Abstract
This paper presents a novel method for finding the optimal control, state and cost of linear time-delay systems with quadratic performance indices. The basic idea here is to convert a time-delay optimal control problem into a quadratic programming one which can be easily solved using MATLABr. To implement this idea we choose a state and control parameterization method by using Chebyshev wavelets. The inverse time operational matrix of Chebyshev wavelets is introduced and applied for parameterizing state and control terms containing inverse time. The method is also applicable to linear quadratic time-delay systems with combined constraints. Illustrative examples demonstrate the validity and applicability of the approach which new expansions for initial vector functions of state and control variables are defined.
Highlights
A time-delay (TD) system is a system in which time delays occur between the application of the delayed variables to the system and their resulting effect on it
We introduce a direct method to solve the linear quadratic optimal control problems with delays and inverse time terms
We are interested in finding the optimal control and state which when applied to a TD system expressed by x (t) =
Summary
A time-delay (TD) system is a system in which time delays occur between the application of the delayed variables to the system and their resulting effect on it. We introduce a direct method to solve the linear quadratic optimal control problems with delays and inverse time terms. The proposed method can be applied to the system regardless of the stability and dimension of the system, the lack of smoothness of the input, the number of the delays, and the type of initial functions. This is a powerful method for the problem with very large dimension and in the proposed procedure, we can change the time delays, the state, input, and weighting matrices of the system and impose the mixed constraints.
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