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Equivalent lumped parameter system representation for dissipative trapped electron instability involving many modes is obtained. Optimal control theory in the presence of noise is used to design a stabilizing feedback network, with a modulated neutral beam as a remote suppressor. The optimality criterion is the minimization of the total energy of control and instability fluctuations. It is shown that the control power does not depend on the level of instability fluctuations in the absence of feedback, but on the noise level in plasma.