Home  About us  Contact
 

Asymptotic Stability (asymptotic + stability)

Distribution by Scientific Domains
Engineering83%
Mathematics and Statistics13%
Distribution within Engineering
Control Systems Technology74%
General & Introductory Electrical & Electronics Engineering10%

Kinds of Asymptotic Stability

  • global asymptotic stability
    		•

    Selected Abstracts

    Fuzzy sliding-mode control with rule adaptation for nonlinear systems

    EXPERT SYSTEMS, Issue 4 2006
    Lon-Chen Hung
    Abstract: A fuzzy sliding-mode control with rule adaptation design approach with decoupling method is proposed. It provides a simple way to achieve asymptotic stability by a decoupling method for a class of uncertain nonlinear systems. The adaptive fuzzy sliding-mode control system is composed of a fuzzy controller and a compensation controller. The fuzzy controller is the main rule regulation controller, which is used to approximate an ideal computational controller. The compensation controller is designed to compensate for the difference between the ideal computational controller and the adaptive fuzzy controller. Fuzzy regulation is used as an approximator to identify the uncertainty. The simulation results for two cart,pole systems and a ball,beam system are presented to demonstrate the effectiveness and robustness of the method. In addition, the experimental results for a tunnelling robot manipulator are given to demonstrate the effectiveness of the system. [source]

    Input-to-state stability, numerical dynamics and sampled-data control

    GAMM - MITTEILUNGEN, Issue 1 2008
    Lars Grüne
    Abstract We investigate the relation between asymptotic stability for dynamical systems and families of approximations. Using suitably perturbed systems and the input-to-state stability property we develop a framework which yields necessary and sufficient conditions on the stability of the approximations ensuring stability of the approximated system. The results are formulated for numerical one step schemes for ordinary differential equations and for sampled-data systems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Indirect adaptive control of a class of marine vehicles

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2010
    Yannick Morel
    Abstract A nonlinear adaptive framework for bounded-error tracking control of a class of non-minimum phase marine vehicles is presented. The control algorithm relies on a special set of tracking errors to achieve satisfactory tracking performance while guaranteeing stable internal dynamics. First, the design of a model-based nonlinear control law, guaranteeing asymptotic stability of the error dynamics, is presented. This control algorithm solves the tracking problem for the considered class of marine vehicles, assuming full knowledge of the system model. Then, the analysis of the zero-dynamics is carried out, which illustrates the efficacy of the chosen set of tracking errors in stabilizing the internal dynamics. Finally, an indirect adaptive technique, relying on a partial state predictor, is used to address parametric uncertainties in the model. The resulting adaptive control algorithm guarantees Lyapunov stability of the errors and parameter estimates, as well as asymptotic convergence of the errors to zero. Numerical simulations illustrate the performance of the adaptive algorithm. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Nonlinear adaptive tracking-control synthesis for functionally uncertain systems

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2010
    Zenon Zwierzewicz
    Abstract The paper is concerned with the problem of adaptive tracking system control synthesis. It is assumed that a nonlinear, feedback linearizable object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that proportional state feedback plus parameter adaptation are able to assure its asymptotic stability. This form of controller permits online compensation of unknown model nonlinearities and exogenous disturbances, which results in satisfactory tracking performance. An interesting feature of the system is that the whole process control is performed without requisite asymptotic convergence of approximator parameters to the postulated ,true' values. It has been noticed that the parameters play rather a role of slack variables on which potential errors (that otherwise would affect the state variables) cumulate. The system's performance has been tested via Matlab/Simulink simulations via an example of ship path-following problem. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Adaptive TS-FNN control for a class of uncertain multi-time-delay systems: The exponentially stable sliding mode-based approach

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2009
    Tung-Sheng Chiang
    Abstract This paper presents an adaptive Takagi,Sugeno fuzzy neural network (TS-FNN) control for a class of multiple time-delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov,Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control-based TS-FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS-FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on-line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2009
    Alexander Leonessa
    Abstract A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed-loop tracking error dynamics in the face of amplitude and rate saturation constraints, the control signal to a given reference (governor or supervisor) system is modified to effectively robustify the error dynamics to the saturation constraints. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Adaptive robust H, state feedback control for linear uncertain systems with time-varying delay

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2008
    Dan Ye
    Abstract This paper considers the problem of adaptive robust H, state feedback control for linear uncertain systems with time-varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H, controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H, performance of the closed-loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Robust H, filtering for switched linear discrete-time systems with polytopic uncertainties

