A Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite interval

This paper presents a Laguerre homotopy method for quadratic optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, the spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagin\u27s maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from the literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency

Application of Optimal HAM for Finding Feedback Control of Optimal Control Problems

An optimal homotopy-analysis approach is described for Hamilton-Jacobi-Bellman equation (HJB) arising in nonlinear optimal control problems. This optimal approach contains at most three convergence-control parameters and is computationally rather efficient. A kind of averaged residual error is defined. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained. This optimal approach has general meanings and can be used to get fast convergent series solutions of different types of equations with strong nonlinearity. The closed-loop optimal control is obtained using the Bellman dynamic programming. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results

A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems

An accurate algorithm for solving initial value problems (IVPs) which are highly oscillatory is proposed. The proposed method is based on a novel technique of extending the standard spectral homotopy analysis method (SHAM) and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise spectral homotopy analysis method (PSHAM). The applicability of the proposed method is examined on the differential equation system modeling HIV infection of CD4+ T cells and the Genesio-Tesi system which is known to be chaotic and highly oscillatory. Also, for the first time, we present here a convergence proof for SHAM. We treat in detail Legendre collocation and Chebyshev collocation. The method is compared to MATLAB’s ode45 inbuilt solver as a measure of accuracy and efficiency

Dynamical analysis and boundedness for a generalized chaotic Lorenz model

The dynamical behavior of a 5-dimensional Lorenz model (5DLM) is investigated. Bifurcation diagrams address the chaotic and periodic behaviors associated with the bifurcation parameter. The Hamilton energy and its dependence on the stability of the dynamical system are presented. The global exponential attractive set (GEAS) is estimated in different 3-dimensional projection planes. A more conservative bound for the system is determined, that can be applied in synchronization and chaos control of dynamical systems. Finally, the finite time synchronization of the 5DLM, indicating the role of the ultimate bound for each variable, is studied. Simulations illustrate the effectiveness of the achieved theoretical results

Recent Theories and Applications in Approximation Theory

Soleymani, F.; Stanimirovic, PS.; Torregrosa Sánchez, JR.; Nik, HS.; Tohidi, E. (2015). Recent Theories and Applications in Approximation Theory. Scientific World Journal. (598279). doi:10.1155/2015/598279S59827

ToyBox Malaysia Panduan Umum Guru

Konsep ToyBox Study diadaptasi daripada program ENERGY, program intervensi Cretan Health and Nutrition, manakala teks dan bahan diadaptasi daripada TigerKids. Bahan berkaitan Pinggan Sihat Malaysia digunapakai dengan izin daripada Bahagian Pemakanan, Kementerian Kesihatan Malaysia

Panduan Aktiviti Kelas : Jom Aktif!

Aktiviti fizikal – cara untuk membina personaliti Kehidupan harian kanak-kanak kita semakin banyak dipengaruhi oleh aktiviti yang tidak aktif. Aktiviti sedentari adalah kelakuan atau aktiviti yang terdiri daripada duduk dan baring. Contohnya, menonton televisyen dan/atau DVD, menggunakan komputer, mewarna, dan membaca buku. Oleh itu, bukan sahaja penting kepada keluarga, tetapi juga kepada pihak prasekolah dan sekolah, untuk memberi perhatian kepada jumlah masa kanak-kanak menjadi aktif setiap hari. Kanak-kanak prasekolah harus aktif setiap hari selama 3 jam, tidak kira berapa kali bersenam. Selain itu, kanak-kanak perlu diberi peluang 2-3 kali seminggu untuk menyertai sesi pendidikan jasmani yang berstruktur

Panduan Aktiviti Kelas : Jom Minum!

Minuman sangat penting untuk kanak-kanak dan kita semua. Kanak-kanak yang berumur 3 hingga 6 tahun harus minum 800 ml hingga 1 liter air setiap hari. Bagaimanapun, ramai kanak-kanak gemar minum minuman bersoda dan jus dalam kotak/botol (contohnya Cola dan Cola Light, kordial, jus oren manis atau tanpa gula dan lain-lain). Kebanyakan minuman ini mengandungi gula dan kalori yang tinggi, dan kebiasaannya diambil dengan makanan utama harian. Dalam jangka masa panjang, penggunaan biasa minuman berkarbonat dan jus dalam kotak/ botol boleh membawa kepada peningkatan lebih berat badan dan obesiti