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    Wyświetlanie 1-12 z 12
    Tytuł:
    ℎ-Stability of set differential equations
    Autorzy:
    Boukthir, Sihem
    Ghanmi, Boulbaba
    Basdouri, Imed
    Ichalal, Dalil
    Lerbet, Jean
    Powiązania:
    https://bibliotekanauki.pl/articles/27324010.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    ℎ-stability
    Lyapunov theory
    set-valued differential
    generalized Hukuhara derivative
    perturbed system
    cascaded systems
    Opis:
    In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems.
    Źródło:
    Archives of Control Sciences; 2023, 33, 4; 761--788
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Design of an adaptive fuzzy variable structure compensator for the nonholonomic mobile robot in trajectory tracking task
    Autorzy:
    Begnini, M.
    Bertol, W.
    Martins, N. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/971054.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonholonomic mobile robot
    trajectory tracking
    variable structure control
    uncertainties and disturbances
    fuzzy compensator
    Lyapunov theory
    Opis:
    A robust adaptive kinematic control strategy, based on the methodology of variable structure control is considered in this paper. Because the dynamics of mobile robots is subject to uncertainties and disturbances, a fuzzy compensator is adopted to estimate them. In order to minimize the tracking errors and to attenuate the chattering phenomenon, an adaptation law for the fuzzy compensator is obtained by Lyapunov stability theory so as to asymptotically stabilize the control system as well as guarantee the convergence of the tracking errors. In terms of comparison with the boundary layer variable structure controller, simulations and experiments verify the feasibility and effectiveness of the proposed kinematic control strategy for the nonholonomic mobile robots under the incidence of uncertainties and disturbances.
    Źródło:
    Control and Cybernetics; 2018, 47, 3; 239-275
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Trajectory tracking of a wheeled mobile robot with uncertainties and disturbances: proposed adaptive neural control
    Autorzy:
    Martins, N. A.
    Alencar, M.
    Lombardi, W. C.
    Bertol, D. W.
    Pieri, E. R.
    Filho, H. F.
    Powiązania:
    https://bibliotekanauki.pl/articles/971045.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    wheeled mobile robot
    trajectory tracking
    kinematic control
    variable structure control
    dynamic control
    sliding mode theory
    neural networks
    Lyapunov theory
    Opis:
    This paper analyses a trajectory tracking control problem for a wheeled mobile robot, Rusing integration of a kinematic neural controller (KNC) and a torque neural controller (TNC), in which both the kinematic and dynamic models contain uncertainties and disturbances. The proposed adaptive neural controller (PANC) is composed of the KNC and the TNC and is designed with use of a modeling technique of Gaussian radial basis function neural networks (RBFNNs). The KNC is a variable structure controller, based on the sliding mode theory and is applied to compensate for the disturbances of the wheeled mobile robot kinematics. The TNC is an inertia-based controller composed of a dynamic neural controller (DNC) and a robust neural compensator (RNC) applied to compensate for the wheeled mobile robot dynamics, bounded unknown disturbances, and neural network modeling errors. To minimize the problems found in practical implementations of the classical variable structure controllers (VSC) and sliding mode controllers (SMC), and to eliminate the chattering phenomenon, the nonlinear and continuous KNC and RNC of the TNC are applied in lieu of the discontinuous components of the control signals that are present in classical forms. Additionally, the PANC neither requires the knowledge of the wheeled mobile robot kinematics and dynamics nor the timeconsuming training process. Stability analysis, convergence of the tracking errors to zero, and the learning algorithms for the weights are guaranteed based on the Lyapunov method. Simulation results are provided to demonstrate the effectiveness of the proposed approach.
    Źródło:
    Control and Cybernetics; 2015, 44, 1; 47-98
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Review, design, stabilization and synchronization of fractional-order energy resources demand-supply hyperchaotic systems using fractional-order PD-based feedback control scheme
    Autorzy:
    Soukkou, Ammar
    Soukkou, Yassine
    Haddad, Sofiane
    Benghanem, Mohamed
    Rabhi, Abdelhamid
    Powiązania:
    https://bibliotekanauki.pl/articles/27322620.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    fractional-order systems
    fractional-order control
    Lyapunov stability theory
    multiobjective optimization
    artificial hummingbird algorithm
    stabilization
    synchronization
    energy resources demand-dupply systems
    Opis:
    This paper introduces a fractional-order PD approach (F-oPD) designed to control a large class of dynamical systems known as fractional-order chaotic systems (F-oCSs). The design process involves formulating an optimization problem to determine the parameters of the developed controller while satisfying the desired performance criteria. The stability of the control loop is initially assessed using the Lyapunov’s direct method and the latest stability assumptions for fractional-order systems. Additionally, an optimization algorithm inspired by the flight skills and foraging behavior of hummingbirds, known as the Artificial Hummingbird Algorithm (AHA), is employed as a tool for optimization. To evaluate the effectiveness of the proposed design approach, the fractional-order energy resources demand-supply (Fo-ERDS) hyperchaotic system is utilized as an illustrative example.
