Search results for: Lyapunov technique

Authors: A. Ghodbane, M. Saad, J. F. Boland, C. Thibeault

Abstract:

Historically, actuators’ redundancy was used to deal with faults occurring suddenly in flight systems. This technique was generally expensive, time consuming and involves increased weight and space in the system. Therefore, nowadays, the on-line fault diagnosis of actuators and accommodation plays a major role in the design of avionic systems. These approaches, known as Fault Tolerant Flight Control systems (FTFCs) are able to adapt to such sudden faults while keeping avionics systems lighter and less expensive. In this paper, a (FTFC) system based on the Geometric Approach and a Reconfigurable Flight Control (RFC) are presented. The Geometric approach is used for cosmic ray fault reconstruction, while Sliding Mode Control (SMC) based on Lyapunov stability theory is designed for the reconfiguration of the controller in order to compensate the fault effect. Matlab®/Simulink® simulations are performed to illustrate the effectiveness and robustness of the proposed flight control system against actuators’ faulty signal caused by cosmic rays. The results demonstrate the successful real-time implementation of the proposed FTFC system on a non-linear 6 DOF aircraft model.

Keywords: actuators’ faults, fault detection and diagnosis, fault tolerant flight control, sliding mode control, geometric approach for fault reconstruction, Lyapunov stability

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

Abstract:

In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Toshinori Nawata

Abstract:

In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designing the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

Abstract:

The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: Grienggrai Rajchakit

Abstract:

This paper is concerned with the exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, time-varying delays, lyapunov-krasovskii functional, leibniz-newton's formula

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Authors: Ahmad Forouzantabar, Mohammad Azadi, Alireza Alesaadi

Abstract:

This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.

Keywords: lyapunov stability, autonomous underwater vehicle, sliding mode controller, electronics engineering

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Authors: Manlika Ratchagit

Abstract:

This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, Lyapunov functional, linear matrix inequalities

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Authors: Manlika Rajchakit

Abstract:

This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, lyapunov functional, linear matrix inequalities

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Authors: Nisha Budhwar, Sunita Daniel

Abstract:

In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Keywords: equilibrium points, exposed, global stability, infective immigrants, Lyapunov function, recovered, reproduction number, susceptible

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Authors: Jalal Eddine Benmansour, Khouane Boulanoir, Nacera Bekhadda, Elhassen Benfriha

Abstract:

This paper introduces a novel composite control approach that addresses the challenge of stabilizing the three-axis attitude of a flexible satellite in the presence of vibrations caused by flexible appendages. The key contribution of this research lies in the development of a disturbance observer, which effectively observes and estimates the unwanted torques induced by the vibrations. By utilizing the estimated disturbance, the proposed approach enables efficient compensation for the detrimental effects of vibrations on the satellite system. To govern the attitude angles of the spacecraft, a proportional derivative controller (PD) is specifically designed and proposed. The PD controller ensures precise control over all attitude angles, facilitating stable and accurate spacecraft maneuvering. In order to demonstrate the global stability of the system, the Lyapunov method, a well-established technique in control theory, is employed. Through rigorous analysis, the Lyapunov method verifies the convergence of system dynamics, providing strong evidence of system stability. To evaluate the performance and efficacy of the proposed control algorithm, extensive simulations are conducted. The simulation results validate the effectiveness of the combined approach, showcasing significant improvements in the stabilization and control of the satellite's attitude, even in the presence of disruptive vibrations from flexible appendages. This novel composite control approach presented in this paper contributes to the advancement of satellite attitude control techniques, offering a promising solution for achieving enhanced stability and precision in challenging operational environments.

Keywords: attitude control, flexible satellite, vibration control, disturbance observer

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Authors: Sabri Arik

Abstract:

In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: Richard L. Summers

Abstract:

The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems are fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady-state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system's steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: meaning, information, Lyapunov, living systems

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Authors: Riaz Ahmad, Jiazhong Zhang, Asma Farooqi

Abstract:

In this study, mass transport between separation bubbles and the flow around a two-dimensional airfoil are numerically investigated using Lagrangian Coherent Structures (LCSs). Finite Time Lyapunov Exponent (FTLE) technique is used for the computation to identify invariant manifolds and LCSs. Moreover, the Characteristic Base Split (CBS) scheme combined with dual time stepping technique is applied to simulate such transient flow at low Reynolds number. We then investigate the evolution of vortex structures during the transport process with the aid of LCSs. To explore the vortex formation at the surface of the airfoil, the dynamics of separatrix is also taken into account which is formed by the combination of stable-unstable manifolds. The Lagrangian analysis gives a detailed understanding of vortex dynamics and separation bubbles which plays a significant role to explore the performance of the unsteady flow generated by the airfoil. Transport process and flow separation phenomena are studied extensively to analyze the flow pattern by Lagrangian point of view.

