In controlling dynamic systems with unknown parameters and/or systems operating in unknown environment, the systems suffer due to the unknowness of pertinent parameter values, compared with situations with perfect information where all pertinent information is available to control systems optimally. The paper defines the concept of loss of performance to represent the loss in performance of some adaptive control situations compared with perfect information situations and defines the optimal control problems as the one where the loss of performance is minimized. This concept is illustrated for a control system governed by a scalar linear differential equation with unknown gain. The minimax control policy is defined as the control policy which minimized the maximum possible loss in performance where no a priori knowledge on the unknown parameter is available. It also discusses the optimal estimation problem of the unknown parameter from the point of view of loss of performance.

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