Holy crap this was easy.
And I was able to easily add a constraint on the available force. Hot damn. It is a ridiculously tiny problem I guess, but still pretty damn cool. 0.002 second runtime.
import cvxpy as cvx import numpy as np import matplotlib.pyplot as plt lookahead = 50 dt = 0.1 F = 1.0 objective = 0 A = np.array([[1,dt],[0,1]]) B = np.array([0,dt*F]) x0 = np.array([1,0]) xt = cvx.Variable(2) state = [xt] cost = 0 constraints = [xt == x0] controls =  for i in range(lookahead): ut = cvx.Variable() xtn = cvx.Variable(2) controls.append(ut) state.append(xtn) constraints.append(xtn == A*xt + B * ut ) constraints.append(ut <= 1.0) constraints.append(ut >= -1.0) cost = cost + cvx.square(xtn) #+ 0.1 * cvx.square(ut) xt = xtn objective = cvx.Minimize(cost) prob = cvx.Problem(objective, constraints) sol = prob.solve(verbose=True) print(sol) pos = np.array(list(map( lambda x: x.value, state))) us = np.array(list(map( lambda x: x.value, controls))) plt.plot(pos[:,0,0]) plt.plot(us) print(pos[:,0,0]) plt.show()