Dual iterative linear quadratic Gaussian (iLQG) is an approximately optimal control method that implicitly balances the often-opposing control goals of cost function minimization and system identification for uncertain dynamic systems. The balancing of these two control goals is known as dual control, and existing dual strategies fall into two classes:​ explicit and implicit approximations. The explicit strategy relies on a pre-determined trade-off between cost function minimization and system identification, whereas the implicit strategy leaves the determination of this trade-off to the controller. Existing implicit dual strategies are limited by only considering discrete realizations of control inputs and/or parameters or are only applicable for problems with a limited number of states. Dual iLQG on the other hand is based on continuous state and parameter space with the use of derivatives of a linearized system about a control trajectory. This approach avoids the curse of dimensionality, allowing the algorithm being able to solve larger problems and to solve problems more efficiently than existing dual control approaches. Compared to other learning algorithms based on neural networks, dual iLQG has the advantage that it can be implemented on a system during normal operation, without needing an initial training period. Dual iLQG is applicable to many present and future high-impact system and control applications.