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Abstract: This paper deals with the problem of observer design for a class of implicit nonlinear systems of index one. To solve this problem, an implicit observer which is given by an implicit system is usually used. The implementation of this kind of observer requires an optimization algorithm to solve at each time the algebraic constraints. Alternatively, an explicit observer which is described by an ordinary differential equation can be used. The advantage of this approach is that no optimization algorithm is required. Moreover the observer initialization may be done outside the constraints. In this paper it is shown that, under some conditions, the existence of an implicit observer implies the existence of an explicit one. Then, an explicit observer is given for implicit state affine systems whose dynamic involves an additional nonlinear term depending on the input, the output and the implicit variable. [Copyright &y& Elsevier]

Abstract: In this paper, two anticontrol algorithms for synthesis of discrete chaos are introduced. In these algorithms, the control parameter of a discrete dynamical system is switched, either randomly or in a deterministic way, between two or more values corresponding to periodic motions, the result being chaotic behavior. These algorithms require no knowledge of specific mathematical properties of the underlying map modeling the system. The existence of chaos is demonstrated using various tools including graphical iteration, histogram, Lyapunov exponent and surrogate tests. In this paper, these very simple and implementable chaotifiers are applied to the logistic map. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the observability of piecewise-affine hybrid systems. Our aim is to give sufficient conditions to observe the discrete and continuous states, in terms of algebraic and geometrical conditions. Firstly, we will give the algebraic conditions to observe the discrete state based on the switch function reconstruction for linear hybrid systems. Secondly, we will give a geometrical condition based on the transversality concept for nonlinear hybrid systems. Throughout this paper, we illustrate our propositions with examples and simulations. [Copyright &y& Elsevier]

Abstract: The problem of Systems Identification starts with a time-series of observed data and tries to determine the simplest model capable of exhibiting the observed behavior. This optimization problem searches the model from a space of possible models. In this paper, we present the theory and algorithms to perform Qualitative and Quantitative Systems Identification for Linear Time-Invariant Dynamic Systems. The methods described here are based on successive elimination of the components of the system''s response. Sinusoidals of high frequencies are eliminated first, then their carrying waves. We continue with the process until we obtain a non-oscillatory carrier. At this point, we determine the order of the carrier. This procedure allows us to determine how many sinusoidal components and exponential components are found in the impulse response of the system under study. The number of components determines the order of the system. The paper is composed of two important parts, the statement of some mathematical properties of the responses of Linear Time Invariant Dynamic Systems, and the proposal of a set of filters that allows us to implement the recognition algorithm. We present the application of the proposed methodology to analyze and model the electrical circuits and electrical power systems. [Copyright &y& Elsevier]

In this paper, by using the theories and methods of mathematical analysis and computer algebra, a new algorithm of symbolic integral was established, a new Maple procedure myint for it was established, too. And it was applied to the automatic proving the mean-value theorems for derivatives. The results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea, excellent property for operation and powerful competence. This would be useful for the problem of solving differential equations, automatic proving some mathematical theorems, and so on. [Copyright &y& Elsevier]

Summary: The Richard’s equation mathematically expressing the infiltration problem is a transport type of equation describing two different phenomena namely advection and diffusion being hyperbolic and parabolic type of differential equation, respectively each having their own physical properties thus a single numerical scheme would not essentially be suitable for both. In this paper a numerical algorithm based on time splitting or fractional step method has been proposed and described. This has allowed designing and applying some different numerical schemes more compatible with the mathematical and physical properties of the corresponding phenomenon. In advection part an implicit characteristic based method has been employed to calculate the cell face fluxes and then the new unknowns have been obtained using finite volume method (FVM) explicitly. Two different speed type quantities namely wave celerity and mass velocity have been distinguished in the advection of infiltrated water to the soil, the magnitude of the first being several times larger than the other. The implicit characteristic based method has been designed specifically to cope with the mentioned high wave celerity. An implicit numerical scheme has been employed in which the space derivative term contributed in definition of cell face flux has been discretized in fourth order accurate manner. The extra cells getting involved due to the higher order discretization have been taken in account in a way not to change the tri-diagonal matrix coefficient shape preserving the efficiency of the algorithm. The performance, accuracy and efficiency of the out coming non-iterative numerical algorithm have been successfully examined by some test cases. The relative importance of the advection and diffusion terms in the concerned transport equation and the ration of their contribution in the overall infiltrated flux also have been discussed in detail. [Copyright &y& Elsevier]