    Źródło:
    Archives of Control Sciences; 2023, 33, 3; 539--563
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New fault tolerant control strategies for nonlinear Takagi-Sugeno systems
    Autorzy:
    Ichalal, D.
    Marx, B.
    Ragot, J.
    Maquin, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/331456.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    model Takagi-Sugeno
    sterowanie tolerujące uszkodzenia
    uszkodzenie równoczesne
    estymacja stanu
    twierdzenie Lapunowa
    Takagi-Sugeno model
    fault tolerant control
    simultaneous fault
    state estimation
    Polya's theorem
    Lyapunov theory
    input to state stability
    Opis:
    New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polya's theorem. Some simulation examples are given in order to illustrate the proposed approaches.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 1; 197-210
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Robust hybrid synchronization control of chaotic 3-cell CNN with uncertain parameters using smooth super twisting algorithm
    Autorzy:
    Siddique, Nazam
    Rehman, Fazal
    Raoof, Uzair
    Iqbal, Shahid
    Rashad, Muhammad
    Powiązania:
    https://bibliotekanauki.pl/articles/27311427.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    hybrid synchronization
    cellular neural network
    sliding mode control
    smooth super twisting algorithm
    Lyapunov stability theory
    synchronizacja hybrydowa
    sieć neuronowa komórkowa
    sterowanie trybem przesuwnym
    teoria Lyapunova
    stabilność Lyapunova
    algorytm super skręcania płynny
    Opis:
    This paper presents the control design framework for the hybrid synchronization (HS) and parameter identification of the 3-Cell Cellular Neural Network. The cellular neural network (CNN) of this kind has increasing practical importance but due to its strong chaotic behavior and the presence of uncertain parameters make it difficult to design a smooth control framework. Sliding mode control (SMC) is very helpful for this kind of environment where the systems are nonlinear and have uncertain parameters and bounded disturbances. However, conventional SMC offers a dangerous chattering phenomenon, which is not acceptable in this scenario. To get chattering-free control, smooth higher-order SMC formulated on the smooth super twisting algorithm (SSTA) is proposed in this article. The stability of the sliding surface is ensured by the Lyapunov stability theory. The convergence of the error system to zero yields hybrid synchronization and the unknown parameters are computed adaptively. Finally, the results of the proposed control technique are compared with the adaptive integral sliding mode control (AISMC). Numerical simulation results validate the performance of the proposed algorithm.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 5; art. no. e146474
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a continuity of characteristic exponents of linear discrete time-varying systems
    Autorzy:
    Czornik, A.
    Mokry, P.
    Niezabitowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/229783.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-varying discrete linear systems
    Lyapunov exponents
    perturbation theory
    characteristic exponents
    Opis:
    In this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on this result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations.
    Źródło:
    Archives of Control Sciences; 2012, 22, 1; 17-27
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modeling shortest path games with Petri nets: A Lyapunov based theory
    Autorzy:
    Clempner, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908393.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Nash equilibrium point
    shortest path game
    game theory
    Lyapunov equilibrium point
    Bellman’s equation
    Lyapunov-like fuction
    stability
    teoria gier
    funkcja Lapunowa
    równanie Bellmana
    stabilność
    Opis:
    In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman’s equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain, allowing the replacement of the Nash equilibrium point by the Lyapunov equilibrium point in game theory. We show that the Lyapunov equilibrium point coincides with the Nash equilibrium point. As a consequence, all properties of equilibrium and stability are preserved in game theory. This is the most important contribution of this work. The potential of this approach remains in its formal proof simplicity for the existence of an equilibrium point.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 3; 387-397
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Zastosowanie wykładników Lapunowa do weryfikacji hipotezy rynku koherentnego
    Application of Lyapunov Exponents to Verify the Hypothesis of Coherent Market
    Autorzy:
    Miśkiewicz-Nawrocka, Monika
    Powiązania:
    https://bibliotekanauki.pl/articles/586313.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Ekonomiczny w Katowicach
    Tematy:
    Rynek kapitałowy
    Szeregi czasowe
    Teoria chaosu
    Wykładniki Lapunowa
    Capital market
    Chaos theory
    Lyapunov exponents
    Time-series
    Opis:
    The research on price volatility in the capital market, which have been conducted for many years led to create a wide variety of analytical approaches. One of them is developed by T. Vage coherent market hypothesis. To describe the volatility in the stock market T. Vaga proposed nonlinear statistical model based on the theory of social imitation. This model assumes transitions between different states of the capital market: from a state of effective market to a state of chaotic and coherent market. In this paper Vaga's hypothesis will be verified in the Polish capital market. Detailed research will be states of chaotic market, which will be verified by Lyapunov exponents.
