Vassilis L. Syrmos

A geometric theory for derivative feedback

The authors use a singular system setting to provide a geometric theory for dynamical systems under derivative feedback. They define the relevant subspace and provide computational design techniques in terms of a generalized Sylvester or Lyapunov equation for which efficient solution techniques are well-known. The authors provide both geometric and algebraic characterizations of the effects of derivative feedback, drawing connections with previous work in state-variable systems as well as extending that work to singular systems. >

On the discrete generalized Lyapunov equation

Abstract In this paper we study the discrete generalized Lyapunov equation for implicit systems. We show how the anticipation phenomenon and the asymptotic stability of the system can be studied in terms of the solutions to the discrete generalized Lyapunov equation. We further study under which conditions these solutions are unique. Numerical examples are provided to illustrate the results presented.

Computational observer design techniques for linear systems with unknown inputs using the concept of transmission zeros

In this paper we present computational observer design techniques for linear systems subject to unknown inputs. Complete and intuitive geometric conditions for the solution of the problem are provided, which result in design matrix equations. These design equations are solved computationally efficient. The synthesis of the reduced-order observer takes full advantage of the concept of transmission zeros. In particular, the presented necessary and sufficient conditions are provided in terms of the transmission zeros of the triple (A,D,C).

On the finite transmission zero assignment problem

Abstract In this paper the problem of finite transmission zero assignment is examined by squaring a system from the outputs to the inputs. In particular, we study this problem for two cases, namely for state-accessible and partially state-accessible systems. We show that the problem of finite transmission zero assignment problem for state-accessible systems is equivalent to a pole-placement problem with state feedback on a reduced-order subspace, which always has a solution. In the case of partially state-accessible systems we show that the finite transmission zero assignment problem is equivalent to a pole-placement problem with output feedback on a reduced-order subspace, which generically has a solution for the case when p + m > n . For both cases we exploit the block Hessenberg form of the system and the concept of Sylvester equations in order to solve this problem in a computationally efficient manner.

Robust eigenvalue assignment for generalized systems

Abstract In this paper we examine the problem of robust pole placement using state-feedback in generalized systems. We develop a robustness theory for the finite generalized spectrum of the system as a partial problem, and for the “infinite” pole placement problem as a second partial problem where perfect conditioning is always achievable. We also give bounds between the complete closed-loop robust eigenvalue problem and the two partial ones. The basic tool that is exploited in the presented theory, is the concept of chordal metric. In this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems. The proposed theory is easy to implement, retrieves the results for the state-variable case as a special case, and takes advantage of well-known computational results.

Support Vector Machines and Wavelet Packet Analysis for Fault Detection and Identification

This paper presents a data driven fault detection and identification (FDI) method using support vector machines (SVM) and the wavelet packet transform (WPT). The primary focus of this paper is to present a robust data driven fault diagnosis scheme. The investigated scheme has the capability to detect and identify faulty components of a given system through examination of its output due to a specified input. The use of the wavelet packet transformation serves to draw out those features of the output response which best characterize each of the fault classes for the various components. Support vector machines are used as the diagnosis phase to detect and isolate faults of a given system.

Navigation of an autonomous underwater vehicle(AUV) using robust SLAM

This paper will present a robust extended Kalman filter (REKF) applied to the navigation of an autonomous underwater vehicle (AUV) using robust Simultaneous Localization and Mapping (SLAM) techniques. Conventional Kalman Filter methods suffer from the assumption of Gaussian noise statistics, which often lead to failures when these assumptions do not hold. Additionally, the linearization errors associated with the implementation of the standard EKF can also severely degrade the performance of the localization estimate. Currently, Stochastic Mapping provides a framework for the concurrent mapping of landmarks and localization of the vehicle with respect to the landmarks. However, the Stochastic Map is essentially an augmented EKF with the limitations thereof. This research addresses the linearization and Guassian assumption errors as they relate to the SLAM problem by proposing a new method, Robust Stochastic Mapping. The Robust Stochastic Map uses a Robust EKF (REKF) in order to address these limitations through the implementation of the bounded H∞ norm. Simulated data are presented to illustrate the advantage of the localization using the proposed estimation procedure.

Robust eigenvalue assignment in generalized systems

The authors examine the problem of robust pole placement using state-feedback in generalized systems. They develop a robustness theory for the finite generalized spectrum of the system as a partial problem. The basic tool that is exploited in this theory is the concept of chordal metric. The feedback laws presented always guarantee the closed-loop regularity. These results led to necessary and sufficient conditions for perfect conditioning, and showed how the results for optimal conditioning can be used for the generalized case.<<ETX>>

A geometric approach to proportional-plus-derivative feedback using quotient and partitioned subspaces

Abstract In this paper a new characterization of invariant subspaces is presented, using the notions of partitioned and quotient subspaces. This classification is based on a feedback approach that exhibits the importance of these subspaces for the problem of proportional-plus-derivative feedback. It also provides the ability to decompose the closed-loop system into two subsystems that completely characterize the closed-loop behavior. A feedback-free formulation is also considered which opens new horizons for the problem of general semistate feedback by utilizing nonsquare pencils for spectrum assignability. The importance of this technique arises from the fact that we deal with reduced order pencils, therefore the computational methods are more stable. In order to accomplish this, we use two generalized Lyapunov equations and exploit the generalized Hessenberg form.

Frame-Based Time-Scale Filters for Underwater Acoustic Noise Reduction

Noise reduction for underwater acoustic signals has attracted considerable attention over the last few decades. Among the numerous techniques, wavelet soft-thresholding (STH) has been considered as one of the most effective noise reduction approaches, as it achieves near complete success in minimizing the mean-squared-error (MSE) and eliminating oscillations caused by noise. However, a limitation with STH is its preference towards lower frequency bands, which may cause distortions in the high frequency bands. Few previous research efforts have reported on the reduction of such frequency distortions. By introducing the time-scale filters (TSF), we present a novel technique for underwater noise reduction that improves the standard STH in reducing distortions in the joint time-frequency (TF) space. TSF is an advanced noise reduction algorithm which utilizes the signals time-scale (TS) support region. It provides smooth reconstructions in both time and frequency spaces. We demonstrate the noise reduction results for two typical underwater noise sources: the snapping shrimp sound and the rainfall sound. We also introduce a TF distortion measurement as a criterion that compares the TF distributions of the denoised signal and the clean signal. For a signal-to-noise ratio (SNR) from -10 to 20 dB, the noise reduction results obtained using TSF have an average of 42.1% lower TF distortion than STH for the snapping shrimp noise, and a 23.3% lower TF distortion for the rainfall noise.