No. of Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER M.TECH DEGREE EXAMINATION, APRIL/MAY 2018

Electrical & Electronics Engineering
Control Systems, Guidance and Navigational Control

01EE6102 Optimal Control Theory

Answer any twofull questions from each part

Limit answers to the requtred points.
Max. Marks: 60 Duration: 3 hours
PART A

1. Explain the steps involved inthe mathematical formulation of an optimal control problem with 5
a proper example.

b. State and prove the fundamental theorem of calculus of variation 4

2. a. 5
Determine the extremal for the functional J(x)— f(i 2 +2xi+4x 2) 01 given that (0) |,

and x(2) is free

b. Derive the necessary condition for a function to be an extremal for the functional 4

%
Jet x,t)dt
J(x) — ‏م‎ . Inthe (t,x) plane, the initial point is specified, final value of

x(tf) is specified and the final time is free

3. Derive the necessary condition for a function to be an extremal for the functional 4
८
[ഫക
J(x) = ^ f . Inthe (t,x) plane, the initial point is specified, final value of x
may be constrained to lie on a specified moving point or curve e(t) such that x(tf ) 9(tf
‏كه‎ |
Determine the extremal for the functional ١ J
terminates on the curve B(t) = —4t+5
PART B
4. From the fundamentals, discuss, derive and comment on the statement, "An Optimal control 4

must minimize the Hamiltonian"