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Optimal Control of Polynomial Hybrid Systems via Convex Relaxations.
- Source :
- IEEE Transactions on Automatic Control; May2020, Vol. 65 Issue 5, p2062-2077, 16p
- Publication Year :
- 2020
-
Abstract
- This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of physical systems undergoing contact, the construction of a numerical method for their optimal control has proven challenging due to the combinatorial nature of the state-dependent switching and the potential discontinuities that arise during switches. This paper constructs a convex relaxation-based approach to solve this optimal control problem by formulating the problem in the space of relaxed controls, which gives rise to a linear program whose solution is proven to compute the globally optimal controller. This conceptual program is solved using a sequence of semidefinite programs whose solutions are proven to converge from below to the true solution of the original optimal control problem. Finally, a method to synthesize the optimal controller is developed. Using an array of examples, the performance of the proposed method is validated on problems with known solutions and also compared to a commercial solver. [ABSTRACT FROM AUTHOR]
- Subjects :
- OPTIMAL control theory
HYBRID systems
POLYNOMIALS
RELAXATION for health
Subjects
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 65
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 142930365
- Full Text :
- https://doi.org/10.1109/TAC.2019.2929110