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2006
    Lixian Zhang
    Abstract In this paper, the problem of robust H, filtering for switched linear discrete-time systems with polytopic uncertainties is investigated. Based on the mode-switching idea and parameter-dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H, performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H, noise-attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Hybrid adaptive control for non-linear uncertain impulsive dynamical systems

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2005
    Wassim M. Haddad
    Abstract A direct hybrid adaptive control framework for non-linear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. Furthermore, hybrid adaptive controllers guaranteeing attraction of the closed-loop system plant states are also developed. Finally, two numerical examples are provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Direct adaptive control for non-linear uncertain systems with exogenous disturbances

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2002
    Wassim M. Haddad
    Abstract A direct adaptive non-linear control framework for multivariable non-linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non-linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. In the case of bounded energy L2 disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input,output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Novel stability criteria for bidirectional associative memory neural networks with time delays

    INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2002
    Xiaofeng Liao
    Abstract In this paper, the bidirectional associative memory (BAM) neural network with axonal signal transmission delay is considered. This model is also referred to as a delayed dynamic BAM model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of a unique equilibrium and global asymptotic stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach for the analysis allows one to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as C1 -smooth sigmoids. It is believed that these results are significant and convenient in the design and applications of BAM neural networks. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    A novel dual-mode predictive control strategy for constrained Wiener systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2010
    Hai-Tao Zhang
    Abstract In process industry, there exist many Wiener systems with input magnitude constraints for which, however, most of the existing control algorithms cannot guarantee to have sufficiently large regions of asymptotic stability. In this paper, the subspace method is applied to separate the nonlinear and linear blocks in a constrained multi-input/multi-output (MIMO) Wiener system and a novel dual-mode nonlinear model predictive control algorithm is developed to maximize the region of the asymptotic stability. Simulation results are presented to demonstrate the virtues of this new control algorithm. The limitation is the requirement that the state and input matrices of the Wiener system's linear block should be accurately identified. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Passivity-based control of a magnetically levitated flexible beam

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2009
    T. Shimizu
    Abstract This paper solves the asymptotic stabilization problem for a magnetically levitated flexible beam using a nested-loop passivity-based controller design. Passivity analyses reveal that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of a flexible beam with both ends free and that defines a passive map from external forces to the velocity of the points on the flexible beam at which the external forces act; and an electrical subsystem that consists of a pair of electromagnets and that defines a strictly output-passive map from voltages applied across the electromagnets to magnetic fluxes. The standard method for designing passivity-based controllers leads to a nonlinear feed-forward controller for the electrical subsystem, which enables the electrical subsystem to generate given desired magnetic forces, and an output feedback compensator for the mechanical subsystem, which computes the desired forces required to regulate the position and vibration of the beam. The asymptotic stability of each controller may be proven using Lyapunov's stability theory and LaSalle's invariant set theorem. Numerical simulations confirm the asymptotic stability of the equilibrium configuration of the closed-loop system formed by the magnetically levitated flexible beam together with the proposed controllers. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Stability and robust stability of positive linear Volterra difference equations

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2009
    Pham Huu Anh Ngoc
    Abstract We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron,Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    LMI optimization approach to robust H, observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2009
    Masoud Abbaszadeh
    Abstract A new approach for the design of robust H, observers for a class of Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H, observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit norm-wise and element-wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H, performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Feedback stabilization of bifurcations in multivariable nonlinear systems,Part II: Hopf bifurcations

