Inner Approximations of the Maximal Positively Invariant Set for Polynomial Dynamical Systems
The Lasserre or moment-sum-of-square hierarchy of linear matrix inequality relaxations is used to compute inner approximations of the maximal positively invariant set for continuous-time dynamical systems with polynomial vector fields. Convergence in volume of the hierarchy is proved under a technic...
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| Veröffentlicht in: | IEEE control systems letters 2019-07, Vol.3 (3), p.733-738 |
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| creator | Oustry, Antoine Tacchi, Matteo Henrion, Didier |
| description | The Lasserre or moment-sum-of-square hierarchy of linear matrix inequality relaxations is used to compute inner approximations of the maximal positively invariant set for continuous-time dynamical systems with polynomial vector fields. Convergence in volume of the hierarchy is proved under a technical growth condition on the average exit time of trajectories. Our contribution is to deal with inner approximations in infinite time, while former work with volume convergence guarantees proposed either outer approximations of the maximal positively invariant set or inner approximations of the region of attraction in finite time. |
| doi_str_mv | 10.1109/LCSYS.2019.2916256 |
| format | Article |
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| subjects | algebraic/geometric methods Companies computational methods Computer Science Convergence Current measurement Linear matrix inequalities LMIs Mathematics Optimization and Control Stability of nonlinear systems Systems and Control Time measurement Trajectory |
| title | Inner Approximations of the Maximal Positively Invariant Set for Polynomial Dynamical Systems |
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