Asymptotic Stability Research Articles

Adaptive expected-time tracking consensus control for multiagent systems with external disturbances and time delays

This paper studies the expected-time tracking control problem for multiagent systems with disturbances and time delays. The expected-time control scheme can ensure that control objectives can be completed within the desired time. In the other words, the output signal can track the reference signal in an expected time. Based on a special error and the adaptive technology, the expected-time tracking consensus control scheme is achieved. Moreover, by using the neural networks technique, the unknown nonlinear functions which often exist in the dynamic of the system are handled. According to the Lyapunov stability theorem and the Lyapunov–Krasovskii function, it is proved that the consensus errors are semi-globally uniformly ultimately bounded. At last, the feasibility of the control method is verified by a simulation example.

A cooperative control method and application for series multivariable coupled system

Series multivariable coupled system is a typical controlled object in process control industry. The interaction of various state variables between multiple inputs and outputs in the system forms a complex series multivariable coupled structure. This coupled structure makes the control of a controlled object in the system affect the controlled object in the upper and lower control loop. As a result, it is difficult to control one or more control loops in the system without changing the state of other links in the system. In this paper, a cooperative control method for series multivariable coupled system is proposed. A decoupling controller is designed to remove the coupling effect caused by the interaction between stages, and the system is decoupled into several independent control loops. Differential leading PI (proportional-integral) error compensation method is introduced to ensure the following performance of the controller without static error. The proposed cooperative control method satisfies the Lyapunov stability, and has been successfully applied in the simulation experiment of cascade pumping station system of Beijing East-to-West water transfer project. The proposed method reduces the difficulty to controlling the water level of forebay of each pumping station and ensures the efficient operation of the cascade pumping station system.

Nonlinear Asymptotic Stability and Transition Threshold for 2D Taylor–Couette Flows in Sobolev Spaces

In this paper, we investigate the stability of the 2-dimensional (2D) Taylor–Couette (TC) flow for the incompressible Navier–Stokes equations. The explicit form of velocity for 2D TC flow is given by u=(Ar+Br)(-sinθ,cosθ)T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u=(Ar+\\frac{B}{r})(-\\sin \ heta , \\cos \ heta )^T$$\\end{document} with (r,θ)∈[1,R]×S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(r, \ heta )\\in [1, R]\ imes \\mathbb {S}^1$$\\end{document} being an annulus and A, B being constants. Here, A, B encode the rotational effect and R is the ratio of the outer and inner radii of the annular region. Our focus is the long-term behavior of solutions around the steady 2D TC flow. While the laminar solution is known to be a global attractor for 2D channel flows and plane flows, it is unclear whether this is still true for rotating flows with curved geometries. In this article, we prove that the 2D Taylor–Couette flow is asymptotically stable, even at high Reynolds number (Re∼ν-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re\\sim \ u ^{-1}$$\\end{document}), with a sharp exponential decay rate of exp(-ν13|B|23R-2t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (-\ u ^{\\frac{1}{3}}|B|^{\\frac{2}{3}}R^{-2}t)$$\\end{document} as long as the initial perturbation is less than or equal to ν12|B|12R-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u ^\\frac{1}{2} |B|^{\\frac{1}{2}}R^{-2}$$\\end{document} in Sobolev space. The powers of ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and B in this decay estimate are optimal. It is derived using the method of resolvent estimates and is commonly recognized as the enhanced dissipative effect. Compared to the Couette flow, the enhanced dissipation of the rotating Taylor–Couette flow not only depends on the Reynolds number but also reflects the rotational aspect via the rotational coefficient B. The larger the |B|, the faster the long-time dissipation takes effect. We also conduct space-time estimates describing inviscid-damping mechanism in our proof. To obtain these inviscid-damping estimates, we find and construct a new set of explicit orthonormal basis of the weighted eigenfunctions for the Laplace operators corresponding to the circular flows. These provide new insights into the mathematical understanding of the 2D Taylor–Couette flows.

