Search results for "Linear"

showing 10 items of 7165 documents

On the Construction of Lusternik-Schnirelmann Critical Values with Application to Bifurcation Problems

1987

An iterative method to construct Lusternik-Schnirelmann critical values is presented. Examples of its use to obtain numerical solutions to nonlinear eigenvalue problems and their bifurcation branches are given. peerReviewed

Lusternik-Schnirelmann critical valuesMathematics::General Topologynonlinear eigenvalue problemsMathematics::Algebraic Topology
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Chaotic dynamics around cometary nuclei

2017

We apply a generalized Kepler map theory to describe the qualitative chaotic dynamics around cometary nuclei, based on accessible observational data for five comets whose nuclei are well-documented to resemble dumb-bells. The sizes of chaotic zones around the nuclei and the Lyapunov times of the motion inside these zones are estimated. In the case of Comet 1P/Halley, the circumnuclear chaotic zone seems to engulf an essential part of the Hill sphere, at least for orbits of moderate to high eccentricity.

Lyapunov function010504 meteorology & atmospheric sciences[PHYS.ASTR.EP]Physics [physics]/Astrophysics [astro-ph]/Earth and Planetary Astrophysics [astro-ph.EP]CometChaoticFOS: Physical sciencesAstrophysics01 natural sciencessymbols.namesake0103 physical sciences010303 astronomy & astrophysics0105 earth and related environmental sciencesPhysicsEarth and Planetary Astrophysics (astro-ph.EP)AstronomyAstronomy and AstrophysicsNonlinear Sciences - Chaotic DynamicsCelestial mechanicsNonlinear Sciences::Chaotic DynamicsSpace and Planetary Science[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]symbolsHill sphereAstrophysics::Earth and Planetary AstrophysicsChaotic Dynamics (nlin.CD)Eccentricity (mathematics)Astrophysics - Earth and Planetary Astrophysics
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Finite-Time H∞ Filtering for T-S Fuzzy Discrete-Time Systems with Time-Varying Delay and Norm-Bounded Uncertainties

2015

In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are propose…

Lyapunov function0209 industrial biotechnology02 engineering and technologyFuzzy logicsymbols.namesake020901 industrial engineering & automationControl theoryArtificial Intelligence0202 electrical engineering electronic engineering information engineeringFiltering problemnorm-bounded uncertaintieslinear matrix inequalities (LMIs)T-S fuzzy systemMathematicsApplied MathematicsFilter (signal processing)Finite-time boundednesstime delayFilter designH-infinity methods in control theoryDiscrete time and continuous timeComputational Theory and MathematicsControl and Systems EngineeringBounded functionsymbols020201 artificial intelligence & image processingHâ filteringFinite-time boundedness; H∞ filtering; linear matrix inequalities (LMIs); norm-bounded uncertainties; T-S fuzzy system; time delay; Control and Systems Engineering; Computational Theory and Mathematics; Artificial Intelligence; Applied Mathematics
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Adaptive feedback linearizing control of linear induction motor considering the end-effects

2016

This paper proposes an input-output feedback linearization techniques for linear induction motors, taking into consideration the dynamic end-effects. As a main original content, this work proposes a new control law based on the on-line estimation of the induced-part time constant. The estimation law is obtained thanks to a Lyapunov based analysis and thus the stability of the entire control system, including the estimation algorithm, is intrinsically guaranteed. Moreover, with such an approach even the on-lihe variation of the induced-part time constant with the speed is retrieved, thus improving the behavior of previously developed approaches where such a variation vs. speed is considered …

Lyapunov function0209 industrial biotechnologyEngineeringLinear induction motorStability (learning theory)02 engineering and technologyAdaptive systemsParameters' estimation.symbols.namesake020901 industrial engineering & automationSettore ING-INF/04 - AutomaticaControl theoryAdaptive system0202 electrical engineering electronic engineering information engineeringFeedback linearizationFeedback linearizationElectrical and Electronic Engineeringbusiness.industryApplied Mathematics020208 electrical & electronic engineeringTime constantControl engineeringEnd-effectsEnd-effectComputer Science ApplicationsControl and Systems EngineeringParameters' estimationControl systemLinear induction motorsymbolsA priori and a posterioriAdaptive systembusinessControl Engineering Practice
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Input-to-state stability for discrete-time nonlinear switched singular systems

2016

Discrete-time nonlinear switched singular systems (SSSs) are investigated.The input-to-state stability (ISS) problems for discrete-time nonlinear SSSs are concerned.The ISS criteria are obtained via average dwell time approach and iterative algorithm of discrete-time systems.The switching rules are optimized and designed. This paper investigates the input-to-state stability (ISS) problems for a class of discrete-time nonlinear switched singular systems (SSSs). Two novel ISS criteria are proposed based on average dwell time (ADT) approach and iterative algorithm of discrete-time systems (IADS). In particular, the following two cases are considered for the underlying systems: the first case i…

