In control theory, the term chattering is used to refer to fast oscillations of controls, such as an infinite number of switchings over a finite time interval. In this paper we focus on three typical instances of chattering: the Fuller phenomenon, referring to situations where an optimal control features an accumulation of switchings in finite time; the Robbins phenomenon, concerning optimal co...

A hybrid nonlinear differentiator being fit for rapid convergence is presented, which is based on singular perturbation technique and consists of linear and nonlinear parts. This differentiator is simple and can converge rapidly at all times, and no chattering phenomena happen. The theoretical results are confirmed by computer simulations and an experiment.

We consider continuous-time average consensus dynamics in which the agents’ states are communicated through uniform quantizers. Solutions to the resulting system are defined in the Krasowskii sense and are proven to converge to conditions of “practical consensus”. To cope with undesired chattering phenomena we introduce a hysteretic quantizer, and we study the convergence properties of the resu...

This paper deals with the design of a moving sliding surface in a variable structure plant for a second order system. The chattering phenomena is also dealt with during the switching process for an unstable sliding surface condition. The simulation examples considered in this paper shows the effectiveness of the sliding mode control method used for the design of the moving sliding surfaces. A s...

An adaptive sliding mode control based on two neural networks is proposed in this paper for Quadrotor stabilization. This approach presents solutions to conventional control drawbacks as chattering phenomenon and dynamical model imprecision. For that reason two ANN for each quadrotor helicopter subsystem are implemented in the control loop, the first one is a Single Hidden Layer network used to...

In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI...

This paper deals with the design of a moving sliding surface in a variable structure plant for a second order system. The chattering phenomena is also dealt with during the switching process for an unstable sliding surface condition. The simulation examples considered in this paper shows the effectiveness of the sliding mode control method used for the design of the moving sliding surfaces. A s...

In this paper, the modified optimal sliding mode control with a proposed method to design a sliding surface is presented. Because of the inability of the previous approach of the sliding mode method to design a bounded and suitable input, the new variation is proposed in the sliding manifold to obviate problems in a structural system. Although the sliding mode control is a powerful method to re...