Keywords: transport phenomena, CBS Method, vortex formation, Lagrangian Coherent Structures

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Authors: Ahmad Forouzantabar, Mohammad Azadi

Abstract:

This paper presents sliding mode controller for bilateral teleoperation systems with robotic master and slave under constant communication delays. We extend the passivity-based coordination architecture to enhance position and force tracking in the presence of offset in initial conditions, environmental contacts and unknown parameters such as friction coefficient. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of master and slave robots and improve both position and force tracking. Using the Lyapunov theory, the boundedness of master- slave tracking errors and the stability of the teleoperation system are also guaranteed. Numerical simulations show that proposed controller position and force tracking performances are superior to that of conventional coordination controller tracking performances.

Keywords: Lyapunov stability, teleoperation system, time delay, sliding mode controller

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Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon; in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general 3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.

Keywords: artificial potential fields, 3-trailer systems, motion planning, posture

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Authors: Mohammad Sahadet Hossain, Shamsil Arifeen, Mehrab Hossian Likhon

Abstract:

In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives low-rank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems.

Keywords: low-rank cholesky factor alternating directions implicit iteration, LTI Descriptor system, Lyapunov equations, Square-root balanced truncation

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

Abstract:

In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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Authors: Swati Tyagi, Syed Abbas

Abstract:

Fractional-order Hopfield neural networks are generally used to model the information processing among the interacting neurons. To show the constancy of the processed information, it is required to analyze the stability of these systems. In this work, we perform Mittag-Leffler stability for the corresponding Caputo fractional-order bidirectional associative memory (BAM) neural networks with various time-delays. We derive sufficient conditions to ensure the existence and uniqueness of the equilibrium point by using the theory of topological degree theory. By applying the fractional Lyapunov method and Mittag-Leffler functions, we derive sufficient conditions for the global Mittag-Leffler stability, which further imply the global asymptotic stability of the network equilibrium. Finally, we present two suitable examples to show the effectiveness of the obtained results.

Keywords: bidirectional associative memory neural network, existence and uniqueness, fractional-order, Lyapunov function, Mittag-Leffler stability

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Authors: K. Raghuwaiya, S. Singh, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon; in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the Distance Optimization Technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios.

Keywords: artificial potential fields, 3-trailer systems, motion planning, posture, parking and collision, free trajectories

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Authors: Maria Ahmadnezhad, Seyedgharani Ghoreishi ‎

Abstract:

Electrohydraulic servo system have been used in industry in a wide ‎number of applications. Its ‎dynamics are highly nonlinear and also ‎have large extent of model uncertainties and external ‎disturbances. ‎In this thesis, a robust back-stepping control (RBSC) scheme is ‎proposed to overcome ‎the problem of disturbances and system ‎uncertainties effectively and to improve the set-point ‎performance ‎of EHS systems. In order to implement the proposed control ‎scheme, the system ‎uncertainties in EHS systems are considered as ‎total leakage coefficient and effective oil volume. In ‎addition, in ‎order to obtain the virtual controls for stabilizing system, the ‎update rule for the ‎system uncertainty term is induced by the ‎Lyapunov control function (LCF). To verify the ‎performance and ‎robustness of the proposed control system, computer simulation of ‎the ‎proposed control system using Matlab/Simulink Software is ‎executed. From the computer ‎simulation, it was found that the ‎RBSC system produces the desired set-point performance and ‎has ‎robustness to the disturbances and system uncertainties of ‎EHS systems.‎

Keywords: electro hydraulic servo system, back-stepping control, robust back-‎stepping control, Lyapunov redesign‎

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Authors: Asma Hanif, A. I. K. Butt, Shabir Ahmad, Rahim Ud Din, Mustafa Inc

Abstract:

This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.

