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Optimal control of dynamical systems with polynomial impulses

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  • The paper is devoted to the $BV$-relaxation of a dynamical system, whose right-hand side is a $p$th degree polynomial with rational powers of control under a uniform bound on its $L_p$-norm, and coefficients containing usual measurable bounded control.
        Under natural convexity assumptions, we give an explicit representation of generalized solutions to the control system by a measure differential equation. The main results concern an optimal impulsive control problem for the relaxed system: We establish the existence of a minimizer, and give necessary optimality conditions in the form of a Maximum Principle.
    Mathematics Subject Classification: Primary: 49N25, 49K99; Secondary: 49J99.


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