By Eduard L. Stiefel

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Saint-Pierre numerical methods”, pp. 177–247. Annals of the international Society of Dynamic Games, M. S. Raghavan, T. Parthasarathy Eds. Birkhäuser (1999). [26] Cardaliaguet P. & Plaskacz S. Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable hamiltonians, SIAM Journal on Control and Optim. 38, no. 5, 1501–1520 (2000). , Quincampoix M. & Saint-Pierre P. , SIAM J. Control and Optimization 39, no. 5, 1615–1632 (2001). , Quincampoix M. & Saint-Pierre P. Differential games with state-constraints.

Differential Games Wiley, New York (1965). [43] Jachimiak W. Stochastic invariance in infinite dimension, Preprint (1998). [44] Kisielewicz M. Viability theorem for stochastic inclusions, Discussiones Mathematicae, Differential Inclusions 15, 61–74 (1995). N. I. Game-Theorical Control Problems Springer-Verlag, New York (1988). [46] Kurzhanski A. B. F. On the theory of trajectory tubes—a mathematical formalism for uncertain dynamics, viability and control. Advances in nonlinear dynamics and control: a report from Russia, 122–188, Progr.

Similarly, Y[t,θ] denotes the set of all measurable selections of Y on [t, θ], and V[t,θ] (y(·)) denotes the set of all measurable selections of the mapping V (y(·)) (for a given y(·)) on the same interval. The following suppositions hold true. 1. U , Y and V¯ are compact subsets of finite-dimensional vector spaces, U is convex, the mapping y −→ V (y) ⊂ V¯ is compact valued and Lipschitz continuous. 2. The function f : Rn × U × Y × V¯ → Rn has the form f (x, u, y, v) = f0 (x, y, v) + B(x, y)u, where f0 and B are continuous, locally Lipschitz in x uniformly with respect to the other variables.

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An Introduction to Numerical Mathematics by Eduard L. Stiefel

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