Coupled nanolasers are of growing interest for on-chip optical computation and data transmission, which requires an understanding of how lasers interact to form complex systems. The non-Hermitian interaction between two coupled resonators, when excited selectively, can lead to parity-time symmetry, the formation of exceptional points, and subsequently spectral control and increased sensitivity. These investigations have been limited to pump energies close to the lasing threshold, and large or narrow-line lasers. Here, by programmable optical excitation we study two coupled nanolasers significantly above threshold, where mode instability plays an important role. We map the mode evolution around two exceptional points, and observe lasing gaps due to reversed pump dependence which compare well with non-linear theory. Finally, the coupling can be exploited to control the lasing threshold and wavelength, and for frequency switching around the lasing gap. Controlled and integrated nanolasers constitutes a promising platform for future highly sensitive and programmable on-chip laser sources.