The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on ...the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms.
Accurate estimation of the state of charge (SOC) of lithium‐ion batteries is quite crucial to battery safety monitoring and efficient use of energy; to improve the accuracy of lithium‐ion battery SOC ...estimation under complicated working conditions, the research object of this study is the ternary lithium‐ion battery; the forgetting factor recursive least square (FFRLS) method optimized by particle swarm optimization (PSO) and adaptive H‐infinity filter (HIF) algorithm are adopted to estimate battery SOC. The PSO algorithm is improved with dynamic inertia weight to optimize the forgetting factor to solve the contradiction between FFRLS convergence speed and anti‐noise ability. The noise covariance matrixes of the HIF are improved to realize adaptive correction function and improve the accuracy of SOC estimation. To verify the rationality of the joint algorithm, a second‐order Thevenin model is established to estimate the SOC under three complex operating conditions. The experimental results show that the absolute value of the maximum estimation error of the improved algorithm under the three working conditions is 0.0192, 0.0131, and 0.0111, respectively, which proves that the improved algorithm has high accuracy and offers a theoretical basis for the safe and efficient operation of the battery management system.
The PSO algorithm is improved with dynamic inertia weight to optimize the forgetting factor to solve the contradiction between FFRLS convergence speed and anti‐noise ability. The noise covariance matrixes of the HIF algorithm are improved to realize adaptive correction function and improve the accuracy of SOC estimation. The experimental results show that the improved algorithms can effectively improve the SOC estimation accuracy.
This paper presents a new set-membership observer design method for discrete-time linear parameter varying systems. The real process is assumed to be perturbed by unknown but bounded disturbances. ...The proposed set-membership observer provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation errors bounds. The observer design process is based on the offline solution of a finite number of linear matrix inequalities conditions that provide both the observer parameters and the ellipsoidal robustly positive invariant (RPI) sets for the estimation error dynamics. The main feature of the proposed approach concerns the fact that these RPI sets are used to frame, at every time-instant, the estimation error in an explicit way. Another novelty concerns the fact that the approach includes uniformly distributed random disturbances which belongs to the family of bounded disturbances. The a posteriori steady-state covariance matrix of the estimation error dynamics, perturbed by such disturbances, is used during the observer synthesis providing small RPI sets. Two numerical examples illustrate the behaviour of such observer and its easy implementation.
We analyze a model for the homotopy theory of complete filtered L∞-algebras intended for applications in algebraic and algebro-geometric deformation theory. We provide an explicit proof of an ...unpublished result of E. Getzler which states that the category Lieˆ∞ of such L∞-algebras and filtration-preserving ∞-morphisms admits the structure of a category of fibrant objects (CFO) for a homotopy theory. Novel applications of our approach include explicit models for homotopy pullbacks, and an analog of Whitehead's Theorem: under some mild conditions, every filtered L∞-quasi-isomorphism in Lieˆ∞ has a filtration preserving homotopy inverse. Also, we show that the simplicial Maurer–Cartan functor, which assigns a Kan simplicial set to each L∞-algebra in Lieˆ∞, is an exact functor between the respective CFOs. Finally, we provide an obstruction theory for the general problem of lifting a Maurer-Cartan element through an ∞-morphism. The obstruction classes reside in the associated graded mapping cone of the corresponding tangent map.
Negation and infinity Trzęsicki, Kazimierz
Studies in logic, grammar and rhetoric : the Journal of University of Bialystok,
06/2018, Letnik:
54, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Infinity and negation are in various relations and interdependencies one to another. The analysis of negation and infinity aims to better understanding them. Semantical, syntactical, and pragmatic ...issues will be considered.
We study the streamlines of ∞-harmonic functions in planar convex rings. We include convex polygons. The points where streamlines can meet are characterized: they lie on certain curves. The gradient ...has constant norm along streamlines outside the set of meeting points, the infinity-ridge.
We show that the category of truncated spaces with finite homotopy invariants (\(\pi\)\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thought of as the ...natural higher analogue of the elementary 1-topos of finite sets. We prove several initiality results for this \oo category. The paper has also an appendix about univalent families in \oo pretopoi.
This article proposes a memory-based event-triggering <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> load frequency control (LFC) method for power systems ...through a bandwidth-constrained open network. To overcome the bandwidth constraint, a memory-based event-triggered scheme (METS) is first proposed to reduce the number of transmitted packets. Compared with the existing memoryless event-triggered schemes, the proposed METS has the advantage to utilize series of the latest released signals. To deal with the random deception attacks induced by open networks, a networked power system model is well established, which couples the effects of METS and random deception attacks in a unified framework. Then, a sufficient stabilization criterion is derived to obtain the memory <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> LFC controller gains and event-triggered parameters simultaneously. Compared with existing memoryless LFC, the control performance is greatly improved since the latest released dynamic information is well utilized. Finally, an illustrative example is used to show the effectiveness of the proposed method.
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