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2007
    Yong Wang
    Abstract In this paper we derive necessary and sufficient conditions of stabilizability for multi-input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non-degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed-loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non-degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov,Belevitch,Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Gain-scheduled H, filtering of parameter-varying systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2006
    Shaosheng Zhou
    Abstract This paper deals with the gain-scheduled H, filtering problem for a class of parameter-varying systems. A sufficient condition for the existence of a gain-scheduled filter, which guarantees the asymptotic stability with an H, noise attenuation level bound for the filtering error system, is given in terms of a finite number of linear matrix inequalities (LMIs). The filter is designed to be parameter-varying and have a nonlinear fractional transformation structure. A numerical example is presented to demonstrate the application of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2005
    Yong He
    Abstract In this paper, an augmented Lyapunov functional is proposed to investigate the asymptotic stability of neutral systems. Two methods with or without decoupling the Lyapunov matrices and system matrices are developed and shown to be equivalent to each other. The resulting delay-dependent stability criteria are less conservative than the existing ones owing to the augmented Lyapunov functional and the introduction of free-weighting matrices. The delay-independent criteria are obtained as an easy corollary. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    On the componentwise stability of linear systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2005
    O. Pastravanu
    Abstract The componentwise asymptotic stability (CWAS) and componentwise exponential asymptotic stability (CWEAS) represent stronger types of asymptotic stability, which were first defined for symmetrical bounds constraining the flow of the state-space trajectories, and then, were generalized for arbitrary bounds, not necessarily symmetrical. Our paper explores the links between the symmetrical and the general case, proving that the former contains all the information requested by the characterization of the CWAS/CWEAS as qualitative properties. Complementary to the previous approaches to CWAS/CWEAS that were based on the construction of special operators, we incorporate the flow-invariance condition into the classical framework of stability analysis. Consequently, we show that the componentwise stability can be investigated by using the operator defining the system dynamics, as well as the standard ,,, formalism. Although this paper explicitly refers only to continuous-time linear systems, the key elements of our work also apply, mutatis mutandis, to discrete-time linear systems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    A dissipative dynamical systems approach to stability analysis of time delay systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2005
    VijaySekhar Chellaboina
    Abstract In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite-dimensional linear dynamical system and an infinite-dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov,Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov,Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputs

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2004
    S. Tarbouriech
    Abstract This paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti-windup strategies. A method for synthesizing anti-windup gains aiming at maximizing a region of admissible states, for which the closed-loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear time-delay system with a dead-zone nonlinearity, constructive delay-dependent stability conditions are formulated by using both quadratic and Lure Lyapunov,Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti-windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Disturbance attenuation of a class of non-linear systems via output feedback

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2003
    Wei Lin
    Abstract This paper studies the problem of disturbance attenuation with internal stability via output feedback for a family of non-linear systems. Using a feedback domination design which substantially differs from the separation principle, we explicitly construct a dynamic output compensator attenuating the disturbance's effect on the output to an arbitrary degree of accuracy in the L2 -gain sense, and achieving global asymptotic stability in the absence of disturbance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    The Liapunov's second method for continuous time difference equations

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2003
    P. PepeArticle first published online: 10 OCT 200
    Abstract Among many other cases such as economic and lossless propagation models, continuous time difference equations are encountered as the internal dynamics in a class of non-linear time delay systems, when controlled by a suitable state feedback which drives the output exponentially to zero. The Liapunov's second method for these infinite dimensional systems has not been extensively investigated in the literature. This paper has the aim of filling this gap. Liapunov's second method theorems for checking the stability and the asymptotic stability of this class of infinite dimensional systems are built up, in both a finite and an infinite dimensional setting. In the finite dimensional setting, the Liapunov function is defined on finite dimensional sets. The conditions for stability are given as inequalities on continuous time. No derivatives are involved, as in the dynamics of the studied systems. In the infinite dimensional setting, the continuous time difference equation is transformed into a discrete time system evolving on an infinite dimensional space, and then the classical Liapunov theorem for the system in the new form is written. In this paper the very general case is considered, that is non-linear continuous time difference equations with multiple non commensurate delays are considered, and moreover the functions involved in the dynamics are allowed to be discontinuous, as well as the initial state. In order to study the stability of the internal dynamics in non-linear time delay feedback systems, an exogenous disturbance is added, which goes to zero exponentially as the time goes to infinity. An example is considered, from non-linear time delay feedback theory. While the results available in the literature are inconclusive as far as the stability of that example is concerned, such stability is proved to hold by the theorems developed in this paper, and is validated by simulation results. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Input-to-state stability with respect to inputs and their derivatives

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2003
    David Angeli
    Abstract A new notion of input-to-state stability involving infinity norms of input derivatives up to a finite order k is introduced and characterized. An example shows that this notion of stability is indeed weaker than the usual ISS. Applications to the study of global asymptotic stability of cascaded non-linear systems are discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Constrained robust sampled-data control for nonlinear uncertain systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2002
    Li-Sheng Hu
    Abstract In industrial process control, computer control, which makes the closed-loop system a sampled-data one containing both continuous- and discrete-time signals, is widely used. In contrast with traditional approximation methods, sampled-data synthesis, a direct digital controller design procedure without approximation, has received increasing attention during the past few years. However, many of the existing results cannot be applied to sampled-data control design for the uncertain systems. In this paper, a result of robust asymptotic stability of sampled-data systems with constraints on the state is presented based on a result on practical stability for these systems. Then the robust sampled-data control for a class of uncertain nonlinear systems with constraints on the output is developed. The problem is formulated from vehicle steering control with constraint on the side slip angle of body. The result is described by some matrix inequalities which could be solved by an iterative algorithm based on the linear matrix inequality technique. Finally, a numerical example is presented to demonstrate the result. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Dynamic Control of a Large Scale of Pneumatic Multichain Systems

