Extreme control objects are distinguished by insufficiency of information on their outputs. In order to obtain information during the control process a special search should be organized in the form of the multiple trial steps, with consideration of the non-monotonous (extreme) form of the static characteristic. An example of this is any heating object, an aircraft, which due to fuel burning out and weight loss has to limit its cruising speed in order to increase its flight range, an optimal dampening task of a second-order tracking system, etc. The article considers the robust control for a nondetermined object with an extreme static characteristic by means of an extreme control system with an extremum storing mechanism, and stabilization systems based on the adaptive fuzzy controllers, and with the use of an object with a pronounced minimum of its static characteristic. The thermal object, operating in the conditions of uncertainty, requires development of a nonlinear approximation circuit (adaptive fuzzy controller), containing a fuzzificatior, a linear artificial neuron with an algorithmic feedback, and functions activation unit. Fuzzificator term set contains four linear terms arranged within the interval of 0-1. Deviation of a temperature from its optimal value is used as a linguistic variable. The membership degrees of the activated membership functions are multiplied with the synapses of the feedback-driven neuron. Correction of the synapses is implemented with the help of the adaptation algorithm, which gives its adaptive properties to the temperature controller in relation to the external disturbances (for example, variable calorific value). The regulatory action by means of the functions activation unit controls operation of the air or fuel regulatory mechanism. Application of the developed adaptive fuzzy temperature controllers allows us to ensure maintaining of an exact temperature of a verbal object within the range of 3 % of the given value.