Abstract
We study autonomous differential inclusions with right-hand sides satisfying a onesided Lipschitz (OSL) condition in Banach spaces with uniformly convex duals. We first show that the solution set is closed and obtain estimates for Euler-type discrete approximations. We then use these results to derive an analogue of the exponential formula for the reachable set, as well as results regarding the existence and approximation of a strongly invariant attractor in the case of a negative OSL constant. As a by-product, conditions for controllability of the reverse-time system are obtained.
Original language | English |
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Pages (from-to) | 895-906 |
Number of pages | 12 |
Journal | SIAM Journal on Optimization |
Volume | 18 |
Issue number | 3 |
DOIs | |
State | Published - 2007 |
Keywords
- Banach space
- Differential inclusion
- Duality mapping
- Euler approximations
- Exponential formula
- Fixed set iterations
- One-sided Lipschitz condition
- Upper hemicontinuous