This paper considers the cooperative control of a group of autonomous underactuated vessels (AUV). The control objective for each vessel is to maintain its position in the formation while Formation Reference Point (FRP) tracks a predefined spatial path. In order to achieve this goal, we use vectorial backstepping to solve two subproblems: one is geometric task, anther is dynamic task. The forme...

This paper is concerned with the control of a class of chaotic systems using adaptive backstepping, which is a systematic design approach for constructing both feedback control laws and associated Lyapunov functions. Firstly, we show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the so-called nonautonomous “strict-feedbac...

Dynamic surface control (DSC) method uses high gain filters to avoid the ”explosion of complexity” issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale separation between them. This paper attempts to design a novel disturbance observer based dynamic surface controller using contraction framework. In doing so the stea...

In this Letter backstepping design is proposed for controlling chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The advantages of the method are the following: (i) it represents a systematic procedure for controlling chaotic or hyperchaotic dynamics; (ii) it can be applied to several circuits and sys...

In this paper, we present a global adaptive output feedback control scheme for a class of 3rd-order uncertain nonlinear systems to which adaptive observer backstepping method may not be applicable directly. In contrast to the existing output feedback form, the allowed extended output feedback structure includes quadratic and multiplicative dependency of unmeasured states. Our novel design techn...

This paper presents a robust backstepping design for motion control in the presence of model uncertainties and exogenous disturbances. The main difficulty in dealing with motion control is to reduce the effect of friction, which exists in the moving mechanism and induces nonlinear behavior. In this study, the friction dynamic is considered as the external disturbance, and the proposed backstepp...

When a mobile robot inspects tasks with complex requirements indoors, the traditional backstepping method cannot guarantee accuracy of trajectory, leading to problems such as instrument not being inside image and focus failure when grabs high zoom. In order solve this problem, paper proposes an adaptive based on double Q-learning for tracking controlling trajectory robots. We design incremental...

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conver...

The method known as backstepping for Partial Differential Equations1 (PDEs), as it is known today, was first introduced in the seminal work of Smyshlyaev and Krstic [1]. Their approach, first developed for a general 1-D linear reactiondiffusion-advection PDE, is based on a constructive strategy of first design (in the continuum setting) and then discretize (for implementation and simulation). T...

A new approach to control system design for systems containing uncertain, nonsmooth friction is proposed. The method is based on a multi-state backstepping approach to variable structure control design. Stability and robustness properties are investigated and an example is given.