### Linear quadratic control an introduction pdf

Don't show me this again. Welcome! This is one of over 2, courses on OCW. Find materials for this course in the pages linked along the left. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.. No enrollment or registration. The ﬁnite horizon, linear quadratic regulator (LQR) is given by x˙ = Ax+Bu x ∈ Rn,u ∈ Rn,x. 0 given J˜= 1 2 Z T 0. ¡ x TQx+u Ru ¢ dt+ 1 2 xT(T)P. 1x(T) where Q ≥ 0, R > 0, P1 ≥ 0 are symmetric, positive (semi-) deﬁnite matrices. Note the factor of 1 2. is left out, but we included it here to simplify the derivation. Chapter 6. LINEAR QUADRATIC OPTIMAL CONTROL. In this chapter, we study a diﬀerent control design methodology, one which is based on optimization. Control design objectives are formulated in terms of a cost criterion. The optimal control law is the one which minimizes the cost criterion.

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