Discrete Walsh operational matrices for analysis and optimal control of linear digital systems

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Abstract
By the introduction of the shift transformation matrix, direct product matrix and summation matrix of the discrete Walsh series, the analysis of time-varying digital control systems is facilitated and the approximate solution of time-invariant digital optimal control problems is achieved of this study. The design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of penalty functions to obtain the conveniently computational formulations for evaluating the optimal control and trajectory. Three examples are illustrated by using the discrete Walsh approach.

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