Solve the batch reactor optimal control problem. The goal is to find the optimal temperature u(t), 0 ≤ t ≤ 1, that maximizes the production of an intermediate product B at the end of one hour of...

Solve the batch reactor optimal control problem. The goal is to find the optimal temperature u(t), 0 ≤ t ≤ 1, that maximizes the production of an intermediate product B at the end of one hour of operation. The objective function and system model is given below.

(i) As in Example 5.24 (also see code given), assume a piecewise linear control u, with the values at discrete time points as variables. (ii) Importantly, start with three variables, obtain the optimal u*(t), and then use this result to interpolate a starting guess with six variables, again obtain an optimum u, and then proceed with 12 variables. Plot optimum u vs. t and corresponding y1 and y2 vs. t. Give the value of the optimized objective function.