Question

Find the optimal control u for the system $\dot{x} = u;x(0)=1$ which minimizes $J=\frac{1}{2}x^2(4)+\frac{1}{2}\int\limits^4_0 {u^2} \, dt$

Answer 1

The flowing liquid will always be very nearly pure solvent S. The product rho*Das can be considered constant, and the diffusion of A in S can be considered by a steady state version of the the continuity equation in terms of molar concentration (equation B.11.2). Note that the presence of a small amount of the reaction product B is ignored.