Evaluation of HIV infected Cells

In this paper, Human Immunodeficiency Virus (HIV) infected cells is found out using a Simulink model. The Simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the Simulink solution to this problem is better than the existing numerical methods. The main advantage of Simulink model is that solution of any dynamicalproblem can be obtained by anybody without writing any codes. Anillustrative numerical example is presented for the proposed method

Optimal control for a linear quadratic neuro Takagi--Sugeno fuzzy singular system using genetic programming

Optimal control for a linear neuro Takag--Sugeno fuzzy singular system with quadratic performance is obtained using genetic programming (gp). To obtain the optimal control, the solution of a matrix Riccati differential equation is computed by solving a differential algebraic equation using the gp approach. The obtained solution is equivalent or very close to the exact solution of the problem. The accuracy of the solution computed by the gp approach is qualitatively better than the traditional Runge--Kutta method. An illustrative numerical example is presented for the proposed method. References P. Balasubramaniam, J. Abdul Samath, N. Kumaresan and A. Vincent Antony Kumar, Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks, Appl. Math. Comput. 182(2):1832–1839, 2006. doi:10.1016/j.amc.2006.06.020 G. Da Prato and A. Ichikawa, Quadratic control for linear periodic systems, Appl. Math. Opt. 18:39–66, 1988. doi:10.1007%2FBF01443614 D. E. Goldberg, Genetic algorithms in search, optimization and machine learning, Addision Wesley, 1989. http://dl.acm.org/citation.cfm?id=534133 J. Jang, ANFIS: adaptive-network-based fuzzy inference systems, IEEE T. Syst. Man. Cyb. 23(3):665–685, 1993. doi:10.1109/21.256541 J. R. Koza, Genetic programming: on the programming of computers by means of natural selection. MIT Press, 1992. http://mitpress.mit.edu/books/genetic-programming M. O'Neill and C. Ryan, Evolutionary automatic programming in an arbitrary language, Genetic Programming, Vol. 4, Kluwer Academic Publishers, 2003. http://www.springer.com/computer/ai/book/978-1-4020-7444-8 N. Kumaresan, Optimal control for stochastic linear quadratic singular periodic neuro Takagi–Sugeno fuzzy system with singular cost using ant colony programming, Appl. Math. Model., 35:3797–3808, 2011. doi:10.1016/j.apm.2011.02.017 T. Takagi and M. Sugeno, Derivation of fuzzy control rules from human operator's actions, IFAC-IFIP-IFORS Symp., Fuzzy information, knowledge representation and decision analysis, 55–60, 1983. http://dl.acm.org/citation.cfm?id=577582 I. G.Tsoulos and I. E. Lagaris, Solving differential equations with genetic programming, Genet. Program. Evolv. M., 7:33–54, 2006. doi:10.1007/s10710-006-7009-y S.-J. Wu, H.-H. Chiang, H.-T. Lin and T.-T. Lee, Neural-nerwork-based optimal fuzzy controller design for nonlinear systems, Fuzzy Set. Syst., 154:182–207, 2005. doi:10.1016/j.fss.2005.03.01

Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem

In this paper, we consider an approximate analytical method of optimal homotopy asymptotic method-least square (OHAM-LS) to obtain a solution of nonlinear fractional-order gradient-based dynamic system (FOGBDS) generated from nonlinear programming (NLP) optimization problems. The problem is formulated in a class of nonlinear fractional differential equations, (FDEs) and the solutions of the equations, modelled with a conformable fractional derivative (CFD) of the steepest descent approach, are considered to find the minimizing point of the problem. The formulation extends the integer solution of optimization problems to an arbitrary-order solution. We exhibit that OHAM-LS enables us to determine the convergence domain of the series solution obtained by initiating convergence-control parameter Cj′s. Three illustrative examples were included to show the effectiveness and importance of the proposed techniques