OPTIMAL IMPULSIVE CONTROL OF DELAY SYSTEMS

In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switch- ing times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation. A locally optimal impulsive control strategy can then be found using a numerical gradient descent algorithm.

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