Adaptive event‐triggered secure control for networked control systems subject to deception and replay cyber‐attacks

SummaryAn adaptive event‐triggered scheme is considered for networked control systems subject to deception and reply cyber attacks. In particular, the adaptive event‐triggered mechanism is used in the closed‐loop controller design to reduce signal transmission and communication burden. The attacker destroys the system's performance by employing deception attacks on sensor‐to‐controller communication channels and replay attacks on controller‐to‐actuator communication channels, respectively. By utilizing the Lyapunov stability approach, the closed‐loop system guarantees mean square stability and ensure security. The adaptive event‐triggered controller gains are presented by solving a set of matrix inequalities. Finally, a simulation result including the model of a batch reactor is presented to demonstrate the efficiency of the methods proposed.

Formation Control of Autonomous Underwater Vehicles Using an Improved Nonlinear Backstepping Method

The characteristics of autonomous underwater vehicles include nonlinearity, strong coupling, multiple inputs and multiple outputs, uncertainty, strong disturbance, underdrive, and multiple constraints. Autonomous underwater vehicle cluster systems are associated with large-scale complex dynamic systems through local perception or network communication, which have the structural characteristics of “complex dynamic + association topology + interaction rules”. To solve the problem of formation trajectory tracking of underactuated autonomous underwater vehicles, a controller was designed on the basis of an improved nonlinear backstepping algorithm, cascade system theory, and the Lyapunov direct method. In this design, the formation is determined from the actual trajectory of the leader autonomous underwater vehicle. The formation control rate is determined using the backstepping method and Lyapunov theory. Nonlinear disturbance observers were added to ensure that the trajectory error of the formation control could be quickly reduced in a real case with interference. The stability and effectiveness of this method were verified through simulation experiments. The robustness of the control algorithm was verified using two simulation cases, and the simulation results show that the proposed control method can maintain the expected formation.

Stochastic response and stability analysis of nonlinear vehicle energy-regenerative suspension system with time delay

With the rapid development of new energy vehicles, a novel vehicle energy-regenerative suspension for simultaneous vibration suppression and energy harvesting has become one of the key development directions of the next generation of vehicle design. In order to improve the performance of suspension system, the time-delayed feedback control is applied to the novel suspension system subjected to different external excitation. At the same time, there are few studies related to the stochastic dynamics of nonlinear vehicle energy-regenerative suspension system with time delay. This paper studies stochastic response and stability of nonlinear vehicle energy-regenerative suspension with time-delayed feedback control under the excitation of Gaussian white noise. First of all, a stochastic dynamic model of the nonlinear vehicle energy-regenerative suspension with time delay system is established. Secondly, using the stochastic averaging method based on generalized harmonic function, the steady-state probability density function (PDF) of amplitude is obtained. The accuracy of the presented approach is verified through the comparison of analytical and numerical solutions. In addition, through combining the stochastic averaging method with the Khasminskii method, the top Lyapunov exponent (TLE) of the system is obtained, and then the influence of time delay and system parameters on the asymptotic Lyapunov stability is discussed. Finally, the effects of time delay and system parameters on system performance are also studied.

Lyapunov stability of the Basener–Ross system

Lyapunov stability of the Basener–Ross system

Neural adaptive dynamic surface control for position tracking of electrohydraulic servo systems based on extended state observer

High-performance motion tracking of electro-hydraulic servo systems plays an important role in developing industrial technology. However, the system itself has parameter uncertainty, uncertain nonlinearity, and measurement noise, significantly decreasing the performance of conventional controllers designed based on nominal models. To improve the tracking performance of electro-hydraulic servo systems, an adaptive dynamic surface control method combining extended state observer and radial basis function neural network is proposed. Firstly, an extended state observer combining neural network output and parameter adaptation technology is designed without the need for speed and pressure feedback to observe the system’s unknown state variables and nonlinear matched disturbance. The design of neural networks is used to approximate mismatched disturbance with significant nonlinearity online. Then, the proposed extended state observer is introduced into the neural adaptive backstepping design, effectively compensating for simultaneous matched and mismatched disturbances, thereby suppressing most of the uncertain nonlinearity of the system. Meanwhile, online update of uncertain parameters further improves the tracking performance of the controller. In addition, the introduction of dynamic surface overcomes the “explosion of complexity” issue in backstepping design. The rigorous stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed controller is validated through comparative experiments on valve-controlled hydraulic cylinder.

