first order system is give (t) = ax(t) + bu he performance index is J = = ² (¹¹ (ar²(t) + 1
first order system is give (t) = ax(t) + bu he performance index is J = = ² (¹¹ (ar²(t) + 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
7
Transcribed Image Text:Problem 2.5 A first order system is given by
(t) = ax(t) + bu(t)
%3D
and the performance index is
1 sts
(qz (t) + ru* (t))dt
2
where, x(to) = ro and r(tf) is free and t being fixed. Show that the
optimal state x* (t) is given by
sinhß(t;-t) B = Va? + b°q/r•
Ox = (1).
sinhßt;
%3D
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