Lyapunov method

This paper proposes a controller design for an omnidirectional mobile platform (OMP) with three wheels using adaptive backstepping control. A kinematic modeling and a dynamic modeling of the system with disturbance and friction are presented. Based on the dynamic modeling, an adaptive backstepping controller (ABC) is designed to stabilize the OMP with parameter variations and uncertainties caused by friction and slip to follow a desired path. The controller and update laws are designed based on an adaptive backstepping control theory. It includes two steps: firstly, a virtual state and a stability function are introduced. Secondly, Lyapunov functions for the system are chosen and an adaptive backstepping controller to make the system stabilisable and the update laws to estimate the unknown parameters are obtained. The system stability is guaranteed by the Lyapunov stability theory. The simulation and experimental results are presented to demonstrate the effectiveness of the proposed...

Abstract A method for online transient stability assessment of large power systems is proposed. It consists of: replacing the multimachine system by a two-machine dynamic equivalent, further amenable to a one-machine-infinite-bus system; reducing the stability problem to a sole algebraic equation, devised from the equal area criterion, or equivalently from the Lyapunov direct criterion; and using this equation to derive one-shot stability analysis strategies. A technique for system admittance matrix reduction is developed that ...

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2010; 20:639–658 Published online 12 May 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rnc.1458 ... Flight control of a rotary wing ...

Abstract The three degree of freedom (3DOF) helicopter is a simplified model, which is used to study the behaviours of the helicopters. It is an example of a so-called underactuated mechanical system that has a fewer control inputs than degrees of freedom. Application of multiple-surface sliding mode control to such model looks attractive, because of the ability of this method to stabilize the underatuated systems and to deal with uncertainties, which usually exist in such systems. In this paper, a multiple-surface sliding mode is proposed to ...

In this paper, a robust motion tracking control algorithm for robotic manipulators is proposed where the higher-order system uncertainties are taken into account. The control structure consists of two main parts: a model-based precompensation part and a robust nonlinear controller one. Specifically, with knowledge of possible upper bounds on uncertainties, we propose the nonadaptive version of robust controller. Stability and

This paper presents a discrete-event switching control of DC–DC converters which belong to a particular class of hybrid systems. Taking advantage of the energetical properties of these converters, Lyapunov function is proposed. This function, which is systematically deduced from the physical model, allows the creation of various stabilizing switching sequences. From a theoretical point of view, asymptotic stability can be

We propose new sufficient conditions for the uniform asymptotic stability of the zero solution of a retarded functional-differential equation with unbounded (infinite) delay. The equation can be nonlinear and nonautonomous. The conditions are formulated in terms of Razumikhin-type functions, and in this case, a function is coupled with a functional related to this function by a certain dependence. In the results presented here, because of additional restrictions imposed on the right-hand side of the equation and the use of the limiting equation techniques, the classical requirements stating that the function and its derivative must be of fixed sign along the solution are weakened to the requirements that the function and its derivative must be of constant signs.

Abstract A novel method to solve the stabilization problem for a class of nonlinear affine single-input systems using neural networks is proposed in this paper. The controller is based on feedback linearization where the control signal is directly estimated by a nonlinear in parameter neural network (NLPNN). A modified Back Propagation (BP) algorithm with e-modification is used to update the weights of the network. The stability of overall closed-loop system is shown using Lyapunov method. To evaluate the performance of the proposed ...

In this brief, a homography-based adaptive visual servo controller is developed to enable a robot end-effector to track a desired Euclidean trajectory as determined by a sequence of images for both the camera-in-hand and fixed-camera configurations. To achieve the objectives, a Lyapunov-based adaptive control strategy is employed to actively compensate for the lack of unknown depth measurements and the lack of an object model. The error systems are constructed as a hybrid of pixel information and reconstructed ...