Data reconciliation for input-output models in linear dynamic systems

This article describes a new framework for data reconciliation in generalized linear dynamic systems, in which the well‐known Kalman filter (KF) is inadequate for filtering. In contrast to the classical formulation, the proposed framework is in a more concise form but still remains the same filtering accuracy. This comes from the properties of linear dynamic systems and the features of the linear equality constrained least squares solution. Meanwhile, the statistical properties of the framework offer new potentials for dynamic measurement bias detection and identification techniques. On the basis of this new framework, a filtering formula is rederived directly and the generalized likelihood ratio method is modified for generalized linear dynamic systems. Simulation studies of a material network present the effects of both the techniques and emphatically demonstrate the characteristics of the identification approach. Moreover, the new framework provides some insights about the connections between linear dynamic data reconciliation, linear steady state data reconciliation, and KF. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Data Reconciliation in Reaction Systems using the Concept of Extents

<p>The article deals with the problem of finding the observer of the state vector of linear continuous non-stationary dynamical systems with uncertainty of the initial conditions, limited external influences and measurement errors over a finite time interval. Sufficient conditions for the existence of an observer are formulated and proved on the basis of the expansion principle. Relationships are obtained for finding the parameters of the observer and the worst laws of change in external influences and measurement errors. As a limiting case, the problem of observer synthesis for stationary linear dynamical systems on a semi-infinite time interval is considered. Two applied problems of estimating the aircraft state vector based on the results of incomplete and inaccurate measurements are solved.</p>

In this paper, we study the Poincare recurrence phenomenon in linear dynamical systems, that is, dynamical systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear dynamical systems. Finally, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a dynamical system

Linear dynamical systems over finite rings

Dynamic texture can be defined as a temporally continuous and infinitely varying stream of images that exhibit certain temporal statistics. Linear dynamic system (LDS) represented by the state-space equation has been proposed to model dynamic texture [12]. LDS can be used to synthesize dynamic texture by sampling the system noise. However, the visual quality of the synthesized dynamic texture using noise-driven LDS is often unsatisfactory. In this paper, we regard the noise-driven LDS as an open-loop control system and analyze its stability through its pole placement. We show that the noise-driven LDS can produce good quality dynamic texture if the LDS is oscillatory. To deal with an LDS not oscillatory, we present a novel approach, called closed-loop LDS (CLDS) where feedback control is introduced into the system. Using the succeeding hidden states as an input reference signal, we design a feedback controller based on the difference between the current state and the reference state. An iterative algorithm is proposed to generate dynamic textures. Experimental results demonstrate that CLDS can produce dynamic texture sequences with promising visual quality.KeywordsUnit CircleVisual QualityHide StateLinear Dynamic SystemTexture SynthesisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The network oriented representation of the 3-D electromagnetic structures is based on two types of linear systems. The former one is a dynamic linear system which describes the interaction of electric and magnetic fields inside the structure while the latter one is a linear system consisting of delay lines meant for the reflection and propagation. The system identification of the linear dynamic system needs the estimation of the poles positions and the maximum duration of the delays of complementary linear system. The improved system identification scheme based on poles set stability criterion is introduced. This scheme offers to divide the restored impulse response into the finite duration entire part and the infinite pole part which pertain to the each linear system correspondingly. The simulation results of the model parameter estimation for the two-port coplanar resonator are demonstrated.

We introduce a family of group action induced distances on spaces of Linear Dynamical Systems (LDSs) of fixed size and order. The distance between two LDSs is computed by finding the change of basis that best aligns the state-space realizations of the two LDSs, hence the name alignment distance. This distance can be computed efficiently, hence it is particularly suitable for applications in modern dynamic data analysis (e.g., video sequence classification and clustering), where a large number of high-dimensional LDSs may need to be compared. Based on the alignment distance, we also define a notion of average between LDSs of the same size and order with the property that the order and in some cases stability are naturally preserved. Various extensions to the basic notion of alignment distance are also proposed.

