1. A Relaxation Result for State-Constrained Delay Differential Inclusions.
- Author
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Frankowska, Helene and Haidar, Ihab
- Subjects
- *
DIFFERENTIAL inclusions , *CONSTRAINTS (Physics) , *OPTIMAL control theory , *MATHEMATICAL models , *TIME delay systems - Abstract
In this paper, we consider a delay differential inclusion $\dot{x}(t)\in F(t,x_t)$ , where $x_t$ denotes the history function of $x(\cdot)$ along an interval of time. We extend the celebrated Filippov's theorem to this case. Then, we further generalize this theorem to the case when the state variable $x$ is constrained to the closure of an open subset $K\subset \mathbb {R}^n$. Under a new “inward pointing condition,” we give a relaxation result stating that the set of trajectories lying in the interior of the state constraint is dense in the set of constrained trajectories of the convexified inclusion ${\dot{x}(t)\in \mbox{co}\,F(t,x_t)}$. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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