caa a22 4500 477118356 CHVBK 20180405111628.0 cr unu---uuuuu 170330e19960701xx s 000 0 eng 10.1007/BF02269425 doi (NATIONALLICENCE)springer-10.1007/BF02269425 Invariance properties of time measurable differential inclusions and dynamic programming [Elektronische Daten] [A. Rapaport, R. Vinter] Take a multifunctionF: [0,T]×ℝ n → ℝ n andP: [0,ℝT] → ℝ n .P is said to be weakly invariant (or "viable”) forF if for anyx 0∈P(0) there exists a solutionx tox∈F(t, x) satisfying the constraintx(t)∈P(t) for allt. If all solutions with initial value inP(0) satisfy the constraint thenP is strongly invariant forF. Weak and strong invariance are important concepts connected with existence of optimal controls and stabilizing controls, and dynamic programming. Weak and strong invariance have previously been proved for multifunctionsF, which are assumed merely to be measurable with respect to the time variable, under a regularity hypothesis onP ("local absolute continuity from the left”). We show how the regularity hypothesis can be reduced when apriori knowledge is available of a closed subsetI⊂[0,T] such thatF is upper semicontinuous at all points inI×ℝ n . The invariance theorems are applied to characterize the value function for optimal control problems with endpoint constraints as the unique generalized solution of the Hamilton-Jacobi equation, under hypotheses which are in certain cases less restrictive than those imposed hitherto. Plenum Publishing Corporation, 1996 Differential inclusions nationallicence invariance properties nationallicence measurable time dependency nationallicence Hamilton-Jacobi equation nationallicence Rapaport A. Department of Electrical and Electronic Engineering and Centre for Process Systems Engineering, Imperial College, Exhibition Road, SW7 2BT, London, U.K. aut Vinter R. Department of Electrical and Electronic Engineering and Centre for Process Systems Engineering, Imperial College, Exhibition Road, SW7 2BT, London, U.K. aut Journal of Dynamical and Control Systems Kluwer Academic Publishers-Plenum Publishers 2/3(1996-07-01), 423-448 1079-2724 2:3<423 1996 2 10883 https://doi.org/10.1007/BF02269425 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02269425 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rapaport A. Department of Electrical and Electronic Engineering and Centre for Process Systems Engineering, Imperial College, Exhibition Road, SW7 2BT, London, U.K aut NATIONALLICENCE 700 1- Vinter R. Department of Electrical and Electronic Engineering and Centre for Process Systems Engineering, Imperial College, Exhibition Road, SW7 2BT, London, U.K aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Kluwer Academic Publishers-Plenum Publishers 2/3(1996-07-01), 423-448 1079-2724 2:3<423 1996 2 10883 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer