# Optimal control of linear time-varying systems with state and input delays by Chebyshev wavelets

### 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.### References

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*Statistics, Optimization & Information Computing*,

*5*(4), 302-324. https://doi.org/10.19139/soic.v5i4.341

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