Keywords: Caputo fractional derivative, existence and uniqueness, gronwall inequality, Lyapunov theory

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Authors: Maria Ahmadnezhad, Mohammad Reza Soltanpour

Abstract:

Electrohydraulic servo systems have been used in industry in a wide number of applications. Its dynamics ‎are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this ‎thesis, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of ‎disturbances and system uncertainties effectively and to improve the tracking performance of EHS ‎systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems ‎are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the ‎virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the ‎Lyapunov control function (LCF). To verify the performance and robustness of the proposed control ‎system, computer simulation of the proposed control system using Matlab/Simulink Software is ‎executed. From the computer simulation, it was found that the RBSC system produces the desired ‎tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.‎

Keywords: electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign

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Authors: Nurudeen Oluwasola Lasisi

Abstract:

The COVID-19 is an infection caused by coronavirus, which has been designated as a pandemic in the world. In this paper, we proposed a model to study the effect of distancing and wearing masks on the transmission of COVID-19 infection dynamics. The invariant region of the model is established. The COVID-19 free equilibrium and the reproduction number of the model were obtained. The local and global stability of the model is determined using the linearization technique method and Lyapunov method. It was found that COVID-19 free equilibrium state is locally asymptotically stable in feasible region Ω if R₀ < 1 and globally asymptomatically stable if R₀ < 1, otherwise unstable if R₀ > 1. More so, numerical analysis and simulations of the dynamics of the COVID-19 infection are presented.

Keywords: distancing, reproduction number, wearing of mask, local and global stability, modelling, transmission

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Authors: Aysegul Sener, Gonca Tuncel Memis, Mirac Kamislioglu

Abstract:

Chaos theory is one of the new paradigms of science since the last century. After determining chaos in the weather systems by Edward Lorenz the popularity of the theory was increased. Chaos is observed in many natural systems and studies continue to defect chaos to other natural systems. Acid rain is one of the environmental problems that have negative effects on environment and acid rains values are monitored continuously. In this study, we aim that analyze the chaotic behavior of acid rains in Turkey with the chaotic defecting approaches. The data of pH degree of rain waters, concentration of sulfate and nitrate data of wet rain water samples in the rain collecting stations which are located in different regions of Turkey are provided by Turkish State Meteorology Service. Lyapunov exponents, reconstruction of the phase space, power spectrums are used in this study to determine and predict the chaotic behaviors of acid rains. As a result of the analysis it is found that acid rain time series have positive Lyapunov exponents and wide power spectrums and chaotic behavior is observed in the acid rain time series.

Keywords: acid rains, chaos, chaotic analysis, Lypapunov exponents

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Authors: Feleke Tsegaye

Abstract:

The work in this thesis mainly focuses on trajectory tracking of fixed wing unmanned aerial vehicle (FWUAV) by using fuzzy based sliding mode controller(FSMC) for surveillance applications. Unmanned Aerial Vehicles (UAVs) are general-purpose aircraft built to fly autonomously. This technology is applied in a variety of sectors, including the military, to improve defense, surveillance, and logistics. The model of FWUAV is complex due to its high non-linearity and coupling effect. In this thesis, input decoupling is done through extracting the dominant inputs during the design of the controller and considering the remaining inputs as uncertainty. The proper and steady flight maneuvering of UAVs under uncertain and unstable circumstances is the most critical problem for researchers studying UAVs. A FSMC technique was suggested to tackle the complexity of FWUAV systems. The trajectory tracking control algorithm primarily uses the sliding-mode (SM) variable structure control method to address the system’s control issue. In the SM control, a fuzzy logic control(FLC) algorithm is utilized in place of the discontinuous phase of the SM controller to reduce the chattering impact. In the reaching and sliding stages of SM control, Lyapunov theory is used to assure finite-time convergence. A comparison between the conventional SM controller and the suggested controller is done in relation to the chattering effect as well as tracking performance. It is evident that the chattering is effectively reduced, the suggested controller provides a quick response with a minimum steady-state error, and the controller is robust in the face of unknown disturbances. The designed control strategy is simulated with the nonlinear model of FWUAV using the MATLAB® / Simulink® environments. The simulation result shows the suggested controller operates effectively, maintains an aircraft’s stability, and will hold the aircraft’s targeted flight path despite the presence of uncertainty and disturbances.

Keywords: fixed-wing UAVs, sliding mode controller, fuzzy logic controller, chattering, coupling effect, surveillance, finite-time convergence, Lyapunov theory, flight path

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Authors: Fatemeh Behbahani, Rubiyah Yusof

Abstract:

To avoid collision between following vehicles and vehicles in front, it is vital to keep appropriate, safe spacing between both vehicles over all speeds. Therefore, the following vehicle needs to have exact information regarding the speed and spacing between vehicles. This project is conducted to simulate the tuning of controller gain for a vehicle-following system through the selected control strategy, spacing control policy and fixed-time headway policy. In addition, the paper simulates and designs an adaptive gain controller for a road-vehicle-following system which uses information on the spacing, velocity and also acceleration of a preceding vehicle in the proposed one-vehicle look-ahead strategy. The mathematical model is implemented using Kirchhoff and Newton’s Laws, and stability simulated. The trial-error method was used to obtain a suitable value of controller gain. However, the adaptive-based controller system was able to optimize the gain value automatically. Model Reference Adaptive Control (MRAC) is designed and utilized and based on firstly the Gradient and secondly the Lyapunov approach. The Lyapunov approach considers stability. The Gradient approach was found to improve the best value of gain in the controller system with fixed-time headway.

Keywords: one-vehicle look-ahead, model reference adaptive, stability, tuning gain controller, MRAC

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Authors: Ramazan Kadiev, Arkadi Ponossov

Abstract:

Semidiscrete systems contain both continuous and discrete components. This means that the dynamics is mostly continuous, but at certain instants, it is exposed to abrupt influences. Such systems naturally appear in applications, for example, in biological and ecological models as well as in the control theory. Therefore, the study of semidiscrete systems has recently attracted the attention of many specialists. Stochastic effects are an important part of any realistic approach to modeling. For example, stochasticity arises in the population dynamics, demographic and ecological due to a change in time of factors external to the system affecting the survival of the population. In control theory, random coefficients can simulate inaccuracies in measurements. It will be shown in the presentation how to incorporate such effects into semidiscrete systems. Stability analysis is an essential part of modeling real-world problems. In the presentation, it will be explained how sufficient conditions for the moment stability of solutions in terms of the coefficients for linear semidiscrete stochastic equations can be derived using non-Lyapunov technique.

Keywords: abrupt changes, exponential stability, regularization, stochastic noises

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Authors: Abdelhak Djoudi, Hachemi Chekireb, El Madjid Berkouk

Abstract:

The doubly fed induction generator (DFIG) received recently an important consideration in medium and high power wind energy conversion systems integration, due to its advantages compared to other generators types. The stator power sliding mode control (SPSMC) proves a great efficiency judge against other control laws and schemes. In the SPSMC laws elaborated by several authors, only the slide surface tracking conditions are elaborated using Lyapunov functions, and the boundedness of the DFIG states is never treated. Some works have validated theirs approaches by experiments results in the case of specified machines, but these verifications stay insufficient to generalize to other machines range. Adding to this argument, the DFIG states boundedness demonstration is widely suggested in goal to ensure that in the application of the SPSMC, the states evaluates within theirs tolerable bounds. Our objective in the present paper is to highlight the efficiency of the SPSMC by stability analysis. The boundedness of the DFIG states such as the stator current and rotor flux is discussed. Moreover, the states trajectories are finding using analytical proves taking into consideration the SPSMC gains.

Keywords: Doubly Fed Induction Generator (DFIG), Stator Powers Sliding Mode Control (SPSMC), lyapunov function, stability, states boundedness, trajectories mathematical proves

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Authors: Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang

Abstract:

We aim to efficiently compute the spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence-free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochastic interacting particle method (IPM) for the reduced principal eigenvalue (Lyapunov exponent) problem of an associated linear advection-diffusion operator with spatially random coefficients. The Fourier representation of the random advection field and the Feynman-Kac (FK) formula of the principal eigenvalue (Lyapunov exponent) form the foundation of our method implemented as a genetic evolution algorithm. The particles undergo advection-diffusion and mutation/selection through a fitness function originated in the FK semigroup. We analyze the convergence of the algorithm based on operator splitting and present numerical results on representative flows such as 2D cellular flow and 3D Arnold-Beltrami-Childress (ABC) flow under random perturbations. The 2D examples serve as a consistency check with semi-Lagrangian computation. The 3D results demonstrate that IPM, being mesh-free and self-adaptive, is simple to implement and efficient for computing front spreading speeds in the advection-dominated regime for high-dimensional random flows on unbounded domains where no truncation is needed.

Keywords: KPP front speeds, random flows, Feynman-Kac semigroups, interacting particle method, convergence analysis

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