Action recognition using linear dynamic systems

In this paper, we propose a novel categorization framework to recognize tactile sequences based on two particular properties of the tactile data. For the first one, tactile sequences are spatio-temporal data which is sequential and dynamic, depicting the process of grasping an object in different grasping stages; therefore, it is reasonable to discover the dynamical pattern by modeling tactile data as integral sequences rather than individual frames. For the second one, a tactile sequence contains various dynamical patterns in different stages of the grasping process; therefore, we decompose the whole sequence into multiple mini-sequences so as to enhance feature resolution. To address both properties in our framework, we take advantage of a Bag-of-System model using parameters of the Linear Dynamic System (LDS) as feature descriptors. Moreover, we employ the LDS with Symmetric Transition matrix (LDSST) rather than the original LDS as the building-block in order to obtain accurate codewords of the codebook of the Bag-of-System. The performance of our framework is evaluated on six real-world databases of three groups. Our experiments show that classification using LDSST is better than the original LDS, and the decomposition of tactile sequences does improve the accuracy of classification. The experiment results also show the superiority of our framework in comparison with other state-of-the-art sequence classifiers.

Introduction: This article is the result of the research “Analysis of the dynamic systems component of the engineering programs in control and automation and technology in industrial electronics,” developed at the Francisco José de Caldas District University in the years 2022-2023. Problem: The document addresses the lack of a clear and comprehensive structure in the analysis of linear dynamic systems, as well as the absence of an innovative approach to addressing these topics in traditional courses, which hinders their understanding and application in different disciplines. Objective: The objective is to present a novel approach to analyzing linear dynamic systems, providing a complete framework of concepts, relationships, and important tools in this analysis, as well as a literature review based on over seventeen years of experience in courses and studies of this kind. Methodology: A journey of concepts is proposed from signals and systems, through modeling with methods such as black box, white box, gray box, to linear analysis based on examples with calculation of differential equations, state representation, transfer function, and block diagrams. Results: The document aggregates and articulates all the concepts of dynamic systems, along with the relationships and tools used, offering a more practical and intuitive approach to understanding the material. Conclusion: The document provides a comprehensive and articulated view of key concepts in the analysis of linear dynamic systems, highlighting an innovative approach that facilitates their understanding. Its main contribution is to aggregate and articulate these concepts, along with the tools and relationships used, to offer a more practical and clear approach for their study. Originality: The originality lies in proposing a novel and structured approach to analyzing linear dynamic systems, addressing the lack of clarity and completeness in traditional approaches. Limitations: Although the document proposes a novel approach, it does not delve into specific aspects of some topics covered, which could limit the detailed understanding of certain concepts. Deepening: The document could delve into the practical application of the proposed concepts and tools in real cases of dynamic systems, as well as into the comparison with traditional approaches to highlight the differences and advantages of the proposed new approach.

The identification of block-oriented systems represented by interconnections of linear dynamic systems and non-memory nonlinear elements have been of great importance for control and for analysis of biological nonlinear systems. In this study, two new algorithms to obtain structural models of nonlinear systems using numerically-given (experimentally obtained) Volterra kernels are proposed. One is to determine the parallel factorable base model; a sum of subsets, each of which has a parallel structure of linear dynamic systems whose outputs are multiplied. Another is called the Sm model; linear dynamic systems and nonlinear power elements in cascade. The results of numerical experiments showed that both methods could be practically useful for identifications and analysis of nonlinear systems.

Max-algebra model of cyclic queueing networks and its explicit eigenvalue formula

This article presents a method of analyzing mixed logic/dynamic systems. The article describes the development of a computational tool for the analysis of piecewise linear (PL) dynamical systems. Unfortunately, many PL controllers are developed from ad hoc "intelligent systems" ideas which do not aim or allow the associated dynamic behavior to be predicted. An example of such a system is the anti-skid braking system in a car, where the controller is rule-based and designed using the engineer's knowledge of the system. The only current viable approach to testing such a system is by using extensive simulation and prototype testing, which must be repeated for each of the different car models on which it is installed. Anything that provides insight into the logic and dynamic interaction of such a system would be useful: hence the development of the work in this article. Similarly, systems with programmable logic controllers and gain schedulers also fall into the class of piecewise linear systems. The authors take ideas and known results from linear systems, convex set theory, and computational geometry and synthesize them to create an analysis tool for studying a class of systems that mix logic and dynamics. We choose to develop a computational analysis tool primarily because the traditional theoretical analysis of piecewise linear processes is intractable, except, that is, for certain local dynamic behavior.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

State-equation fitting from frequency-response data