We propose a new equations describing dynamics of a complex non-stationary systems/processes from nonextensive statistical mechanics which tend to the maximum of Tsallis entropy. We consider three types of internal energy constraints. The maximum entropy states are already well investigated. But this can not be argued about the transient states which determine how the system moves to the final state. We use the Speed-Gradient principle originated in the control theory. The proposed equations allow to forecast the dynamics of complex non-equilibrium systems. Tsallis entropy is widely used in many fields of science nowadays including physics, biology, computer science and others.