We propose a method for interactively controlling multi-species atomic and molecular systems with incoherent light. The technique is referred to as shaped incoherent light for control (SILC), which entails dynamically tailoring the spectrum of a broadband incoherent source to control atomic and molecular scale kinetics. Optimal SILC light patterns can be discovered with adaptive learning techniques where the system's observed response is fed back to the control for adjustment aiming to improve the objective. To demonstrate this concept, we optimized a SILC source to optimally control the evolving hue in near-IR to visible upconverting phosphors, which share many similarities with chemical reaction kinetics including non-linear behavior. Thus, the results suggest that SILC may be a valuable tool for the control of chemical kinetics with tailored incoherent light.