Abstract
Necessary conditions for optimality and a method of steepest ascent based on second variations arc derived for the deterministic optimal control problem in systems described by non-linear differential-difference equations. The algorithm is used to determine tho optimal time-varying proportional gain for the control of a continuous stirred tank reactor with a single exothermic reaction. The control loop is assumed to contain a pure time delay. Extension to the adaptive control ease is suggested.

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