u+1(t)_ uz(t) for tEIl r(t) f or tEIk where ui and r are the present control and a control maximizing the related Hamiltonian function, respectively. The idea of the switching scheme is based on the concept of chattering controls first proposed by Gamkrelidze. It is proved that accumulation points generated by the algorithm, if exist, satisfy maximum principle. Some examples are given to show t...

In this paper, we address the rigid body pose stabilization problem using dual quaternion formalism. We propose a hybrid control strategy to design a switching control law with hysteresis in such a way that the global asymptotic stability of the closed-loop system is guaranteed and such that the global attractivity of the stabilization pose does not exhibit chattering, a problem that is present...

An asymptotically stable direct adaptive fuzzy PI sliding mode controller is proposed for a class of nonlinear uncertain systems. In contrast to other existing approaches of handling disturbances, the proposed approach does not require this bound to be known, only requiring that it exists. Moreover, a PI control structure is used to attenuate chattering. The approach is applied to stabilize an ...

This paper presents an adaptive variable structure con-troller(VSC) for set-point regulation of a class of non-linear systems. Due to the existence of the sign function , the conventional VSC has the input chattering phenomenon even in the steady state. The method used in this paper essentially solves the problem by using a decreasing switching control input whose size is proportional to the tr...

In this paper, we have exploited the first-order sliding mode control method to track the ECG data of the human heart by three different nonlinear control laws. In order to lessen the intrinsic chattering of the classic sliding mode control system, smooth function approximations of the control input, by means of the hyperbolic tangent and the saturation function, were used. The fast Fourier tra...