Moving particles that rest along their trajectory lead to time-fractional diffusion equations for the scaling limit distributions. For power law waiting times with infinite mean, the equation contains a fractional time derivative of order between 0 and 1. For finite mean waiting times, the most revealing approach is to employ two time scales, one for the mean and another for deviations from the...

in this paper, a finite-time control scheme is presented for stabilization ofthe satellite chaotic attitude around its equilibrium point whenits attitude is confused by a disturbed torque. controllers and settling timeof stabilizaton are obtained, based on the lyapunov stability theoremand finite-time control scheme. this method is satisfied for any initial condition.numerical simulations are ...

In the present contribution we study the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a viscous Cahn–Hilliard type equation for the phase variable with a reaction-diffusion equation for the nutrient. First, we prove the well-posedness and some regularity results for the state system modified by the state-feedback control law. Then, we show that the chos...

We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type π(dx) = e γx ν(e x − 1) dx, where ν is the density of the stable Lévy measure and γ is a positive parameter which depends on its characteristics. These processes were introduced in [10] as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processe...

We investigate the finite-time boundary stabilization of a 1-D first order quasilinear hyperbolic system of diagonal form on [0,1]. The dynamics of both boundary controls are governed by a finite-time stable ODE. The solutions of the closed-loop system issuing from small initial data in Lip([0,1]) are shown to exist for all times and to reach the null equilibrium state in finite time. When only...

In this paper, we consider an optimal control problem arising from the optimal guidance of a lunar module to achieving soft landing, where the description of the system dynamics is in a three-dimensional coordinate system. Our aim is to construct an optimal guidance law to realize the soft landing of the lunar module with the terminal attitude of the module to be within a small deviation from b...

When a detector sensitive to the target plume IR seeker is used for tracking airborne targets, the seeker tends to follow the target hot point which is a point farther away from the target exhaust and its fuselage. In order to increase the missile effectiveness, it is necessary to modify the guidance law by adding a lead bias command. The resulting guidance is known as target adaptive guidance ...

In this work, a dynamic feedback control law based on the well known “Twisting” algorithm is under study. Dynamic compensation is added to the Twisting algorithm, in order to use position feedback only, and keep properties such as finite time stability. In some mechanical applications, an observer or a differentiator design is required for control purposes when the whole state space is not avai...