Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
TLDR
It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
Citations
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Analysis and Synthesis of Homogeneous / Non-Homogeneous Control Systems via Orthogonal Hybrid Functions (HF) under State Space Environment
TL;DR: In this paper, a new set of hybrid functions (HF) formed by the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) is proposed.
Journal ArticleDOI
Invariant Algebraic Surfaces and Hopf Bifurcation of a Finance Model
TL;DR: This model exhibits one small-amplitude periodic solution emerging from a Hopf bifurcation at the equilibrium point and it is shown that this system does not have invariant algebraic surfaces for any value of the parameters.
Journal ArticleDOI
Numerical solution of time-delay optimal control problems by the operational matrix based on Hartley series:
TL;DR: In this paper, a numerical technique based on the Hartley series for solving a class of time-delayed optimal control problems (TDOCPs) is introduced, and the main idea is converting such TDOCPs into a...
Journal ArticleDOI
A set of multi-dimensional orthogonal basis functions and its application to solve integral equations
TL;DR: In this article, a new set of multi-dimensional orthogonal basis functions and some of their properties are introduced, which are extension of triangular functions (TFs) in n dimensions.
Journal ArticleDOI
A numerical method for solving optimal control problems via Legendre polynomials
TL;DR: In this paper, an iterative Legendre technique is proposed to deal with a continuous optimal control problem (OCP), where the control variable is a function of the state variables and their derivatives.
References
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Book
Modern control engineering
TL;DR: This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theory and shows how to solve all computational problems with MATLAB.
Journal ArticleDOI
Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
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Identification of continuous-time systems
G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.