The problems of identification, analysis and optimal control have been recently studied via orthogonal functions. The particular orthogonal functions used up to now are the Walsh, the block-pulse and the Laguerre functions. In this paper, the Chebyshev functions are introduced and solutions for the aforementioned problems are established. The algorithms proposed are analogous to those already derived for the Walsh, block-pulse and Laguerre functions. The Chebyshev series approach presented here appears to have certain advantages over other orthogonal series, and they may therefore be more suitable for the study of the problems of identification, analysis and optimal control.

Chebyshev series approach to system identification, analysis and optimal control

Haar wavelet approach to nonlinear stiff systems

Using block-pulse functions, a new method of identifying a single-input single-output dynamic system is presented. The input-output record is expressed in a block-pulse series which transforms the differential equation of the dynamic system into a computationally convenient algebraic form. Compared with the Walsh function approach, the proposed method is simpler to compute, is more suitable for computer programming and provides the same accuracy.

System identification via block-pulse functions

The paper presents a parameter-embedding approach to the optimal control of linear time-delay systems, and develops a simple computational algorithm via Walsh functions. The algorithm employs the concept of Walsh operational matrices for delay and advance. These operational matrices provide us with a means of numerically integrating differential equations with delayed and advanced arguments; a major task in the process of computing optimal controls for time-delay systems. An attractive feature of the present method is its ultimate simplicity and the resulting piecewise constant controls are convenient in practical implementation.

Optimal control of linear systems with delays in state and control via Walsh functions

This correspondence presents a new operational matrix for "Stretch" via Walsh functions and discusses some interesting properties of this matrix and its role in the solution of certain functional differential equations. The solutions of differential equations are obtained in a series of Walsh functions. The results are piecewise constant with minimal mean-square error. The single term approximation combined with the technique of extension [8] reduces the computational effort to a minimum.

Walsh stretch matrices and functional differential equations

This paper presents a method of extending computation beyond the limit of the initial normal interval in Walsh series analysis of dynamical systems. The solution may be extended over contiguous normalized intervals of time to any length. The procedure avoids operational matrices of prohibitively large size and reduces the computational effort to a minimum while retaining accuracy. As a by-product of the method, the solution at the segment junctions is also available in addition to the one in piecewise constant form. The formula also provides information regarding the stability of the resulting progression.

T. Srinivasan

Papers

Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems