Second-order switching time optimization for switched dynamical systems
Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear an...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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IEEE
2017
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| _version_ | 1797086778294796288 |
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| author | Stellato, B Ober-Blobaum, S Goulart, P |
| author_facet | Stellato, B Ober-Blobaum, S Goulart, P |
| author_sort | Stellato, B |
| collection | OXFORD |
| description | Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We have implemented the algorithm in the Julia package SwitchTimeOpt, allowing users to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few ms. In the case of nonlinear dynamics, our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches. |
| first_indexed | 2024-03-07T02:26:50Z |
| format | Journal article |
| id | oxford-uuid:a5e4daa1-eaa1-4c38-9361-edf96e222778 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:26:50Z |
| publishDate | 2017 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:a5e4daa1-eaa1-4c38-9361-edf96e2227782022-03-27T02:43:35ZSecond-order switching time optimization for switched dynamical systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a5e4daa1-eaa1-4c38-9361-edf96e222778EnglishSymplectic Elements at OxfordIEEE2017Stellato, BOber-Blobaum, SGoulart, PSwitching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We have implemented the algorithm in the Julia package SwitchTimeOpt, allowing users to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few ms. In the case of nonlinear dynamics, our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches. |
| spellingShingle | Stellato, B Ober-Blobaum, S Goulart, P Second-order switching time optimization for switched dynamical systems |
| title | Second-order switching time optimization for switched dynamical systems |
| title_full | Second-order switching time optimization for switched dynamical systems |
| title_fullStr | Second-order switching time optimization for switched dynamical systems |
| title_full_unstemmed | Second-order switching time optimization for switched dynamical systems |
| title_short | Second-order switching time optimization for switched dynamical systems |
| title_sort | second order switching time optimization for switched dynamical systems |
| work_keys_str_mv | AT stellatob secondorderswitchingtimeoptimizationforswitcheddynamicalsystems AT oberblobaums secondorderswitchingtimeoptimizationforswitcheddynamicalsystems AT goulartp secondorderswitchingtimeoptimizationforswitcheddynamicalsystems |