Event-based appointed-time cooperative formation for linear multiagent systems with actuator saturation

This paper considers the time-varying formation (TVF) tracking issue of a class of multiagent systems (MASs) with input saturation. Meanwhile, the prescribed transient and steady-state performance of MASs is guaranteed. Compared to the existing prescribed performance control (PPC) approaches, the maximum convergence time of the designed algorithm is preassigned. To save network resources, an event-based protocol is introduced to achieve lower information communication frequency, where Zeno behavior is excluded. Furthermore, an improved control strategy is employed where an auxiliary system is designed to improve the performance under actuator saturation. According to Lyapunov stability theory, the expected practical TVF tracking control problem is solved for the MASs. Finally, the effectiveness of the designed schemes is demonstrated by the simulation examples.

Global Stabilization of a Bounded Controlled Lorenz System

In this work, we present a method for the Global Asymptotic Stabilization (GAS) of an affine control chaotic Lorenz system, via admissible (bounded and regular) feedback controls, where the control bounds are given by a class of (convex) polytopes. The proposed control design method is based on the control Lyapunov function (CLF) theory introduced in [Artstein, 1983; Sontag, 1998]. Hence, we first recall, with parameters including those in [Lorenz, 1963], that these equations are point-dissipative, i.e. there is an explicit absorbing ball [Formula: see text] given by the level set of a certain Lyapunov function, [Formula: see text]. However, since the minimum point of [Formula: see text] does not coincide with any rest point of Lorenz system, we apply a modified solution to the “uniting CLF problem” (to unify local (possibly optimal) controls with global ones, proposed in [Andrieu & Prieur, 2010]) in order to obtain a CLF [Formula: see text] for the affine system with minimum at a desired equilibrium point. Finally, we achieve the GAS of “any” rest point of this system via bounded and regular feedback controls by using the proposed CLF method, which also contains the following controllers: (i) damping controls outside [Formula: see text], so they collaborate with the beneficial stable free dynamics, and (ii) (possibly optimal) feedback controls inside [Formula: see text] that stabilize the control system at “any” desired rest point of the (unforced) Lorenz system.

A model-based proportional-integral observer design for adhesion estimation in the wheel-rail interface: LMI approach

Adhesion estimation in wheel and rail interface is a crucial element as it has a direct effect on the locomotive characteristics and performance. Since the adhesion condition depends on unpredictable factors and dynamic models, its estimation is a complex task. In this paper, a dynamic model for a single wheelset including parameters in detail is developed to improve the accuracy of the model. Then, a model-based Proportional–Integral Observer (PIO) is designed to estimate adhesion during uncertainties and nonlinear parameters. The stability of the proposed PI observer is proved with Lyapunov theory and Linear Matrix Inequality (LMI). Finally, the performance of the method is evaluated via numerical simulation in MATLAB software, and it is validated with a model set-up in the SIMPACK Multibody Simulation (MBS) software.

Anti-swing control of varying rope length tower crane based on adaptive neural network sliding mode

