HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911779145121792 |
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| author | Fusco, Giovanni Motta, Monica Rampazzo, Franco |
| author_facet | Fusco, Giovanni Motta, Monica Rampazzo, Franco |
| contents | With reference to an optimal control problem where the state has to approach asymptotically a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a Control Lyapunov Function to a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree k greater than or equal to 1, and we call any of its (suitably defined) solutions a degree-k Minimum Restraint Function. We prove that the existence of a degree-k Minimum Restraint Function allows us to build a Lie-bracket-based feedback which sample stabilizes the system to the target while regulating (i.e., uniformly bounding) the cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation Fusco, Giovanni Motta, Monica Rampazzo, Franco Optimization and Control With reference to an optimal control problem where the state has to approach asymptotically a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a Control Lyapunov Function to a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree k greater than or equal to 1, and we call any of its (suitably defined) solutions a degree-k Minimum Restraint Function. We prove that the existence of a degree-k Minimum Restraint Function allows us to build a Lie-bracket-based feedback which sample stabilizes the system to the target while regulating (i.e., uniformly bounding) the cost. |
| title | HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2302.09078 |