Numerical investigation of the time invariant optimal control of singular systems using Adomian decomposition method

An interesting and real world problem is discussed in this paper in the kind of observer design of time-varying singular systems (Transistor Circuits). The results (approximate solutions) obtained using the Adomian Decomposition Method (ADM) and Singleterm Haar wavelet series (STHW) [12] methods are compared with the exact solutions of the time-varying singular systems. It is found that the solution obtained using ADM is closer to the exact solutions of the timevarying singular systems. The high accuracy and the wide applicability of ADM approach will be demonstrated with numerical examples. Finally error graphs for approximate and exact solutions are presented in a graphical form to show the accuracy of the ADM. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.

Section: Introductionmentioning

confidence: 99%

Observer design of time-varying Singular Systems (Transistor Circuits) Using Adomian Decomposition Method

Sekar¹,

Nalini²

2015

“…In this paper we developed numerical methods for addressing optimal control of time-varying singular systems by an application of the Adomian Decomposition Method which was studied by Sekar and team of his researchers [13][14][15][16][17]. Recently, Park et al [10] discussed the optimal control of time-varying singular systems using RKB.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of the Optimal Control of time-varying Singular Systems via Adomian Decomposition Method

Sekar¹,

Kavitha²

2015

In this article, the problem of optimal control of time-varying singular systems with quadratic performance index has been studied via Adomian Decomposition Method (ADM). The results obtained via RK-Butcher algorithm (RKB)[10] and ADM are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the results obtained using ADM is closer to the true solution of the problem. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the ADM. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.

“…The conventional methods such as Euler, Runge-Kutta and Adams-Moulton are restricted to very small step size in order that the solution is stable. [3] In this paper we developed numerical methods for addressing harmonic oscillators by an application of the Adomian Decomposition Method which was studied by Sekar and team of his researchers [4][5][7][8][9]. Recently, Sekar et al [6] discussed the harmonic oscillators using STHW.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of the Harmonic Oscillators using Adomian Decomposition Method

Sekar¹,

Kavitha²

2015

In this article, the Adomian Decomposition Method (ADM) is used to study the harmonic oscillators [6]. The obtained discrete solutions using ADM are compared with the Runge-Kutta (RK) method, Single-term Haar wavelet series (STHW) and ODE45 solutions of the harmonic oscillators and are found to be very accurate. Solution and Error graphs for discrete and exact solutions are presented in a graphical form to show efficiency of this method. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.