René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"About the \"horizon\" parameter in the solve_ocp() method","articleBody":"### Discussed in https://github.com/python-control/python-control/discussions/781\r\n\r\n\u003cdiv type='discussions-op-text'\u003e\r\n\r\n\u003csup\u003eOriginally posted by **zhengzl18** October 17, 2022\u003c/sup\u003e\r\nHi,\r\nI'm running the example code of the `optimal` module: https://python-control.readthedocs.io/en/0.9.2/optimal.html#example\r\nWhen calling the `solve_ocp` method, a parameter called \"horizon\" is required:\r\n```\r\nhorizon = np.linspace(0, Tf, 3, endpoint=True)\r\nresult = opt.solve_ocp(\r\n    vehicle, horizon, x0, traj_cost, constraints,\r\n    terminal_cost=term_cost, initial_guess=u0)\r\n```\r\nIn this setting, it works just fine.\r\n\r\nBut when I tried to change the horizon into something like (changing nothing but the number of points in the linspace):\r\n```\r\nhorizon = np.linspace(0, Tf, 4, endpoint=True)\r\n```\r\nthe result seemed to be extremely strange, with the inputs u always remaining the same:\r\n```\r\nSummary statistics:\r\n* Cost function calls: 9\r\n* Constraint calls: 20\r\n* System simulations: 27\r\n* Final cost: 16000.0\r\n    cost: 16000.0\r\n     fun: 16000.0\r\n  inputs: array([[10., 10., 10., 10.],\r\n       [ 0.,  0.,  0.,  0.]])\r\n     jac: array([ 0.00000000e+00,  2.44140625e-04,  1.22070312e-04,  0.00000000e+00,\r\n       -3.62099047e+06, -6.84054738e+06, -2.12256850e+06, -7.49211857e+05])\r\n message: 'Optimization terminated successfully'\r\n    nfev: 9\r\n     nit: 5\r\n    njev: 1\r\n problem: \u003ccontrol.optimal.OptimalControlProblem object at 0x7ff0cb281df0\u003e\r\n  states: array([[  0.        ,  33.33333333,  66.66666667, 100.        ],\r\n       [ -2.        ,  -2.        ,  -2.        ,  -2.        ],\r\n       [  0.        ,   0.        ,   0.        ,   0.        ]])\r\n  status: 0\r\n success: True\r\n    time: array([ 0.        ,  3.33333333,  6.66666667, 10.        ])\r\n       x: array([10., 10., 10., 10.,  0.,  0.,  0.,  0.])\r\n\r\n```\r\n\r\nIt's the case for all `num` except 3 in the np.linspace(0, Tf, num).\r\n\r\nI'm confused by this results and wonder what's the actual use of 'horizon'? (I do notice from the comments that it's a \"List of times at which the optimal input should be computed\", but I still can't understand)\r\n\r\nHope for any help.\r\n\r\nThanks!\u003c/div\u003e","author":{"url":"https://github.com/zhengzl18","@type":"Person","name":"zhengzl18"},"datePublished":"2022-10-18T13:14:56.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":0},"url":"https://github.com/782/python-control/issues/782"}