= = Exercise 6.6 Consider the scalar system i = ax + bu and the cost J(u) = Soo (quº(t) + ru²(t))dt, where a, q, r > 0 a

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Exercise 6 6 Consider The Scalar System I Ax Bu And The Cost J U Soo Quo T Ru T Dt Where A Q R 0 A 1 (51.87 KiB) Viewed 18 times

= = Exercise 6.6 Consider the scalar system i = ax + bu and the cost J(u) = Soo (quº(t) + ru²(t))dt, where a, q, r > 0 and b is arbitrary. Suppose that a, b, q are fixed but r can vary. Show that for r - 0 (the "cheap control” case) the eigenvalue of the optimal closed-loop system moves off to -o, while for r + (the “expensive control" case) the eigenvalue of the optimal closed-loop system tends to -a, i.e., the opposite of the open-loop eigenvalue.