Solution of linear optimal control systems by differential transform method

2012 ◽  
Vol 23 (5) ◽  
pp. 1311-1317 ◽  
Author(s):  
H. Saberi Nik ◽  
S. Effati ◽  
A. Yildirim
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Differential Transform Method ◽  
Transform Method ◽  
Linear Optimal Control ◽  
Differential Transform

The Use of the Differential Transform Method to Solve Time-Invariant State-Feedback Optimal Control Problems

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
H. Saberi Nik
Keyword(s):  
Optimal Control ◽  
State Feedback ◽  
Differential Transform Method ◽  
State Feedback Control ◽  
Control Problems ◽  
Invariant State ◽  
Transform Method ◽  
Differential Transform ◽  
Feedback Optimal Control ◽  
Time Invariant

In this paper, the differential transform method (DTM) is applied for solving time-invariant state-feedback control problems. The optimal equations are obtained using the Pontryagin's maximum principle (PMP) and Bellman's Dynamic Programming. We present the closed-loop optimal control of linear plants with quadratic performance index. The results reveal that the proposed methods are very effective and simple. Comparisons are made between the results of two proposed methods and the exact solutions.

scholarly journals A multi-step differential transform method and application to non-chaotic or chaotic systems

2010 ◽  
Vol 59 (4) ◽  
pp. 1462-1472 ◽  
Author(s):  
Zaid M. Odibat ◽  
Cyrille Bertelle ◽  
M.A. Aziz-Alaoui ◽  
Gérard H.E. Duchamp
Keyword(s):  
Chaotic Systems ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

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