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 4 2004
    M. Guihard
    The aim of this paper is to propose a general principle able to manage the supervision, coordination, and control problems of a large scale of multichain structures in dynamic and interacting tasks. The main originality lays in its modular feature. The number of chains and of joint per chain are indeed not restricted. The only assumption is that all the chains are linked to a principal element from which the dynamic stability will be computed. This is for example the case for multi-finger and multi-legged structures for which respectively the palm and the trunk represent the principal element. The principle consists in controlling the stability of this element and distributing the effort on the other chains to maintain the stability of the whole. To increase the compliant feature, we consider that each joint is pneumatically actuated. Each joint is then dynamically controlled to ensure the asymptotic stability of the local chain it belongs to. A global architecture is presented where each part is detailed. An example is then displayed showing the performances of a two-legged robot in the standing posture under external perturbation effects. © 2004 Wiley Periodicals, Inc. [source]

    A Class of Transpose Jacobian-based NPID Regulators for Robot Manipulators with an Uncertain Kinematics

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2002
    C. Q. Huang
    Transpose Jacobian-based controllers present an attractive approach to robot set-point control in Cartesian space that derive the end-effector posture to a specified desired position and orientation with neither solving the inverse kinematics nor computing the inverse Jacobian. By a Lyapunov function with virtual artificial potential energy, a class of complete transpose Jacobian-based Nonlinear proportional-integral-derivative regulators is proposed in this paper for robot manipulators with uncertain kinematics on the basis of the set of all continuous differentiable increasing functions. It shows globally asymptotic stability for the result closed-loop system on the condition of suitable feedback gains and suitable parameter selection for the corresponding function set as well as artificial potential function, and only upper bound on Jacobian matrix error and Cartesian dynamics parameters are needed. The existing linear PID (LPID) regulators are the special cases of it. Nevertheless, in the case of LPID regulators, only locally asymptotic stability is guaranteed if the corresponding conditions are satisfied. Simulations demonstrate the result and robustness of transpose Jacobian-based NPID regulators. © 2002 Wiley Periodicals, Inc. [source]

    A position/force control for a robot finger with soft tip and uncertain kinematics

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2002
    Zoe Doulgeri
    We consider the position and force regulation problem for a soft tip robot finger in contact with a rigid surface under kinematic and dynamic parametric uncertainties. The reproducing force is assumed to be related to the displacement through a nonlinear function whose characteristics are unknown, but both the actual displacement and force can be directly measured. Kinematic uncertainties concern the rigid surface orientation and the contact point location. Kinematic parameters involved in the contact point location concern the length from the last joint to the contact point and the rest of the link lengths in the general case. An adaptive controller with a composite update parameter law is proposed, and the asymptotic stability of the force and estimated position errors under dynamic and kinematic uncertainties is shown for the planar case. Simulation results for a three-degrees-of-freedom planar robotic finger are presented. © 2002 Wiley Periodicals, Inc. [source]

    Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2009
    Yoshihiro Ueda
    Abstract We study a semilinear hyperbolic system with relaxation and investigate the asymptotic stability of travelling wave solutions with shock profile. It is shown that the travelling wave solution is asymptotically stable, provided the initial disturbance is suitably small. Moreover, we show that the time convergence rate is polynomially (resp. exponentially) fast as t,, if the initial disturbance decays polynomially (resp. exponentially) for x,,. Our proofs are based on the space,time weighted energy method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    On the asymptotic stability of steady solutions of the Navier,Stokes equations in unbounded domains

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2007
    Francesca Crispo
    Abstract We consider the problem of the asymptotic behaviour in the L2 -norm of solutions of the Navier,Stokes equations. We consider perturbations to the rest state and to stationary motions. In both cases we study the initial-boundary value problem in unbounded domains with non-compact boundary. In particular, we deal with domains with varying and possibly divergent exits to infinity and aperture domains. Copyright © 2007 John Wiley & Sons, Ltd. [source]