Abstract: Richardson Extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations (ODEs) obtained by different numerical methods (including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods). Some stability results related to two implementations of the Richardson Extrapolation (Active Richardson Extrapolation and Passive Richardson Extrapolation) are formulated and proved in this paper. An advanced atmospheric chemistry scheme, which is commonly used in many well-known operational environmental models, is applied in a long sequence of experiments in order to demonstrate the fact that [(a)] it is indeed possible to improve the accuracy of the numerical results when the Richardson Extrapolation is used (also when very difficult, badly scaled and stiff non-linear systems of ODEs are to be treated), [(b)] the computations can become unstable when the combination of the Trapezoidal Rule and the Active Richardson Extrapolation is used, [(c)] the application of the Active Richardson Extrapolation with the Backward Euler Formula is leading to a stable computational process, [(d)] experiments with different algorithms for solving linear systems of algebraic equations are very useful in the efforts to select the most suitable approach for the particular problems solved and [(e)] the computational cost of the Richardson Extrapolation is much less than that of the underlying numerical method when a prescribed accuracy has to be achieved. [Copyright &y& Elsevier]

Abstract: We consider a class of global optimization problems, in which the objective function is Lebesgue integrable. In this paper, we present a sufficient and necessary condition for computing the essential infimum. This optimality condition can be used to design algorithms for solving the global optimization problem. [Copyright &y& Elsevier]

Abstract: In this paper, a new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems: find the solutions converge to the true Pareto-front and uniform spread along the front. [Copyright &y& Elsevier]

Abstract: Population initialization is a crucial task in evolutionary algorithms because it can affect the convergence speed and also the quality of the final solution. If no information about the solution is available, then random initialization is the most commonly used method to generate candidate solutions (initial population). This paper proposes a novel initialization approach which employs opposition-based learning to generate initial population. The conducted experiments over a comprehensive set of benchmark functions demonstrate that replacing the random initialization with the opposition-based population initialization can accelerate convergence speed. [Copyright &y& Elsevier]

Abstract: In this paper, we will discuss elliptic partial differential equation whose coefficients are constants. On basis of a new computing technique for Green function, we will propose a new effective finite element algorithm for that problem. Finally, we will give some numerical examples to investigate that finite element algorithm. [Copyright &y& Elsevier]

Abstract: Many practical problems can be formulated as constrained optimization problems. Due to the simple concept and easy implementation, the penalty function method has been one of the most common techniques to handle constraints. However, the performance of this technique greatly relies on the setting of penalty factors, which are usually determined by manual trial and error, and the suitable penalty factors are often problem-dependent and difficult to set. In this paper, a differential evolution approach based on a co-evolution mechanism, named CDE, is proposed to solve the constrained problems. First, a special penalty function is designed to handle the constraints. Second, a co-evolution model is presented and differential evolution (DE) is employed to perform evolutionary search in spaces of both solutions and penalty factors. Thus, the solutions and penalty factors evolve interactively and self-adaptively, and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously. Simulation results based on several benchmark functions and three well-known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis, ordinary differential equation and computer algebra, a reliable algorithm for solving ordinary differential equation (ODE) was established, and a new Maple procedure mechodeproc was established, too. The results of the examples indicated that the procedure mechodeproc based on Taylor polynomial method was simple and effective, and could provide an accuracy approximate solution or exact solution of the ordinary differential equation. This would be useful for solving differential equation. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis and computer algebra, a reliable algorithm for solving high-order nonlinear Volterra–Fredholm integro-differential equations was established, and a new Maple procedure voltfredproc was established too. The results of the examples indicated that the procedure voltfredproc of Taylor polynomial method is simple and effective, and could provide an accuracy approximate solution or exact solution of the high-order nonlinear Volterra–Fredholm integro-differential equation. This would be useful for solving integro-differential equation, integral equations and ordinary differential equation. [Copyright &y& Elsevier]

Abstract: In this paper, a receding horizon control strategy is applied to a dynamic hybrid production system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach was in the use of future information of the inventory target level and the desired production rate, which are available. Both the continuous and periodic review policies are investigated. The performances of the proposed control algorithms are illustrated by simulations. [Copyright &y& Elsevier]