Exerc (Solutions on p. 222) Show that, when m = 1, a controllable problem is also normal. Suppose we have a normal problem with m= 1 and that the eigenvalues of A are distinct and real. Show that the optimal control is given by the sign of an expression of the form 4.1 M Pn(t) = Σ c₁ exp(- A¡t), 1 where λ, is an eigenvalue of A and c, is a constant. Prove that the optimal control has at most n - 1 switches. f 100 1.
Exerc (Solutions on p. 222) Show that, when m = 1, a controllable problem is also normal. Suppose we have a normal problem with m= 1 and that the eigenvalues of A are distinct and real. Show that the optimal control is given by the sign of an expression of the form 4.1 M Pn(t) = Σ c₁ exp(- A¡t), 1 where λ, is an eigenvalue of A and c, is a constant. Prove that the optimal control has at most n - 1 switches. f 100 1.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercises 4
(Solutions on p. 222)
4.1 Show that, when m = 1, a controllable problem is also normal.
Suppose we have a normal problem with m = 1 and that the
eigenvalues of A are distinct and real. Show that the optimal control is
given by the sign of an expression of the form
И
Pn(t) = [c₁ exp(-2;t),
Ci
1
where is an eigenvalue of A and c, is a constant. Prove that the
optimal control has at most n - 1 switches.
100
71
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