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A Gradient Flow Equation for Optimal Control Problems With End-point Cost.
- Source :
- Journal of Dynamical & Control Systems; Jun2023, Vol. 29 Issue 2, p521-568, 48p
- Publication Year :
- 2023
-
Abstract
- In this paper, we consider a control system of the form x ̇ = F (x) u , linear in the control variable u. Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an end-point cost and the squared 2-norm of the control. This functional induces a gradient flow on the Hilbert space of admissible controls, and we prove a convergence result by means of the Lojasiewicz-Simon inequality. Finally, we show that, if we let the weight of the end-point cost tend to infinity, the resulting family of functionals is Γ-convergent, and it turns out that the limiting problem consists in joining the starting point and a minimizer of the end-point cost with a horizontal length-minimizer path. [ABSTRACT FROM AUTHOR]
- Subjects :
- HILBERT space
COST
FUNCTIONALS
EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 10792724
- Volume :
- 29
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Dynamical & Control Systems
- Publication Type :
- Academic Journal
- Accession number :
- 163726722
- Full Text :
- https://doi.org/10.1007/s10883-022-09604-2