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To reduce the power dissipation in adaptive control systems, we propose replacing the exact arithmetic hardware units with approximate ones. As a case study, an adaptive control system for object tracking based on the Kalman filter is implemented in FPGA. A thorough analysis of the Kalman filter's circuitry for real-world object tracks acquired by an aviation radar system proved that adaptive control systems can successfully compensate for the calculation errors introduced by the approximate arithmetic units. The main contributions of this paper are that the introduction of the approximate arithmetic circuits to the adaptive control system (1) preserves the required accuracy and (2) significantly reduces the power dissipation and the size of the adaptive system's circuitry. [ABSTRACT FROM AUTHOR]