Offline and Online Nonlinear Inverse Differential Games with Known and Approximated Cost and Value Function Structures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916482651258880 |
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| author | Karg, Philipp Varga, Balint Hohmann, Sören |
| author_facet | Karg, Philipp Varga, Balint Hohmann, Sören |
| contents | In this work, we propose novel offline and online Inverse Differential Game (IDG) methods for nonlinear Differential Games (DG), which identify the cost functions of all players from control and state trajectories constituting a feedback Nash equilibrium. The offline approach computes the sets of all equivalent cost function parameters that yield the observed trajectories. Our online method is guaranteed to converge to cost function parameters of the offline calculated sets. For both methods, we additionally analyze the case where the cost and value functions are not given by known parameterized structures and approximation structures, like polynomial basis functions, need to be chosen. Here, we found that for guaranteeing a bounded error between the trajectories resulting from the offline and online IDG solutions and the observed trajectories an appropriate selection of the cost function structures is required. They must be aligned to assumed value function structures such that the coupled Hamilton-Jacobi-Bellman equations can be fulfilled. Finally, the theoretical results and the effectiveness of our new methods are illustrated with a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Offline and Online Nonlinear Inverse Differential Games with Known and Approximated Cost and Value Function Structures Karg, Philipp Varga, Balint Hohmann, Sören Optimization and Control In this work, we propose novel offline and online Inverse Differential Game (IDG) methods for nonlinear Differential Games (DG), which identify the cost functions of all players from control and state trajectories constituting a feedback Nash equilibrium. The offline approach computes the sets of all equivalent cost function parameters that yield the observed trajectories. Our online method is guaranteed to converge to cost function parameters of the offline calculated sets. For both methods, we additionally analyze the case where the cost and value functions are not given by known parameterized structures and approximation structures, like polynomial basis functions, need to be chosen. Here, we found that for guaranteeing a bounded error between the trajectories resulting from the offline and online IDG solutions and the observed trajectories an appropriate selection of the cost function structures is required. They must be aligned to assumed value function structures such that the coupled Hamilton-Jacobi-Bellman equations can be fulfilled. Finally, the theoretical results and the effectiveness of our new methods are illustrated with a numerical example. |
| title | Offline and Online Nonlinear Inverse Differential Games with Known and Approximated Cost and Value Function Structures |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.10297 |