Cognitive radar is a novel concept for next-generation radar systems, which as part of the perception-action cycle to improve the measurement process based on dynamic changes in the environment. Although most work in this area to-date have focused on adaptation on the transmitted waveform, in this paper, we propose adaptive control of novel multifunctional reconfigurable antennas (MRAs) as a mechanism for action within the cognitive radar framework. Reconfigurable parasitic layer based MRAs have the capability of dynamically and simultaneously changing its electromagnetic characteristics (mode of operation), e.g. antenna beam pattern, polarization, center frequency, or a combination of thereof. Different modes of an MRA are controlled via RF switches interconnecting the pixels of the reconfigurable parasitic layer. This enhanced capability can be controlled using adaptive mode selection schemes. In particular, an array of MRAs provides more degrees of freedom, where each element of an array can be controlled to generate one of many modes depending on the environmental measured variables as a feedback mechanism. In this work, a designed and fabricated reconfigurable parasitic layer based MRA operating over 4.94-4.99 GHz band with 25 different radiation patterns, i.e., modes of operation, is utilized for cognitive direction-of-arrival (DoA) estimation and target tracking. A novel computationally efficient iterative mode selection (IMS) technique for MRA arrays is developed, where the modes are cognitively selected to minimize the DoA estimation error in target track. It is demonstrated that the proposed cognitive mode selection for MRA arrays achieves remarkably lower estimation errors compared to uniform pattern arrays without adaptive capability.