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4 International Journal of Applied Mathematics and Computer Science

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Robust extremum seeking for a second order uncertain plant using a sliding mode controller

Solis Cesar, Clempner Julio, Poznyak Alexander

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 4

703--712

This paper suggests a novel continuous-time robust extremum seeking algorithm for an unknown convex function constrained by a dynamical plant with uncertainties. The main idea of the proposed method is to develop a robust closed-loop controller based on sliding modes where the sliding surface takes the trajectory around a zone of the optimal point. We assume that the output of the plant is given by the states and a measure of the function. We show the stability and zone-convergence of the proposed algorithm. In order to validate the proposed method, we present a numerical example.

Local stability conditions for discrete-time cascade locally recurrent neural networks

Patan K.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 1

23-34

The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem, a gradient projection method is adopted. The efficiency and usefulness of the proposed approach are justified by using a number of experiments.

Derivative-free nonlinear optimization filter simplex

Correia A., Matias J., Mestre P., Serodio C.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

679-688

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Unilateral Contact Applications Using Fem Software

Stavroulaki M. E., Stavroulakis G. E.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 1

115-125

Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with MARC, are briefly presented, together with elements of the underlying theory.