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Question 1 : Consider the following problem minJ = 0 T 1 2 u ( t ) 2 d t subject t o x (
Question :
Consider the following problem
minJ
subject
where
a Augment the system dynamics by adding time as a new state variable, to obtain a
timeinvariant system. Present the state variables, new system dynamics, and boundary
conditions for the augmented system.
b Find the Hamiltonian, and write the costate equations, state equations, and optimal control
policy using the Pontryagin's Minimum Principle.
c Calculate the terminal time and optimal control input by solving the equations presented
in part b
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