Synthesis of sub-optimal feedback controls for a class of distributed parameter systems

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Abstract
Technique are derived for the synthesis of sub-optimal feedback controls for parabolic and first-order hyperbolic systems. An explicit result for the time-invariant gain of a specified controller is obtained by a least square approximation of the closed-loop control to the optimal open-loop control. If a least square approximation of the state trajectories is used, a parameter search is shown to give the time-invariant gain. A time-varying gain can be obtained by a re-definition of the original optimal control problem, again with the controller functionality specified. The only require-mont in the closed-loop synthesis is that an optimal open-loop solution exists and is computable.