Due to its complex nonlinear, underdriven, and strongly coupled characteristics, the tower crane will cause the load to swing violently when working, which will cause the tower crane to tip over in serious cases, and there exists a huge safety hazard. In this article, a new artificial neural network sliding mode control method is designed for the control problems of tower crane lifting in position and load swing prevention, which has strong robustness to disturbances and unmodeled dynamics, and ensures that the tower crane lifting is accurately tracked in position and suppresses the load swing at the same time. First, a nonlinear dynamics model of a five-degree-of-freedom tower crane considering the actual working conditions is established. Aiming at the problem that it is difficult to effectively control the nonlinear model of the tower crane system, a new neural sliding mode controller and compensation controller are designed based on the sliding mode control theory and using radial basis function neural network. The neural sliding mode controller is used to approximate the sliding mode equivalent controller with uncertainty and strong nonlinearity, and the compensation controller realizes the compensation of the neural sliding mode controller for the difference between the system control inputs and the uncertainty of the system. The convergence and stability of the proposed control system is rigorously demonstrated using the Lyapunov stability theory. Simulation studies have been carried out to verify the correctness of the model established in this article, as well as the excellent control performance of the control system and the ability to deal with system uncertainty, proving its strong robustness.

Leader-follower and leaderless bipartite formation-consensus over undirected coopetition networks and under proximity and collision-avoidance constraints

We propose a method to control networks involving both cooperative and competitive interactions simultaneously under proximity and collision-avoidance constraints. The control design is of gradient type, using a barrier-Lyapunov function. Then, under the assumption that the network is structurally balanced, we establish asymptotic stability of the leaderless and leader-follower bipartite formation-consensus manifold. We assume that the agents are modelled by second-order integrators, but we also demonstrate the utility of our theoretical findings via numerical simulations on a problem of formation-consensus control of nonholonomic vehicles.

GESO based RISE Controller for Active Flutter Suppression for Aeroelastic System

Abstract The paper presents a Robust Integral of Signum of Error (RISE) controller for active suppression of flutter of a two dimensional aerofoil and it is integrated with a General Extended State Observer (GESO). Towards this, aerofoil model in state space is first changed into a canonical form. Then, the controller is designed using RISE control technique. As equations of system dynamics are not into integral chain form, a GESO is formulated to observe system states and disturbances. The controller is implemented using estimated states and it is robustified using estimated disturbance. Stability of the proposed GESO-RISE controller is established using the Lyapunov theory. Simulations are performed to check the proposed controller's performance against variations in airspeed, uncertainties in model parameters, external disturbances, time delay and unmodeled dynamics. Comparison of the proposed GESO-RISE controller is carried out with existing controllers using two performance criteria i.e. Control Efforts and Integral of Absolute Error (IAE). It is discovered from simulations that the proposed GESO-RISE controller significantly reduces IAE and control efforts. Additionally, Monte Carlo method is utilized to check robustness of the proposed GESO-RISE controller. The proposed GESO-RISE controller significantly enhances flutter boundary of aerofoil and is completely implementable.

Integral reinforcement learning–based adaptive fuzzy fault tolerant control of hypersonic flight vehicle

The fault tolerant control (FTC) of hypersonic flight vehicle (HFV) with actuator fault is proposed in this paper. The fault model considered in this paper is a general model which HFV may encounter in practice. For designing the FTC, the nonlinear model of HFV is represented by T-S fuzzy models, and policy iteration (PI) strategy is utilized to solve the design problem of T-S controller for the built T-S model of HFV without actuator fault. Then, based on the normal T-S controller, an adaptive fuzzy FTC controller is proposed, in which the feedback gain matrices can improve themselves according to the special fault. The stability of the proposed adaptive fuzzy FTC is proved by Lyapunov theory, and an integral reinforcement learning (IRL)–based solving algorithm is proposed. Simulations on three different kinds of actuator faults are proposed, and the simulation results show that, under three different faults, the designed adaptive FTC can ensure the reliable flight of HFV.

