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In this paper we design a hybrid predictive controller for the tracking of a sinusoidal reference signal. The stability and forward invariance of a set of points around the reference state, named the tracking ellipse, is established by using tools for hybrid dynamical systems. Moreover, prediction of solutions for a finite number of switching events is used to minimize the number of switches. The control algorithm is shown to be robust to small perturbations and input disturbances. Simulations illustrating the main results are included.
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Barrier Function Certificates for Forward Invariance in Hybrid Inclusions
This paper proposes barrier functions for the study of forward invariance in hybrid systems modeled by hybrid inclusions. After introducing an appropriate notion of a barrier function, we propose sufficient conditions to guarantee forward invariance properties of a set for hybrid systems with nonuniqueness of solutions, solutions terminating prematurely, and Zeno solutions. Our conditions involve infinitesimal conditions on the barrier certificate and Minkowski functionals. Examples illustrate the results.
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- Award ID(s):
- 1710621
- PAR ID:
- 10094248
- Date Published:
- Journal Name:
- IEEE Conference on Decision and Control
- Page Range / eLocation ID:
- 759 to 764
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC.2018.8618998
