Given the following system x vector (k + 1) = G x vector (k) + H u vector (k) G

Question

Given the following system x vector (k + 1) = G x vector (k) + H u vector (k) G = [1 1 1 0], H = {1 0], x vector = [1 0] (a) Hand-calculate and Determine the optimal control sequence u(k) that will minimize the following performance index: J = 1/2 x vector^T(8) S x vector (8) + 1/2 sigma^7 _k=0 (x vector^T (k) Q x vector (k) + u vector^T (k) R u vector(k)) where Q = [1 0 0 1], R = 1, S = [1 0 0 1] (b) What is the minimum value of J? (c) Program a Matlab file to verify your hand-calculated results.

Explanation / Answer

x = linspace(-10,5, 10) c.) start = -10; stop = 5; num_elements = 10; index = 4; x = linspace(-10,5, 10) start = -10; stop = 5; num_elements = 10; index = 4; out = start + (index-1)*(stop - start)./(num_elements-1) out = start + (index-1)*(stop - start)./(num_elements-1)

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