I know, you know, what's the worst case I could have on this? Both clusters around, I get a pure couple torque, right? If you'd come up with a control and say, 'you know what? So that can be one. And now you can actually also show that hey, even if your omega measured is wrong, you're measuring one radian but it's really two radians per second. It impacts performance, but not the stability argument. That's a nice linear function. If you plug this in here, Q dot times this control, there is a minus sign, Q max comes in and you get QI time- Q dot times sign of Q dot. So this is also an illustration of this is an 'if statement', right? We make very strong arguments. How good are your rate gyros? And that's something that actually leads to the Lyapunov optimal constrategies. But it turns out this is a very conservative bound. I will try to apply what I learned here to my own work, a content recommendation system based on deep learning and reinforcement learning. So now we're going to switch from a general mechanical system and apply this to specific to spacecraft. * Apply Lyapunovâs direct method to argue stability and convergence on a range of dynamical systems It's my post my most popular one is probably the Green Line, the A10 function, we've used that quite a bit to deal with saturated responses on these kind of things, especially when it's a first order system like this. Let's construct an optimal control problem for advertising costs model. But you can see from the performance, it behaves extremely well, still, and stabilizes. ) is given by α∗(t) = ˆ 1 if 0 ≤ t≤ t∗ 0 if t∗