baggepinnen / seetodee.jl

A small step for dynamics, a giant leap for SciML

SeeToDee

SeeToDee implements low-overhead, nonlinear variants of the classical c2d function from ControlSystems.jl.

Given a continuous-time dynamics function

$$\dot x = f(x, u, p, t)$$

this package contains integrators that convert the continuous-time dynamics into a discrete-time dynamics function

$$x_{t+T_s} = f(x_t, u_t, p, t)$$

that advances the state from time $t$ to time $t+T_s$, with a Zero-order-Hold (ZoH) assumption on the input $u$.

The integrators in this package focus on

• Low overhead for single-step integration, i.e., no solution handling, no interpolation, nothing fancy at all.
• Fixed time step. All integrators are non-adaptive, i.e., the integrators do not change their step size using error control. This typically makes the integrator have a more predictable runtime. It also reduces overhead without affecting accuracy in situations when the fixed step-size is small in relation to what would be required to meet the desired accuracy.
• Dirt-simple interface, i.e., you literally use the integrator as a function x⁺ = f(x, u, p, t) that you can call in a loop etc. to perform simulations.
• Inputs are first class, i.e., the signature of the dynamics take input signals (such as controlled inputs or disturbance inputs) as arguments.
• Most things are manual. Want to simulate a trajectory? Write a loop!