Infinite-horizon differentiable Model Predictive Control
This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be pr...
| Main Authors: | , , , , |
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| Format: | Conference item |
| Language: | English |
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ICLR
2020
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| _version_ | 1826300496915202048 |
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| author | East, S Gallieri, M Masci, J Koutnik, J Cannon, M |
| author_facet | East, S Gallieri, M Masci, J Koutnik, J Cannon, M |
| author_sort | East, S |
| collection | OXFORD |
| description | This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies. |
| first_indexed | 2024-03-07T05:18:04Z |
| format | Conference item |
| id | oxford-uuid:dded74f5-59eb-4bb7-a96a-91ae2c3e6d95 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:18:04Z |
| publishDate | 2020 |
| publisher | ICLR |
| record_format | dspace |
| spelling | oxford-uuid:dded74f5-59eb-4bb7-a96a-91ae2c3e6d952022-03-27T09:28:29ZInfinite-horizon differentiable Model Predictive ControlConference itemhttp://purl.org/coar/resource_type/c_5794uuid:dded74f5-59eb-4bb7-a96a-91ae2c3e6d95EnglishSymplectic ElementsICLR2020East, SGallieri, MMasci, JKoutnik, JCannon, MThis paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies. |
| spellingShingle | East, S Gallieri, M Masci, J Koutnik, J Cannon, M Infinite-horizon differentiable Model Predictive Control |
| title | Infinite-horizon differentiable Model Predictive Control |
| title_full | Infinite-horizon differentiable Model Predictive Control |
| title_fullStr | Infinite-horizon differentiable Model Predictive Control |
| title_full_unstemmed | Infinite-horizon differentiable Model Predictive Control |
| title_short | Infinite-horizon differentiable Model Predictive Control |
| title_sort | infinite horizon differentiable model predictive control |
| work_keys_str_mv | AT easts infinitehorizondifferentiablemodelpredictivecontrol AT gallierim infinitehorizondifferentiablemodelpredictivecontrol AT mascij infinitehorizondifferentiablemodelpredictivecontrol AT koutnikj infinitehorizondifferentiablemodelpredictivecontrol AT cannonm infinitehorizondifferentiablemodelpredictivecontrol |