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Strongly nonlinear impulsive system and necessary conditions of optimality. (English) Zbl 1081.49027
The authors consider an infinite dimensional impulsive system governed by an evolution differential equation with a monotone type main part in the presence of an impulsive control in infinite dimensions. The existence of a solution is proved and necessary conditions of optimality for a general Bolza problem are given. As an example, a system governed by a quasi-linear impulsive parabolic equation is considered.

MSC:
49N25 Impulsive optimal control problems
34A37 Ordinary differential equations with impulses
34G20 Nonlinear differential equations in abstract spaces
49J27 Existence theories for problems in abstract spaces
49K20 Optimality conditions for problems involving partial differential equations
49K27 Optimality conditions for problems in abstract spaces
93C25 Control/observation systems in abstract spaces
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