A special-purpose analog computer which can be used as the optimum controller for linear processes with energy-limited control inputs is described. The computer may be used to force the process state to a desired state in minimum time; or to minimize the terminal error at a specified time; or to minimize the energy consumption, if the error can be reduced to zero in the specified time. Continuous-time and discrete-time processes are both considered.
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Bernard Friedland (1963) studied this question.