some connections between such approach and that based on bilinear- and quadratic differential forms arising in the behavioral framework
Model validation and consistency
No full textThis thesis addresses model validation, important in robust control system modeling, for the identification method developed by Antoulas. Given a system model, the problem is to assess whether the model is consistent with the data.
This work formulates the validation problem in the form of a quadratic optimization problem subject to a spherical constraint. This new, computationally tractable method allows us to find a necessary and sufficient condition on the energy of the input sequence required to invalidate a given model. Therefore, for a given energy level, not all the models can be invalidated. For fixed noise level, the set of invalidatable models decreases as the energy of the input sequence decreases. Moreover, even if infinite length measurements are taken, the set of plants which cannot be invalidated does not shrink to the true model. The true model, in addition, can never be invalidated using an input of finite energy
Modeling Systems from Measurements of their Frequency Response
No full textThe problem of modeling systems from frequency response measurements is of interest to many engineers. In electronics, we wish to construct a macromodel from tabulated impedance, admittance or scattering parameters to incorporate it into a circuit simulator for performing circuit analyses. Structural engineers employ frequency response functions to determine the natural frequencies and damping coefficients of the underlying structure. Subspace identification, popular among control engineers, and vector fitting, used by electronics engineers, are examples of algorithms developed for this problem. This thesis has three goals. 1. For multi-port devices, currently available algorithms arc expensive. This thesis therefore proposes an approach based on the Loewner matrix pencil constructed in the context of tangential interpolation with several possible implementations. They are fast, accurate, build low dimensional models, and are especially designed for a large number of terminals. For noise-free data, they identify the underlying system, rather than merely fitting the measurements. For noisy data, their performance is analyzed for different noise levels introduced in the measurements and an improved version, which identifies an approximation of the original system even for large noise values, is proposed. 2. This thesis addresses the problem of generating parametric models from measurements performed with respect to the frequency, but also with respect to one or more design parameters, which could relate to geometry or material properties. These models are suited for performing optimization over the design variables. The proposed approach generalizes the Loewner matrix to data depending on two variables. 3. This thesis analyzes the convergence properties of vector fitting, an iterative algorithm that relocates the poles of the model, given some "starting poles" chosen heuristically. It was recognized as a reformulation of the Sanathanan-Koerner iteration and several authors attempted to improve its convergence properties, but a thorough convergence analysis has been missing. Numerical examples show that for high signal to noise ratios, the iteration is convergent, while for low ones, it may diverge. Hence, incorporating a Newton step aims at making the iteration always convergent for "starting poles" chosen close to the solution. A connection between vector fitting and the Loewner framework is exhibited, which resolves the issue of choosing the starting poles
Discrete-time linear periodically time-varying systems: Analysis, realization and model reduction
No full textDiscrete-time linear periodically time-varying (LPTV) systems, considered as a bridge between the well-studied linear time-invariant (LTI) model and the nonlinear time-varying problems in real world, have been receiving increasing attention in recent a few decades.
In this research project, we try to understand discrete-time LPTV systems both internally and externally and derive basic theories for analysis, realization and model reduction of LPTV systems. Firstly we review the system model for LPTV systems, define its transfer function matrix, Markov parameters, stability, reachability and observability. Then we emphasize on the numerically efficient and stable methods to compute LPTV system grammians and to approximate the eigenvalue decay rate.
Another main result of this thesis is Krylov-based moment matching algorithm for model reduction of LPTV systems, which is derived afterwards, and is also compared to the other approach: balancing and balanced truncation of LPTV systems.
Almost any application of discrete-time LPTV systems, including periodic digital filters and periodic control theories, demands a periodic state-space model from input-output maps. This periodic realization problem is treated at the end of the thesis with demonstration of applicable non-minimal and quasi-minimal realization methods
System identification for robust control
No full textIn the design of a robust control system, one needs a nominal model together with a quantitative bound on the uncertainty that results from under-modeling and disturbances. In this thesis we do not intentionally seek a nominal model and a quantitative bound, instead, the uncertainty is directly parameterized so that the resulting uncertain model family can be characterized by means of a real parameter vector with at most unit length.
This is an innovative approach to the control-oriented system identification, since it is not in accordance with the general philosophy of robust identification. However, it is applicable to the robust synthesis problem by taking advantage of a convex parameterization of robust controllers that simultaneously stabilize the uncertain models in the family. The robust performance problem becomes tractable since it can be converted into a quasi-convex optimization problem with Linear Matrix Inequality (LMI) constraints. The relation between the optimal robust performance and the uncertainty is studied by analyzing the explicit bounds of the maximal robust margin.
Model (in)validation is a complement to system identification. In our approach it is an integral ingredient of the process of obtaining robust control-oriented system models. A single model is not invalidated if it is inside the ellipsoid, and thus the intersection of the ellipsoids is not invalidated. In order to make the unfalsified model set (the intersection) fit in our framework, we can compute an optimal ellipsoid bounding the intersection of the ellipsoids. (Abstract shortened by UMI.
On Loewner data-driven control for infinite-dimensional systems
No full textInternational audienceIn this paper, we address extensions of the Loewner Data-Driven Control (L-DDC) methodology. First, this approach is extended by incorporating two alternative approximation methods known as Adaptive-Antoulas-Anderson (AAA) and Vector Fitting (VF). These algorithms also include least squares fitting which provides additional flexibility and enables possible adjustments for control tuning. Secondly, the standard model reference data-driven setting is extended to handle noise affecting the data and uncertainty in the closedloop objective function. These proposed adaptations yield a more robust data-driven control design
Congestion control and complexity reduction of large-scale networks
No full textThe current version of Transport Control Protocol (TCP) does not meet the high demands of the exponentially growing Internet. The packet loss is one of the major limiting factors on the performance and the quality of services over Internet (especially for multimedia applications). Also, other improved versions of TCP (Vegas) cannot be deployed in the heterogeneous environment of current Internet. In this paper we propose a new protocol which not only enhances the network performance, but also is deployable in the large scale networks. We study the stability and the fairness of the proposed protocol in the framework of dynamical systems and finally verify the results by simulation
Geometric nonlinear filtering theory with application to the maneuvering aircraft tracking problem
No full textA geometric nonlinear filter (GNF) is designed for application to the problem of tracking a maneuvering aircraft. The aircraft tracking problem is a state estimation problem and a state prediction problem. A nonlinear aircraft maneuver model is proposed for use in the state estimation as well as the state prediction. This nonlinear model is based on the so-called coordinated turn and describes planar trajectories.
The GNF design approach involves state transformations with output injection to transform the nonlinear system model to a linear form, known as the observer canonical form. For many nonlinear systems, such as the proposed aircraft maneuver model, this linearizing transformation does not exist. Therefore, for the maneuvering aircraft model, a transformation to an approximate observer canonical form is given.
Utilizing a Lyapunov stability approach, sufficient conditions for stability of the GNF estimation error are derived. No such conditions exist for the extended Kalman filter (EKF). The GNF was found to be stable in cases where the EKF was not stable. The tracking performance of the GNF compares favorably with the EKF for various levels of measurement noise. However, the GNF offers a substantial savings in computational time making it more attractive than the EKF for use in a fire control computer
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