Global asymptotic stabilization of visually-servoed manipulators

A design procedure for simultaneous position and force control is developed, using Lyapunov's direct method, for manipulators in contact with a rigid environment that can be described by holonomic constraints. Many manipulators that interact with their environment require taking into account the effects of these constraints in the control design. The forces of constraint play a critical role in constrained motion and are, along with displacements and velocities, to be regulated at specified values. Lyapunov's direct method is used to develop a class of position and force feedback controllers. The conditions for gain selection demonstrate the importance of the constraints. Force feedback has been shown not to be mandatory for closed-loop stabilization, but it is useful in improving certain closed-loop robustness properties.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new approach is presented to improve power swings damping of nonlinear power system model based on direct Lyapunov method. The approach combines superconducting magnetic energy storage (SMES) system with static series synchronous compensator (SSSC). Considering the energy absorption/injection ability of SMES, in transient states the combination exchanges both active and reactive powers with power system. Since direct Lyapunov method implies time derivative of both active and reactive powers, prepares an effective control strategy for the integrated SSSC-SMES system to decrease power swings damping time. Using direct Lyapunov method for structure preserving model (SPM) of power system, dq components of SSSC injecting voltage are calculated. Decentralizing method is used to locally control the SSSC-SMES independent of state variables of synchronous generators which require wide area measurements. PSCAD/EMTDC simulations verify the effectiveness of proposed method.

This paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

This article reveals the detailed analyses of the uniform stability and the transient stability of an adaptive sliding-mode load-torque observer. Using the Lyapunov's direct method, the stability c...

Lyapunov's direct method has been applied extensively to the stability analysis of nonlinear systems. The method enables one to directly judge stability without solving the nonlinear differential equations representing motor involved. In the paper, the effect of important parameters on trasient stability of a three-phase reluctance motors have been assessed from the data obtained for load and applied voltage changes by applying the Lyapunov's direct method.

PurposeThe purpose of this paper is to present the control of six degrees of freedom (PUMA560) robotic arm using visual servoing, based upon linear matrix inequality (LMI). The aim lies in developing such a method that neither involves camera calibration parameters nor inverse kinematics. The approach adopted in this paper includes transpose Jacobian control; thus, inverse of the Jacobian matrix is no longer required. By invoking the Lyapunov's direct method, closed‐loop stability of the system is ensured. Simulation results are shown for three different cases, which exhibit the system stability and convergence even in the presence of large errors.Design/methodology/approachThe paper presents LMI‐based visual servo control of PUMA560 robotic arm.FindingsThe proposed method is implementable in the dynamic environment due to its independence to camera and object model.Research limitations/implicationsVisibility constraint is not included during servoing – this may cause features to leave the camera field of view (fov).Originality/valueLMI optimization is employed for visual servo control in an uncalibrated environment. Lyapunov's direct method is utilized which ensures system stability and convergence.

This paper proposes a new nonlinear control system to realize a zero power control of magnetic bearing system using only electromagnets. The nonlinear control system is designed based on Lyapunov's direct method. The electromagnets is switched by the nonlinear algorithm depend on the displacement and the velocity of a rotor. It is very easy to design the nonlinear control system because it consists of only two parameters. Also, the characteristics of closed loop can be changed easily. Stability of magnetic bearing system controlled by the proposed nonlinear control is proved. It is clarified through the simulation that the proposed nonlinear control in this paper is a very useful approach to realize a zero power control of magnetic bearing system.

Lyapunov's direct method has been adapted to the study of an electrostatic instability of a plasma by using Zubov's extension of the method to distributed parameter systems. Specifically, the linear stability of two inhomogeneous interpenetrating electron streams in a finite one-dimensional system is considered. Proper Lyapunov functionals are constructed for both stability and instability. It is seen that, as in the homogeneous case, the stability or instability depends on whether or not the thermal speed is greater or less than the streaming speed. In contrast to the methods of energy principle, the complete generality of Lyapunov's direct method is discussed.

Feedback control design by Lyapunov's direct method

Regulation of a flexible slider–crank mechanism by Lyapunov's direct method

The extension of some of the results contained in Part I [1] to the case when only the plant outputs rather than all its state variables are accessible for measurement is discussed. A unified approach to the synthesis of an adaptive observer is presented whereby the plant state and parameters are simultaneously estimated. Uniform asymptotic stability of the scheme is proved using Lyapunov's direct method. The information provided by the adaptive observer is used to synthesize an adaptive controller for the plant. While all the principal results obtained here are for the case of a single-input single-output plant, extensions to special classes of multivariable systems is indicated.

In this paper, sufficient criteria for the existence of solutions to uniform asymptotic stability and boundedness problems associated with certain second order nonlinear non autonomous ordinary differential equation are established with the aid of Lyapunov's direct method. Furthermore, the appropriate complete Lyapunov function is given explicitly. Our results complement some well known results on the second order differential equations in the literature.

The Direct and Indirect Methods of Ionospheric TEC Predictions and Their Comparison

Uniform asymptotic stability of impulsive differential-difference equations of neutral type by Lyapunov's direct method

This paper deals with the stability of continuous-time multidimensional nonlinear systems in the Roesser form. The concepts from 1D Lyapunov stability theory are first extended to 2D nonlinear systems and then to general continuous-time multidimensional nonlinear systems. To check the stability, a direct Lyapunov method is developed. While the direct Lyapunov method has been recently proposed for discrete-time 2D nonlinear systems, to the best of our knowledge what is proposed in this paper are the first results of this kind on stability of continuous-time multidimensional nonlinear systems. Analogous to 1D systems, a sufficient condition for the stability is the existence of a certain type of the Lyapunov function. A new technique for constructing Lyapunov functions for 2D nonlinear systems and general multidimensional systems is proposed. The proposed method is based on the sum of squares (SOS) decomposition, therefore, it formulates the Lyapunov function search algorithmically. In this way, polynomial nonlinearities can be handled exactly and a large class of other nonlinearities can be treated introducing some auxiliary variables and constrains.