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In this paper, an linear matrix inequalities (LMI)-based second-order fast terminal sliding mode control technique is investigated for the tracking problem of a class of non-linear uncertain systems with matched and mismatched uncertainties. Using the offered approach, a robust chattering-free control scheme is presented to prove the presence of the switching around the sliding surface in the finite time. Based on the Lyapunov stability theorem, the LMI conditions are presented to make the state errors into predictable bounds and the parameters of the controller are obtained in the form of LMI. The control structure is independent of the order of the model. Then, the proposed method is fairly simple and there is no difficulty in the use of this scheme. Simulations on the well-known Genesio's chaotic system and Chua's circuit system are employed to emphasize the success of the suggested scheme. The simulation results on the Genesio's system demonstrate that the offered technique leads to the superior improvement on the control effort and tracking performance.

Abstract. This paper investigates a novel nonsingular fast terminal sliding-mode control method for the stabilization of the uncertain time-varying and nonlinear thirdorder systems. The designed disturbance observer satis es the nite-time convergence of the disturbance approximation error and the suggested nite-time stabilizer assures the presence of the switching behavior around the switching curve in the nite time. Furthermore, this approach can overcome the singularity problem of the fast terminal sliding-mode control technique. Moreover, knowledge about the upper bounds of the disturbances is not required and the chattering problem is eliminated. Usefulness and e ectiveness of the o ered procedure are con rmed by numerical simulation results.

This paper proposes a new state-feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous-bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady-state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master-slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

In this paper, a novel adaptive global sliding mode control technique is suggested for the tracking control of uncertain and non-linear time-varying systems. The proposed scheme composed of a global sliding mode control structure to eliminate reaching mode and an adaptive tracker to construct the auxiliary control term for eliminating the impacts of unwanted perturbations. Using the Lyapunov direct method, the tracking control of the non-linear system is guaranteed. Moreover, superior position tracking performance is obtained, the control effort is considerably decreased and the chattering phenomenon is removed. Furthermore, using adaptation laws, information about the upper bounds of the system perturbations is not required. To indicate the effectiveness of the suggested scheme, three simulation examples are presented. Simulation results demonstrate the superiority and capability of the offered control law to improve the transient performance of a closed-loop system using online adaptive parameters.

In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations. KeywordsFractional partial differential equations, reduced differential transform method, local fractional derivative operator Date

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