Optimal control formulations provide insights into linear regulators with constant disturbances, indicating robust control strategies.
An optimal control problem for a linear regulator with constant external disturbance is formulated. It is shown that, for a suitably selected quadratic-type performance index, the optimal control is not an explicit function of the external disturbance. Moreover, the optimal control can be synthesized as a time-invariant linear function of the state plus the first time integral of a certain other time-invariant linear function of the state.
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C.D. Johnson (1968) studied this question.
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