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Adaptive Wavelet Control of Nonlinear Systems
"... This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a statefeedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semiglobal stability r ..."
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This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a statefeedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semiglobal stability results are obtained under the key assumption that the system uncertainty satisfies a "matching" condition. The localization properties of adaptive networks are discussed and formal definitions of interference and localization measures are proposed. Keywordswavelets, neural networks, adaptive nonlinear control, Lyapunov stability theory, localization. 1 Introduction The analytical study of adaptive nonlinear control systems involving online approximation structures has evolved considerably during the last five years [1][6]. The design of online approximation based controllers can be broken up into two stages: first, the unknown nonlinearity is represented by some online approximator....
Beppo Levi's Theorem for the VectorValued McShane Integral and Applications
"... Using only elementary properties of the McShane integral for vectorvalued functions, we establish a convergence theorem which for the scalar case of the integral yields the classical Beppo Levi (monotone) convergence theorem as an immediate corollary. As an application, the convergence theorem is u ..."
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Using only elementary properties of the McShane integral for vectorvalued functions, we establish a convergence theorem which for the scalar case of the integral yields the classical Beppo Levi (monotone) convergence theorem as an immediate corollary. As an application, the convergence theorem is used to prove that the space of McShane integrable functions, although not usually complete, is ultrabornological. 1
The Integral: An Easy Approach after Kurzweil and Henstock.
"... A simple definition. Riemann’s integral of 1867 can be summarized as f(t)dt = lim � f(τi)(ti − ti−1). This summary conceals some of the complexity—for example, the limit is of a net, not a sequence—but it displays what we wish to emphasize: The integral is formed by combining the values f(τi) in a v ..."
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A simple definition. Riemann’s integral of 1867 can be summarized as f(t)dt = lim � f(τi)(ti − ti−1). This summary conceals some of the complexity—for example, the limit is of a net, not a sequence—but it displays what we wish to emphasize: The integral is formed by combining the values f(τi) in a very direct fashion. The values of f are used less directly in Lebesgue’s integral (1902), which � b can be described as limn→ ∞ a gn(t)dt. The approximating functions gn must be chosen carefully, using deep, abstract notions of measure theory. Simpler definitions are possible—for example, functional analysts might consider the metric completion of C[0, 1] using the L1 norm—but such a definition does not give us easy access to the Lebesgue integral’s simple and powerful properties such as the Monotone Convergence Theorem. We generally think in terms of those simple properties, rather than the various complicated definitions, when we actually use the Lebesgue integral.
On the Utility of Laguerre Series for the Envelope PDF in Multipath Fading Channels
"... Abstract — It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases we need to calculate the probability density function (PDF) of the received sign ..."
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Abstract — It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases we need to calculate the probability density function (PDF) of the received signal envelope in multipath fading channels. In this paper, we consider a general multipath fading channel with arbitrary number of paths, where the amplitudes of multipath components are arbitrary correlated positive random variables, independent of phases, whereas the phases are independent and identically distributed random variables with uniform distributions. Since the integral form of the envelope PDF for such a general channel model is too complicated to be used for analytic calculations, we propose two infinite expansions for the PDF, a Laguerre series and a power series. Based on the tight uniform upper bounds on the truncation error of these two infinite series, we show that the Laguerre series is superior to the power series due to the fact that for a fixed number of terms, it yields a smaller truncation error. This Laguerre series with a finite number of terms, which expresses the envelope PDF just in terms of simple polynomialexponential kernels, is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments, where the number of strong multipath components is small.
Adaptive Nonlinear Design Without a Priori Knowledge of Control Directions
, 1998
"... Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this paper, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system ..."
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Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this paper, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system dynamics due to the fault are modeled as nonlinear functions of the state and input variables, while the time profile of the failure is assumed to be exponentially developing. An automated fault diagnosis architecture using nonlinear online approximators with an adaptation scheme is designed and analyzed. A simulation example of a simple nonlinear massspring system is used to illustrate the results. Index TermsFailure detection, nonlinear estimator, online approximators. I. INTRODUCTION Increased productivity requirements and stringent performance specifications lead to more demanding operating conditions of many modern engineering systems. Such conditions increase the possibility Man...
Gerald B. Folland
"... spirit is always mathematical. This is very possibly the best "mathematics for the nonmathematician" book that I have seenand that includes popular (nontextbook) books that one would find in a general bookstore. This one doesn't lapse into the pitfalls often found in such books. It preaches th ..."
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spirit is always mathematical. This is very possibly the best "mathematics for the nonmathematician" book that I have seenand that includes popular (nontextbook) books that one would find in a general bookstore. This one doesn't lapse into the pitfalls often found in such books. It preaches the beauty and fascination of mathematics in the introduction and then follows through. It does not cut mathematical corners: Its explanations are complete and accurate, its theorems are stated precisely, and its proofs are intuitive and often colloquially presented without being sloppy. The book could also be of benefit to mathematicians. Teachers often say that they learn something new every time they teach a course, but they usually mean something subtle. I have to confess that I learned some nonsubtle things from reading this book. For example, I hadn't heard of Newcomb's Paradox or Conway tiles, and I hadn't realized that no one knows whether the builders of the Parthenon were consciou
Holography and Quantum Gravity in 3+1 Dimensions
, 2004
"... Abstract: A holographic theory on N is described by a holographic dual theory on the boundary of N with action S, an integral over the boundary of N. Thus, in the limit of a vanishing boundary, the action of the holographic dual is S = 0, the action of a topological field theory. So, if general rela ..."
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Abstract: A holographic theory on N is described by a holographic dual theory on the boundary of N with action S, an integral over the boundary of N. Thus, in the limit of a vanishing boundary, the action of the holographic dual is S = 0, the action of a topological field theory. So, if general relativity is holographic, then when formulated on M a manifold without boundary it must be topological. In this article we prove that on M, a 3 + 1 dimensional manifold without boundary, general relativity with a positive cosmological constant is equivalent to a so(4,1) DonaldsonWitten theory. For the case of a negative cosmological constant, we find it is equivalent to a so(3,2) DonaldsonWitten theory. As theories of DonaldsonWitten type are exactly solvable, this proves that exact, nonperturbative calculations can be preformed in 3 + 1 dimensional quantum gravity. We then go on to perform a representative set of such exact calculations. Next we show that the familiar structure of general relativity arises through spontaneous symmetry breaking of the DonaldsonWitten theory’s “topological symmetry. ” We then prove that general relativity on N, a 3 + 1 dimensional manifold with boundary, is holographic, i.e. all local degrees of freedom in the bulk are described by a theory residing on the boundary. Next we
BMC Cardiovascular Disorders BioMed Central
, 2005
"... Research article Characteristic wave detection in ECG signal using morphological transform ..."
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Research article Characteristic wave detection in ECG signal using morphological transform
unknown title
, 2008
"... We show that, for a class of systems described by a Lagrangian the propagator ..."
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We show that, for a class of systems described by a Lagrangian the propagator