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Owing to an increasing need of control community for providing a precise and integrated model of natural and practical structures switching systems have attracted much attention. On the other hand, the multi-model inherent in many practical systems has increased the importance of reviewing these types of systems. In this paper, the problem of adaptive fault tolerant finite-time control of a class of nonlinear switching systems in the presence of actuator fault, external disturbances and dead-zone input nonlinearity is investigated. The boundary of the uncertain terms of the system is assumed to be unknown and adaptive rules are used to eliminate the destructive effects of these terms on the system response. The subsystems of switching system are considered as nonlinear systems with a canonical structure. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the purpose is to propose a controller that works under any desired switch signal and can overcome the actuator fault, disturbances and dead-zone input nonlinearity. To achieve this purpose, after providing a smooth sliding manifold, an adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite-time sense. Finally, by using the Lyapunov stability theory, it is proved that the origin is the finite-time stable equilibrium point of the overall closed-loop system. The simulation results provided by MATLAB software show the performance of the proposed controller.

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In this article, an efficient method to minimize energy losses is presented. The proposed method uses intermittent load conditions over a future time interval instead of an instantaneous network condition. This method obtains the optimal condition during the given period according to the current value of the condition. A given time interval is divided into many smaller subintervals. By increasing the number of subintervals or load profiles, the dimensions of the problem increase, for which an optimal value must be obtained. In this method, the variables are divided into the group of continuous and discrete control variables. While only continuous control variables are allowed to change in each sub-interval, continuous and discrete variables are set at the beginning of each time interval. This problem is solved by using the GBD general bend decomposition method. Using this method, the load conditions for each subinterval in the NLP subproblem are solved. Then, the results of the NLP subproblem are used in the main subproblem. As shown in the simulation results, the proposed method not only improves the voltage profile but also reduces the total energy wasted in the desired period.