Optimality conditions for the linear optimal control of non-linear equations via a Laplace type method and two-scales like expansions
Optimality conditions for the linear optimal control of non-linear equations via a Laplace type method and two-scales like expansions
We propose a fine analysis of second order optimality conditions for the optimal control of semi-linear parabolic equations with respect to the initial condition. More precisely, we investigate the following problem: maximise with respect to $u_0\in L^\infty(\Omega)$ or $y\in L^\infty(\Omega\times(0,T))$ the cost functional $J(u_0,y)=\iint_{\Omega\times (0,T)}j_1(t,x,u)+\int_\Omega j_2(x,u(T,\cdot))$ where $\partial_t u-\Delta u=f(t,x,u)+y\,, …