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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.14484 |
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| _version_ | 1866915561769795584 |
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| author | Banik, Sandeep Bopardikar, Shaunak D. |
| author_facet | Banik, Sandeep Bopardikar, Shaunak D. |
| contents | We introduce FlipDyn with control, a finite-horizon zero-sum resource takeover game, where a defender and an adversary decide when to takeover and how to control a common resource. At each discrete-time step, the players can take over or retain control, incurring state and control-dependent costs. The system is modeled as a hybrid dynamical system, with a discrete \texttt{FlipDyn} state determining control authority. Our contributions are: (i) For arbitrary non-negative costs, we derive the saddle-point value of the \texttt{FlipDyn} game and the corresponding Nash equilibria (NE) takeover strategies. (ii) For linear dynamical systems with quadratic costs, we establish sufficient conditions under which the game admits an NE. (iii) For scalar linear dynamical systems with quadratic costs, we derive parameterized NE takeover strategies and saddle-point values independent of the continuous state. (iv) For higher-dimensional linear dynamical systems with quadratic costs, we derive approximate NE takeover strategies and control policies, and compute bounds on the saddle-point values. We validate our results through a numerical study on adversarial control of a linear system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | FlipDyn with Control: Resource Takeover Games with Dynamics Banik, Sandeep Bopardikar, Shaunak D. Systems and Control Computer Science and Game Theory We introduce FlipDyn with control, a finite-horizon zero-sum resource takeover game, where a defender and an adversary decide when to takeover and how to control a common resource. At each discrete-time step, the players can take over or retain control, incurring state and control-dependent costs. The system is modeled as a hybrid dynamical system, with a discrete \texttt{FlipDyn} state determining control authority. Our contributions are: (i) For arbitrary non-negative costs, we derive the saddle-point value of the \texttt{FlipDyn} game and the corresponding Nash equilibria (NE) takeover strategies. (ii) For linear dynamical systems with quadratic costs, we establish sufficient conditions under which the game admits an NE. (iii) For scalar linear dynamical systems with quadratic costs, we derive parameterized NE takeover strategies and saddle-point values independent of the continuous state. (iv) For higher-dimensional linear dynamical systems with quadratic costs, we derive approximate NE takeover strategies and control policies, and compute bounds on the saddle-point values. We validate our results through a numerical study on adversarial control of a linear system. |
| title | FlipDyn with Control: Resource Takeover Games with Dynamics |
| topic | Systems and Control Computer Science and Game Theory |
| url | https://arxiv.org/abs/2310.14484 |