First and second-order optimality conditions for a b ilinear controlled wave equation on an infinite horizon
Keywords:
Bilinear control, wave equation, optimality conditions, second-order analysis. Mathematics Subject Classification: 49K20, 49J20, 35L05, 35Q93Abstract
This paper investigates the optimal control of a bilinear damped wave equation over an infinite time horizon. We establish the well-posedness of the controlled system and derive uniform energy estimates. The existence of optimal controls is proven by constructing a minimizing sequence. We prove that the control-to-state mapping is twice continuously Fréchet differentiable
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