first order system is give (t) = ax(t) + bu he performance index is J = = ² (¹¹ (ar²(t) + 1

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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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
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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