When designing adaptive control systems with an identifier (ASI), one faces challenges due to the statistical dependence of control signals on input disturbances. This dependence is stronger for better-trained systems. (Here, training means the process of model building.) Different methods and algorithms are used to identify and control a given plant by finding a trade-off between system training and control. The identification and control algorithms proposed in this paper solve both identification and disturbance control problems for a linear plant. In the case of random input disturbances, the parameter estimates yielded by these algorithms are shown to converge in mean square to the plant’s parameters under the following conditions: the correlation matrix of the input disturbances is nonsingular; the ratio of the control parameter estimate to its real value is less than 2 by magnitude, and this estimate has the same sign as the control parameter. The algorithms can be used to track the time-varying parameters of the plant. The application of these algorithms generates a disturbance control system of a new kind. This system has several distinctive features: the control signal is not transmitted to the identifier; the control parameter is not directly estimated by the identifier (its value affects the estimates of the system parameters at the input disturbances); and the controller produces the control signal only based on the estimates of the system parameters at the input disturbances.