Lyapunov function0209 industrial biotechnologyInformation Systems and ManagementIterative method02 engineering and technologyStability (probability)Theoretical Computer Sciencesymbols.namesake020901 industrial engineering & automationExponential stabilityControl theoryArtificial IntelligenceIterative algorithm0202 electrical engineering electronic engineering information engineeringMathematicsSwitched singular systemInput-to-state stabilityProcess (computing)Computer Science Applications1707 Computer Vision and Pattern RecognitionAverage dwell time; Discrete-time system; Input-to-state stability; Iterative algorithm; Nonlinear system; Switched singular system; Control and Systems Engineering; Theoretical Computer Science; Software; Computer Science Applications1707 Computer Vision and Pattern Recognition; Information Systems and Management; Artificial IntelligenceComputer Science ApplicationsNonlinear systemDwell timeDiscrete time and continuous timeDiscrete-time systemControl and Systems EngineeringsymbolsNonlinear system020201 artificial intelligence & image processingAverage dwell timeSoftware
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Stationary and Initial-Terminal Value Problem for Collective Decision Making via Mean-Field Games

2017

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, following some optimality criteria. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, thus introducing mean-field terms in the running and the terminal cost. The first contribution is a mean-field model that takes into account the macroscopic and the microscopic dynamics. The second contribution is the study of the mean-field equilibrium resulting from solving the initial-terminal value problem, involving the Kolmogorov equat…

Lyapunov function0209 industrial biotechnologyMathematical optimization010102 general mathematicsMarkov processContext (language use)02 engineering and technology01 natural sciencesTerminal valueNonlinear systemsymbols.namesake020901 industrial engineering & automationStability theoryKolmogorov equationssymbolsGames Mathematical model Markov processes Sociology Statistics Microscopy RobustnessApplied mathematicsLimit (mathematics)0101 mathematicsSettore MAT/09 - Ricerca OperativaMathematics
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On constrained Volterra cubic stochastic operators

2020

We consider constrained Volterra cubic stochastic operators and construct several Lyapunov functions for the constrained Volterra cubic stochastic operators. We prove that such kind operators do no...

Lyapunov functionAlgebra and Number TheoryApplied Mathematics010102 general mathematicsConstruct (python library)01 natural sciences010101 applied mathematicssymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsTrajectorysymbolsQuantitative Biology::Populations and EvolutionApplied mathematics0101 mathematicsAnalysisMathematicsJournal of Difference Equations and Applications
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Invariant varieties of discontinuous vector fields

2004

We study the geometric qualitative behaviour of a class of discontinuous vector fields in four dimensions around typical singularities. We are mainly interested in giving the conditions under which there exist one-parameter families of periodic orbits (a result that can be seen as one analogous to the Lyapunov centre theorem). The focus is on certain discontinuous systems having some symmetric properties. We also present an algorithm which detects and computes periodic orbits.

Lyapunov functionApplied MathematicsMathematical analysisGeneral Physics and AstronomyStatistical and Nonlinear PhysicsDiscontinuous systemssymbols.namesakeSingularitysymbolsPeriodic orbitsGravitational singularityVector fieldInvariant (mathematics)Mathematical PhysicsMathematicsNonlinearity
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Neural Petri Control: an application on a mobile robot

2006

In the present work, an innovative nonlinear controller of nonholonomic mechanical systems, characterized by a dynamic not well known model a priori, using a new neural model obtained by the combination of a Petri net with a neural network, is proposed. The performances of the control algorithm are evaluated for tasks of tracking of time trajectories. The study of the stability of the total system to closed loop is based on the Lyapunov theory. Simulation experiments, made taking into consideration a nonholonomic mobile robot, to two wheels, allowed to verify the theoretical results.

Lyapunov functionArtificial neural networkComputer scienceStability (learning theory)Mobile robotControl engineeringPetri netsFuzzy systemsPetri netfuzzy reasoningComputer Science::Roboticssymbols.namesakeNonlinear systemControl theorysymbolsNonholonomic mobile robot
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The Lyapunov dimension formula for the global attractor of the Lorenz system

2015

The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the …

Lyapunov functionClass (set theory)Mathematics::Dynamical SystemsKaplan-Yorke dimensionFOS: Physical sciencesLyapunov exponentDynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)010305 fluids & plasmassymbols.namesakeDimension (vector space)Lorenz system0103 physical sciencesAttractorFOS: MathematicsMathematics - Dynamical Systems010301 acousticsMathematicsNumerical AnalysisApplied MathematicsMathematical analysista111Lyapunov exponentsLorenz systemNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsModeling and SimulationsymbolsLyapunov dimensionself-excited Lorenz attractorVariety (universal algebra)Chaotic Dynamics (nlin.CD)
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