please do both if you can. as soon as you can.

thanks in advance!

3. Consider the same Problem 2 with performance index 1=1 / \x7(e) +zce) + u?()}dt. Design a Linear Quadratic Gaussian (LQG) controller and find the numerical values of (a) the algebraic Riccati coefficient P., (30 points (b) the controller gain K., and (5 points) (c) draw the complete state variable block diagram showing the nu- merical values for the plant, the estimator of Problem 2 and the controller of Problem 3. (5 points) 2. A noisy dynamical system is described by (t) = x2(t), iz(t) = -39.4x1(t) 3.812(t) + u(t) + w(t). and the output as g(t) = x(t) + (t), where, w and v are plant and measurement noises respectively with covariances as qu = 10; 7. = 1. For infinite-horizon condition, design an optimal estimator and find the numerical values of (a) the State Estimate Error Covariance (SEEC) P, and (b) the estimator gain K. 3. Consider the same Problem 2 with performance index 1=1 / \x7(e) +zce) + u?()}dt. Design a Linear Quadratic Gaussian (LQG) controller and find the numerical values of (a) the algebraic Riccati coefficient P., (30 points (b) the controller gain K., and (5 points) (c) draw the complete state variable block diagram showing the nu- merical values for the plant, the estimator of Problem 2 and the controller of Problem 3. (5 points) 2. A noisy dynamical system is described by (t) = x2(t), iz(t) = -39.4x1(t) 3.812(t) + u(t) + w(t). and the output as g(t) = x(t) + (t), where, w and v are plant and measurement noises respectively with covariances as qu = 10; 7. = 1. For infinite-horizon condition, design an optimal estimator and find the numerical values of (a) the State Estimate Error Covariance (SEEC) P, and (b) the estimator gain K