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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 1:
Consider the following problem
minJ=0T12u(t)2dt
subject tox(t)=u(t)-t
where 0tT
a) Augment the system dynamics by adding time as a new state variable, t=1 to obtain a
time-invariant 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 T, and optimal control input by solving the equations presented
in part b).
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