    Źródło:
    Studia Ekonomiczne; 2013, 146; 79-88
    2083-8611
    Pojawia się w:
    Studia Ekonomiczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Colored decision process Petri nets: Modeling, analysis and stability
    Autorzy:
    Clempner, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908525.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    proces decyzyjny
    kolorowane sieci Petriego
    metoda Lapunowa
    teoria gier
    decision process
    colored decision process Petri nets
    stability
    Lyapunov methods
    optimization
    game theory
    Opis:
    In this paper we introduce a new modeling paradigm for developing a decision process representation called the Colored Decision Process Petri Net (CDPPN). It extends the Colored Petri Net (CPN) theoretic approach including Markov decision processes. CPNs are used for process representation taking advantage of the formal semantic and the graphical display. A Markov decision process is utilized as a tool for trajectory planning via a utility function. The main point of the CDPPN is its ability to represent the mark-dynamic and trajectory-dynamic properties of a decision process. Within the mark-dynamic properties framework we show that CDPPN theoretic notions of equilibrium and stability are those of the CPN. In the trajectory-dynamic properties framework, we optimize the utility function used for trajectory planning in the CDPPN by a Lyapunov-like function, obtaining as a result new characterizations for final decision points (optimum point) and stability. Moreover, we show that CDPPN mark-dynamic and Lyapunov trajectory-dynamic properties of equilibrium, stability and final decision points converge under certain restrictions. We propose an algorithm for optimum trajectory planning that makes use of the graphical representation (CPN) and the utility function. Moreover, we consider some results and discuss possible directions for further research.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 3; 405-420
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the book ``An Introduction to Differential Equations: Stochastic Modeling, Methods and Analysis'' by A.G.Ladde and G.S.Ladde
    Autorzy:
    Jurlewicz, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/747711.pdf
    Data publikacji:
    2015
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    General theory of stochastic systems
    stochastic modeling
    ODE with randomness
    Lyapunov method
    Stochastic functional-differential equations
    ogólna teoria systemów stochastycznych
    modelowanie stochastyczne
    stochastyczne równania różniczkowe
    metoda Lyapunowa
    Opis:
    Niniejsza książka stanowi kontynuację podręcznika, tych samych autorów, przedstawiającego tematykę równań różniczkowych. Tom 1. (Deterministic Modeling, Methods and Analysis) dotyczył teorii klasycznych, natomiast omawiany tu tom 2. prezentuje ideę równań różniczkowych stochastycznych i ich zastosowania w modelowaniu matematycznym. Książka adresowana jest głównie do studentów i doktorantów kierunków interdyscyplinarnych.
    The book under review presents advanced tools of stochastic calculus and stochastic differential equations of Ito type, illustrated by several problems and applications. It is a continuation of Volume 1: Deterministic Modeling, Methods and Analysis. It is addressed to interdisciplinary graduate/undergraduate students and to interdisciplinary young researchers.
    Źródło:
    Mathematica Applicanda; 2015, 43, 2
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    J-energy preserving well-posed linear systems
    Autorzy:
    Staffans, O. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/908123.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ zachowawczy
    system liniowy
    równanie Lyapunova
    równanie różniczkowe Riccatiego
    well-posed linear systems
    system node
    transfer function
    Lax-Phillips semigroup
    dissipative systems
    conservative system
    model theory
    conservative realization
    J-energy-preserving system
    Lyapunov equations
    Riccati equation
    Opis:
    The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE's, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foias. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H2- and Hinfty-theories).
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1361-1378
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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