Presently, distributed network systems are extensively used in a wide range of applications such as war field supervision, target tracing and positioning, error recognition, etc. However, a mechanism such as Kalman is needed to resolve issues such as configuration of topologies at the physical layer of sensor networks and delay in measurement time and data transmission in order to guarantee correctness and accuracy of parameter measured by the sensors. On the other hand, fractional calculus which is a generalization of integer order operators allows for highly precise modelling of physical systems. Thus, a new fractional-order distributed Kalman filter algorithm is presented for state estimation in measurement time-delay sensor networks in this paper. Therefore, at first fractional distributed Kalman filter algorithms and then their performance metrics such as means squared deviation and average will be evaluated to investigate feasibility of the algorithm. Finally, simulations show that performance of the proposed algorithm in terms of accuracy and efficiency has considerably improved as compared with previously proposed approaches such as conventional fractional-order Kalman filter.

Wireless sensor networks are applied in a broad range of applications such as medical, industrial and military fields.Therefore, a precise Kalman filter mechanism is needed for fixed configuration of topologies in sensor networks in order to ensure accuracy and precision of sensor measurements.On the other hand, fractional calculus as a generalization of integer order operators enables modeling of physical systems with high accuracy.Hence, a new fractional-order distributed Kalman filter algorithm is presented in this study to estimate the states in sensor networks.Therefore, as a generalization of filtering algorithm a fractional order Kalman filter algorithm is proposed.For this purpose, fractional-order distributed Kalman filter algorithms and fractional diffusion Kalman filters are formulated and their performance is evaluated based on mean squares for algorithm feasibility analysis. Simulations show that performance of the proposed algorithm is improved in terms of accuracy and efficiency compared to previous methods such as conventional fractional Kalman filter.

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique.

The aim of this manuscript is to investigate an efficient iterative approach for the nonlinear fractional optimal control problems affected by the external persistent disturbances. For this purpose, first the internal model principle is employed to transform the fractional dynamic system with disturbance into an undisturbed system with both integer- and fractional-order derivatives. The necessary optimality conditions are then reduced into a sequence of linear algebraic equations by using a series expansion approach and the Grunwald-Letnikov approximation for the fractional derivatives. The convergence of the latter sequence to the optimal solution is also studied. In addition, an iterative algorithm designing the suboptimal control law is presented. Numerical simulations confirm that the new approach is efficient to reject the external disturbance and provides satisfactory results compared to the other existing methods. (C) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

: This paper presents a novel hybrid technique based on the modal series method and linear programming strategy for solving the optimal control problem of nonlinear fractional-order systems. The fractional derivative is defined in the sense of Riemann-Liouville with order less than one. The performance index includes the terminal cost in addition to the integral quadratic cost functional. Both the fixed and free final states cases have been taken into account. In this approach, first we extend the modal series method in order to convert the original nonlinear fractional-order two point boundary value problem (FTPBVP) derived from the Pontryagin’s maximum principle into a sequence of linear time-invariant FTPBVPs. This sequence is then transformed into a sequence of linear programming problems by defining a new variational problem in the calculus of variations, using a discretization technique based on the first-order Grünwald-Letnikov approximation and introducing a new transformation. The convergence analysis of the proposed approach is also provided. To achieve an accurate suboptimal control, we apply a fast iterative algorithm with low computational effort. Finally, two numerical examples are included to illustrate the effectiveness of the proposed approach.