Systems _ x(t) = F(t; x(t); ") depending on a small parameter " are considered. We introduce a concept of convergence of such a system to a system _ x(t) = G(x(t)). Assuming this convergence, we prove that global asymptotic stability for _ x(t) = G(x(t)) implies some notion of \practical stability" for _ x(t) = F(t; x(t); ") if F(; x; ") satisses a periodicity assumption. We apply this theory t...

Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. The present paper reviews the mathematical and theoretical foundation of quantum annealing. In particular, theorems are presented for convergence con...

Differential evolution (DE) is a simple, fast, and efficient evolutionary algorithm for global numerical optimization. The major advantage of DE is its self-adaptation in both search direction and step size of the differential mutation.. On the other hand, DE is good at exploring. The search space and locating the region of global minimum, but it is slow at exploitation of the solution. In orde...

This paper discusses a methodology to manage wireless sensor networks (WSN) with self-organising feature maps, using co-operative Extended Kohonen Maps (EKMs). EKMs have been successfully demonstrated in other machine-learning contexts such as learning sensori-motor control and feedback tasks. Through a quantitative analysis of the algorithmic process, an indirect-mapping EKM can self-organise ...

The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various ...

This paper addresses the problem of stabilizing the dynamic model of a nonholonomic mobile robot. A discontinuous adaptive state feedback controller is derived to achieve global stability and convergence of the trajectories of the of the closed loop system in the presence of parameter modeling uncertainty. This task is achieved by a non smooth transformation in the original system followed by t...

The paper proposed to use decentralized and centralized I-term neural sliding mode control of distributed parameter wastewater anaerobic digestion bioprocess plant. The bioprocess plant is described by partial differential equations simplified by means of the orthogonal collocation method and used as an input/output data generator. The obtained process data are identified by means of decentrali...

We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a trad...

In this paper a thermodynamic approach is presented to the problem of convergence of evolutionary algorithms. The case of the Simulated Annealing algorithm for optimisation is considered as a simple evolution strategy with a control parameter allowing balance between the probability of obtaining an optimal or near-optimal solution and the time that the algorithm will take to reach equilibrium. ...

in this paper, a new smooth second order sliding mode control is proposed. this algorithm is a modified form of super twisting algorithm. the super twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular lyapunov function. the proposed algorithm which is able to control nonlinear systems with matched structured u...