Existing numerical methods for fractional PDEs suffer from low accuracy and inefficiency in dealing with three-dimensional problems or with long-time integrations. We develop a unified and spectrally accurate Petrov–Galerkin (PG) spectral method for a weak formulation of the general linear Fractional Partial Differential Equations (FPDEs) of the form 0D t u + d j=1 c j [a jD 2μ j x j u ] + γ u...

We present a filter linesearch method for solving general nonlinear and nonconvex optimization problems. The method is of the filter variety, but uses a robust (always feasible) subproblem based on an exact penalty function to compute a search direction. This contrasts traditional filter methods that use a (separate) restoration phase designed to reduce infeasibility until a feasible subproblem...

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain ...

Many key aspects of control of quantum systems involve manipulating a large quantum ensemble exhibiting variation in the value of parameters characterizing the system dynamics. Developing electromagnetic pulses to produce a desired evolution in the presence of such variation is a fundamental and challenging problem in this research area. We present such robust pulse designs as an optimal contro...

Recently Bernstein [4] has provided a simpler proof of unpredictability of CBC construction [3] which is giving insight of the construction. Unpredictability of any function intuitively means that the function behaves very closely to a uniform random function. In this paper we make a unifying and simple approach to prove unpredictability of many existing constructions. We first revisit Bernstei...

Thermo-Electric Modules (TEMs) are being increasingly used in power generation as a valid alternative to batteries, providing autonomy to sensor nodes or entire Wireless Sensor Networks, especially for energy harvesting applications. Often, manufacturers provide some essential parameters under determined conditions, like for example, maximum temperature difference between the surfaces of the TE...