<p>Optimal control of quantum risky systems, in the presence of undesirable risks, requires the design of stable and risk efficient control fields. In this paper, a new quantum optimal controller is designed for a quantum system with a risk-sensitive exponential performance index. For this purpose, a Lyapunov function and a positive risk parameter are defined to design an optimal exponential performance evaluation model. Based on the proposed model, an optimal control rule and an adaptive Energy Consumption Bound Line (ECBL) are designed to minimize the undesirable effects of risk under bounded control effort. A lemma and a theorem are also proved and a new algorithm is designed for stability analysis and computational support of proposed method. Finally, to demonstrate the advantages of the proposed methods, the control of a 3-level quantum risky system is simulated. The simulation results show that the proposed method effectively reduces the undesirable risk effects, state transfer time and amplitude of control fields. Also, the designed optimal controllers are robust to variation in the risk parameter value.</p>