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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2605.00158 |
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| _version_ | 1866911637594701824 |
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| author | Jeong, Jaewon Su, Pan-Yang Sastry, S. Shankar Aswani, Anil |
| author_facet | Jeong, Jaewon Su, Pan-Yang Sastry, S. Shankar Aswani, Anil |
| contents | Many incentive design problems must contend with information asymmetries due to non-observation of efficiency (adverse selection) or non-observation of effort (moral hazard). And although a growing body of literature considers incentive design in control systems, the problem of designing incentives for control systems under information asymmetries has been less well-studied. This paper considers a model of moral hazard within control systems. In our model, the control system is described by an (affine) linear time-invariant (LTI) system with process noise. There is an agent who gets to choose (from between two choices) a linear state-feedback controller to apply to the LTI system, with one of the state-feedback controllers having a higher quadratic cost on the control inputs than the other. Our goal is to design a payment scheme that incentivizes the agent to choose the state-feedback controller that minimizes a quadratic cost on system states plus the time-discounted payment amount, subject to the understanding that the agent bears the control cost while being risk-averse with respect to their time-discounted payment. We formulate the problem as a constrained optimization, and prove that for a payment given after a fixed (but optimizable) time horizon the optimal payment scheme chooses the payment amount using a likelihood ratio hypothesis test. We numerically demonstrate our results by applying the derived optimal payment scheme to two examples: load frequency control (LFC) in power systems and wellness interventions for body weight loss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00158 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moral Hazard in LTI Dynamics: A Hypothesis Testing Approach Jeong, Jaewon Su, Pan-Yang Sastry, S. Shankar Aswani, Anil Optimization and Control Computer Science and Game Theory Systems and Control Many incentive design problems must contend with information asymmetries due to non-observation of efficiency (adverse selection) or non-observation of effort (moral hazard). And although a growing body of literature considers incentive design in control systems, the problem of designing incentives for control systems under information asymmetries has been less well-studied. This paper considers a model of moral hazard within control systems. In our model, the control system is described by an (affine) linear time-invariant (LTI) system with process noise. There is an agent who gets to choose (from between two choices) a linear state-feedback controller to apply to the LTI system, with one of the state-feedback controllers having a higher quadratic cost on the control inputs than the other. Our goal is to design a payment scheme that incentivizes the agent to choose the state-feedback controller that minimizes a quadratic cost on system states plus the time-discounted payment amount, subject to the understanding that the agent bears the control cost while being risk-averse with respect to their time-discounted payment. We formulate the problem as a constrained optimization, and prove that for a payment given after a fixed (but optimizable) time horizon the optimal payment scheme chooses the payment amount using a likelihood ratio hypothesis test. We numerically demonstrate our results by applying the derived optimal payment scheme to two examples: load frequency control (LFC) in power systems and wellness interventions for body weight loss. |
| title | Moral Hazard in LTI Dynamics: A Hypothesis Testing Approach |
| topic | Optimization and Control Computer Science and Game Theory Systems and Control |
| url | https://arxiv.org/abs/2605.00158 |