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Wellposed Approximate Method for Initial State Determination of Discretetime Distributed
A General Theory of Necessary Conditions
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algorithm apply assume assumptions Banach space bilinear system Borel set boundary bounded Castaing closed-valued compact computation consider constraints continuous control problem control system convergence convex functions convex set Corollary corresponding countable defined definition denote differential equation dynamics equivalent example exists finite dimensional given Gr F Hausdorff Hence homomorphic Hypothesis implies inequality initial integral invertible Lagrangian submanifold Lebesgue measurable Legendre transformation Lemma Lie algebra linear lower semicontinuous Lusin Math Mathematics matrix measurable function measurable selections method metric minimize NCSSOPC necessary conditions neighborhood nonlinear Note obtain operator optimal control optimal solution output parameter players Polish space positive programming Proof properties pure strategies Riccati equation satisfied semiconvex semismooth sequence set-valued functions SIAM Journal space stochastic subset Suppose Suslin family Suslin type Theorem 3.1 theory topological University vector fields weakly zero