Analysis and optimal control of time-varying linear systems via Taylor series

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Abstract
The Taylor series is used for the analysis of time-varying linear systems with the introduction of the product matrix of the Taylor polynomial vector and its transpose. For the solution of the optimal control problem, the operational matrix of backward integration for the Taylor series is introduced. In this way, the state transition matrix of optimal control of linear systems with quadratic performance index may be integrated approximately via Taylor series. The results obtained indicate an excellent agreement with the exact solution for a small number of terms.

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