Bernstein polynomials, Constrained global optimization, Subdivision, Pruning,

In this paper, an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed algorithm is based on the Bernstein polynomial approach. Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point, modified rules for the selection of the subdivision direction, and a new acceleration device to avoid some unnecessary subdivisions. The performance of the proposed algorithm is numerically tested on a collection of 16 test problems. The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.

Recent developments and advancements in the areas of permanent magnets, power electronics and modern control technologies have significantly influenced the widespread use of Brushless DC (BLDC) motor drives. BLDC motors are now, widely used in many applications such as servo drives, computer peripheral equipments and electric vehicles due to their high power density, high efficiency, compact size and easier control. In this paper a control scheme is presented which uses the traditional PID controller for the speed control of BLDC motor. PID controller is designed both by Zeigler-Nichols tuning method and Genetic Algorithm. A controller based on fractional order PID is also designed using Genetic algorithm and the performances of fractional PID controller are compared with the performance of PID controller. MATLAB/SIMULINK software is used to simulate and test the performances of the designed controllers.

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In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.

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