In this paper, a Haar wavelets based numerical method to solve a system of linear or nonlinear fractional differential equations has been proposed. Numerous nontrivial test examples along with practical problems from fluid dynamics and chemical engineering have been considered to illustrate applicability of the proposed method. We have derived a theoretical error bound which plays a crucial role whenever the exact solution of the system is not known and also it guarantees the convergence of approximate solution to exact solution.
In this paper, we propose a new algorithm for performing blind source separation and signal recovery for the narrowband case. This algorithm seeks to estimate and implement the Wiener filter directly using the second and fourth order cumulants. The estimated filter is asymptotically consistent with or without noise, is not subject to the bound imposed by pre-whitening as with some existing algorithms, and outperforms these algorithms. In fact, in many cases it nearly achieves the Wiener limit as performance studies show.
This paper considers the problem of the second-moment stabilisation of a scalar linear plant with process noise. It is assumed that the sensor communicates with the controller over an unreliable channel, whose state evolves according to a Markov chain, with the transition matrix on a timestep depending on whether there is a transmission on that timestep. Under such a setting, an event-triggered transmission policy is proposed which meets the objective of exponential convergence of the second moment of the plant state to an ultimate bound. Further, upper bounds on the transmission fraction of the proposed policy are provided. The results are illustrated through an example scenario of control in the presence of a battery-equipped energy-harvesting sensor. The proposed control design as well as the analytical guarantees are verified through simulations for the example scenario.
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