A simple observer for nonlinear systems applications to bioreactors
TL;DR: In this paper, an observer for nonlinear systems is constructed under rather general technical assumptions (the fact that some functions are globally Lipschitz) and a tentative application to biological systems is described.
Abstract: An observer for nonlinear systems is constructed under rather general technical assumptions (the fact that some functions are globally Lipschitz). This observer works either for autonomous systems or for nonlinear systems that are observable for any input. A tentative application to biological systems is described. >
Citations
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TL;DR: A survey of modern nonlinear filtering methods for attitude estimation based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance is provided.
Abstract: This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST and the backwards-smoothing extended Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A twostep approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.
1,116 citations
TL;DR: Algorithms for wavelet network construction are proposed for the purpose of nonparametric regression estimation and particular attentions are paid to sparse training data so that problems of large dimension can be better handled.
Abstract: Wavelet networks are a class of neural networks consisting of wavelets. In this paper, algorithms for wavelet network construction are proposed for the purpose of nonparametric regression estimation. Particular attentions are paid to sparse training data so that problems of large dimension can be better handled. A numerical example on nonlinear system identification is presented for illustration.
760 citations
TL;DR: This survey describes the 'activation' of stability, optimality and uncertainty concepts into design tools and constructive procedures in nonlinear control theory and concludes with four representative applications.
720 citations
Cites background or methods from "A simple observer for nonlinear sys..."
...To achieve global convergence of high-gain observers, Gauthier, Hammouri, and Othman (1992) resorted to a global Lipschitz condition* a common restriction in most global designs....
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...Magnitude and rate limits have been treated by optimization-based methods in Gilbert and Tan (1991), Megretski (1996), Shewchun and Feron (1997), and by anti-windup techniques in Teel and Kapoor (1997), and Teel (1998). A bibliography of some 150 papers is given in Bernstein and Michel (1995)....
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...Magnitude and rate limits have been treated by optimization-based methods in Gilbert and Tan (1991), Megretski (1996), Shewchun and Feron (1997), and by anti-windup techniques in Teel and Kapoor (1997), and Teel (1998)....
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TL;DR: The topic of synchronization of the response of systems has received considerable attention and this concept is revisited in the light of the classical notion of observers from (non)linear control theory.
Abstract: In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory,.
716 citations
Cites background from "A simple observer for nonlinear sys..."
...For nonlinear systems a few partial results exist [15], [16], [26]–[28]....
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...If we limit ourselves to dynamics defined on some compact set, then the following result is available [16]....
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TL;DR: This talk is a brief introduction to high-gain observers in nonlinear feedback control, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it.
Abstract: In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.
663 citations
Cites background from "A simple observer for nonlinear sys..."
...The work by Gauthier, Hammouri, and Othman [7] started a line of work that is exemplified by [8–13]....
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References
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Book•
07 Jun 1995
TL;DR: Striking a balance between theory and applications, Linear System Theory and Design, 3/e, is ideal for use in advanced undergraduate/first-year graduate courses in linear systems and multivariable system design in electrical, mechanical, chemical, and aeronautical engineering departments.
Abstract: From the Publisher:
An extensive revision of the author's highly successful text, this third edition of Linear System Theory and Design has been made more accessible to students from all related backgrounds. After introducing the fundamental properties of linear systems, the text discusses design using state equations and transfer functions. The two main objectives of the text are to: use simple and efficient methods to develop results and design procedures; enable students to employ the results to carry out design. Striking a balance between theory and applications, Linear System Theory and Design, 3/e, is ideal for use in advanced undergraduate/first-year graduate courses in linear systems and multivariable system design in electrical, mechanical, chemical, and aeronautical engineering departments. It assumes a working knowledge of linear algebra and the Laplace transform and an elementary knowledge of differential equations.
4,017 citations
TL;DR: Observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection.
1,384 citations
TL;DR: In this article, a method for designing asymptotic observers for a class of nonlinear systems is presented, where the error between the state of the systems and the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.
Abstract: A new method for designing asymptotic observers for a class of nonlinear systems is presented. The error between the state of the systems and the state of the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.
1,062 citations
TL;DR: Results from studies of continuous cultures of Aerobacter aerogenes growing in chemically denned media indicate that specific growth rate (R) is a function of population density as well as the concentration of the limiting nutrient.
Abstract: SUMMARY: Results from studies of continuous cultures of Aerobacter aerogenes growing in chemically denned media indicate that specific growth rate (R) is a function of population density (P) as well as the concentration of the limiting nutrient (S). From these observations, and those of others, the following model for bacterial growth is derived: mic-21-1-40-si1.gif where um and B are growth parameters that are constants under defined conditions. This model is believed to have general applicability and to account for bacterial growth in both batch and continuous cultures.
590 citations
01 Dec 1980
TL;DR: This paper deals with a class of nonlinear systems, linear with respect to the inputs, and a necessary and sufficient condition of observability for any input function is obtained.
Abstract: This paper deals with a class of nonlinear systems, which are linear with respect to the inputs. After a necessary and sufficient condition of observability for any input function is obtained. A canonical form is then given.
337 citations