I do not understand how to approach this question please help as much as possible!

Problem 4 : Given the continuous LTI system: 0 0 1 0 0 0 0 1 i(t) = (t) 0 0 0 0 1 0 0 1 ut) -2 1 -1 1 1 -2 1 - 1 z(e) = 1 1 0 0 0 0 1 0 0 :] a. (3 points) Consider the infinite horizon quadratic cost: 1 = 5 *x1(0)2 + x2(0)2 + u ()2 + uz(e)? dt Solve the ARE for the cost function, using Matlab. b. (3 points) Using the solution P, obtain the K matrix using Matlab. C. (6 points) Use Matlab to plot the trajectory xi(t), xz(t) of the system for the following cases open-loop system with zero input and initial condition x(0) = (1,0,0,0]'. Plot for timet e [0, 15). closed-loop system (u = -Kx) with initial condition x(0) = (1,0,0,0]'. Plot for timet e [0, 10]. d. (4 points) Use Matlab to plot the optimal control inputs ui(t),uz(t). Plot for time te [0, 10). e. (9 points) Consider the modified cost function: 1 = 5 x2(e)2 + x2(0)2 +a+u4 (0)2 + uz(t)? dt Write a loop in Matlab that finds the minimal value of a E [0.01: 0.01: 2] for which the optimal control input satisfies max (uit)) = 0.2. Using the same condition in part c, plot xi(t) and ui(t) of the closed loop system for this value of a. Compare to the trajectories in the nominal case a = 1. Problem 4 : Given the continuous LTI system: 0 0 1 0 0 0 0 1 i(t) = (t) 0 0 0 0 1 0 0 1 ut) -2 1 -1 1 1 -2 1 - 1 z(e) = 1 1 0 0 0 0 1 0 0 :] a. (3 points) Consider the infinite horizon quadratic cost: 1 = 5 *x1(0)2 + x2(0)2 + u ()2 + uz(e)? dt Solve the ARE for the cost function, using Matlab. b. (3 points) Using the solution P, obtain the K matrix using Matlab. C. (6 points) Use Matlab to plot the trajectory xi(t), xz(t) of the system for the following cases open-loop system with zero input and initial condition x(0) = (1,0,0,0]'. Plot for timet e [0, 15). closed-loop system (u = -Kx) with initial condition x(0) = (1,0,0,0]'. Plot for timet e [0, 10]. d. (4 points) Use Matlab to plot the optimal control inputs ui(t),uz(t). Plot for time te [0, 10). e. (9 points) Consider the modified cost function: 1 = 5 x2(e)2 + x2(0)2 +a+u4 (0)2 + uz(t)? dt Write a loop in Matlab that finds the minimal value of a E [0.01: 0.01: 2] for which the optimal control input satisfies max (uit)) = 0.2. Using the same condition in part c, plot xi(t) and ui(t) of the closed loop system for this value of a. Compare to the trajectories in the nominal case a = 1