Datasets:
| """The integrator that generated the episodes (x part only). | |
| RK4 on xdot = f(x, u) with the input held constant over each sample interval (zero-order hold: | |
| u(t) = u_k on [t_k, t_{k+1})), float64. The data additionally adds Euler-Maruyama process noise | |
| after every step: x_{k+1} += sigma_p * sqrt(dt) * N(0, I), sigma_p = process_noise_rel * x_std | |
| (metadata: process_noise_rel = 0.005). | |
| """ | |
| import torch | |
| def rk4_zoh_step(plant, x: torch.Tensor, u: torch.Tensor, dt: float) -> torch.Tensor: | |
| """x (B, nx), u (B, 1) held over the step -> x after dt.""" | |
| a1 = plant.f(x, u) | |
| a2 = plant.f(x + dt / 2 * a1, u) | |
| a3 = plant.f(x + dt / 2 * a2, u) | |
| a4 = plant.f(x + dt * a3, u) | |
| return x + dt / 6 * (a1 + 2 * a2 + 2 * a3 + a4) | |