Set-valued Euler’s Method with Interpolated Distance Functions and Optimal Control Solvers∗
نویسندگان
چکیده
where U ⊂ R denotes the control region and X0 ⊂ R the starting set. If not only one optimal trajectory and corresponding optimal control have to be determined, but the end points of all admissible solutions of the control problem, the so-called reachable set R(T, t0, X0) at end time T has to be computed. Defining a set-valued map F (t, x) = ⋃ u∈U{f(t, x, u)}, we can consider the equivalent differential inclusion x′(t) ∈ F(t,x(t)) (a.e. t ∈ [t0, T ]) , (4) x(t0) ∈ X0 . (5)
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