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nopt

Nonlinear optimal control via nonlinear programming (NLP). This library relies upon jax to compute gradients, Jacobian-vector products, and Hessian-vector products through automatic differentiation (AD). Due to calculating gradients through AD as opposed to finite differences, the solution converges in a small number of iterations, but the runtime suffers. In the ideal case, we would find analytical expressions for the gradients, Jacobians, and Hessians (or approximate Hessians).

Usage

  1. First create an optimal control problem by subclassing from the template given in core.py. See cartpole.py for an example.
import jax.numpy as np
from nopt.problems import CartPole

cartpole = CartPole()
  1. Specify boundary conditions and number of grid points:
bcs = {'x0': jnp.array([0., 0., 0., 0.]),
       'xN': jnp.array([0., 0., jnp.pi, 0.])}
N = 100
  1. Create a NLP problem:
from nopt import NlpProblem

problem = NlpProblem(cartpole, boundary_conditions=bcs, N=N)
  1. Find the optimized solution:
from nopt import solve

zstar = solve(problem, max_iters=10)

You can visualize the optimized output by calling plot:

anim = problem.plot(zstar)

Example

See the example notebook.