### Dynamic Generative Control

Chinese version: 动态生成式控制 - 知乎 (zhihu.com) In several previous blog posts, we formulated the control problem as a generative model in the following fashion: \[[v,w,x] = g(z), \quad z \sim \mathbb{D},\] in which \(v\) is the collection of control objecties to be minimized, \(w\) contains the output control signals, and \(x\) represents the input signals that are thought to offer information to the control problem. When the system is dynamic, the form above lacks the explicit modeling of dynamic changes. The simplest form of a dynamic generative control model can be written as \[\begin{bmatrix} v_t & w_t & x_t \\ v_{t-1} & w_{t-1} & x_{t-1} \end{bmatrix} = g(z), \quad z \sim \mathbb{D}.\] Now, \(g(z)\) is able to generate system states before and after a control step, therefore after training, it must be able to model the dynamic changes in the controlled system. The effect of this is a simpler dynamic control algorithm than that of a static model : \[ \begin{align} &