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Strongly nonlinear impulsive evolution equations and optimal control. (English) Zbl 1065.49023
The system is described by the evolution equation $x'(t) + A(t, x(t)) = g(t, x(t)) + B(t)u(t)$ satisfied in an interval $$0 < t < T$$ minus a finite set $$\{t_k\},$$ $$0 < t_1 < t_2 < \dots < t_n < T.$$ The solution satisfies an initial condition at $$t = 0$$ and jump conditions at the other points, $x(0) = x_0, \quad x(t_k^+) - x(t_k) = F_k(x(t_k)) , \quad k = 1, 2, \dots, n .$ The author discusses existence of solutions to a control problem that consists of minimizing an integral functional $$J(x, u)$$ over trajectories of the system.

##### MSC:
 49N25 Impulsive optimal control problems 49J27 Existence theories for problems in abstract spaces 34G20 Nonlinear differential equations in abstract spaces 93C25 Control/observation systems in abstract spaces 34A37 Ordinary differential equations with impulses 49J15 Existence theories for optimal control problems involving ordinary differential equations
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