Asymptotic adaptive output-feedback stabilisation of nonlinear systems with unknown growth rate and sensor uncertainty

For a class of nonlinear systems with sensor uncertainty, the problem of adaptive output feedback stabilisation is investigated in this paper. It is assumed that only the output is available for feedback control, which suffers from sensor uncertainty. At the same time, the nonlinear function in the system model has an unknown growth rate. To solve this problem, a set of state observers is designed to estimate the unknown system states based on the uncertain output, and an adaptive output-feedback control is designed based on this. By using the corollary of Barbalet's Lemma, it is shown that the equilibrium of the closed-loop system is asymptotically stable. Finally, simulation results verify the effectiveness of the control scheme

A Lyapunov-based control design for centralised networked control systems under false-data-injection attacks

ABSTRACT A central processing unit receives data from all agents and transmits control commands in a Networked Control System (NCS) which is centralised. Centralised NCSs have numerous applications in industrial settings due to their efficiency, simplicity and cost-effective design. However, centralised NCSs are vulnerable to false data injection (FDI) attacks. Despite the fact that researchers have developed detection and mitigation defense mechanisms during past several years, most of these methods have focused on systems with linear dynamics. Furthermore, the existing literature only assumes the injection of FDI attacks on measurement signals. In this paper, we assume that an adversary has injected the FDI attack into both state measurements and control signals with nonlinear dynamics while considering communication noises and disturbances. We propose a secure nonlinear control design that mitigates FDI attacks in real time by combining learning and model-based approaches. We used Lyapunov stability analysis to design the controller, estimator and updating laws of the neural network (NN). In addition, we selected a network of two robots with Euler–Lagrange dynamics to illustrate the robustness of the proposed controller and estimator.

Study of chronic myeloid leukemia with T-cell under fractal-fractional order model

Abstract This research work is devoted to investigate myeloid leukemia mathematical model. We give some details about the existence of trivial and nontrivial equilibrium points and their stability. Also, local asymptotical stability of disease-free and endemic equilibrium points is discussed. Also, positivity of the solution has been discussed. Some sufficient results are achieved to study the local existence and uniqueness of solution to the considered model for Mittag–Leffler kernel using the Banach contraction theorem. Three numerical algorithms are derived in obtaining the numerical solution of suggested model under three different kernels using Adams–Basforth technique. Numerical results have been presented for different fractals and fractional orders to show the behavior of the proposed model.

A novel hybrid PI–backstepping cascade controller for battery–supercapacitor electric vehicles considering various driving cycles scenarios

AbstractThe integration of supercapacitors as hybrid energy storage systems in electric vehicles has attracted the attention of many researchers and has been considered as a promising solution. Bidirectional DC/DC converters (BDDCs) play a fundamental role in HESS, as they manage the power flow by controlling currents and regulating the DC bus voltage. However, they encounter the challenge of uncertainties and high fluctuation power loads, necessitating the fast dynamics, stability, and high robustness of the controller. This paper proposes a novel hybrid proportional–integral and backstepping cascade controller to regulate the DC‐bus voltage under uncertainties and load variations, and to control the current references of the on‐boarded sources. To confirm the asymptotic stability of the whole system, a nonlinear stability analysis is conducted using the Lyapunov theorem. A power management strategy is applied to distribute the power loads and generate reference currents for the BDDCs controller. Simulations results under various driving cycles using MATLAB/Simulink demonstrate the superiority of the proposed controller compared to conventional proportional–integral and backstepping controllers. A real‐time controller‐hardware‐in‐the‐loop test bench is developed to validate the effectiveness of the proposed strategy.

Nonlinear Robust Control of Vehicle Stabilization System with Uncertainty Based on Neural Network

To effectively suppress the effects of uncertainties including unmodeled dynamics and external disturbances in the vehicle stabilization system, a nonlinear robust control strategy based on a multilayer neural network is proposed in this paper. First, the mechanical and electrical coupling dynamics model of the vehicle stabilization system, considering model uncertainty and actuator dynamics, is refined. Second, the lumped uncertainty of the vehicle stabilization system is estimated by a multi-layer neural network and compensated by feedforward control. The high robustness of the system is ensured by constructing the sliding mode feedback control law. The proposed control method overcomes the limitations of sliding mode technology and the neural network and is naturally applied to the vehicle stabilization system, avoiding the adverse effects of high-gain feedback. Based on Lyapunov theory, it is demonstrated that the proposed controller is able to achieve the desired stability tracking performance. Finally, the effectiveness of the proposed control strategy is verified by co-simulation and comparative experiments.