Question

Problem 5: (10 points extra credit) Given the state space differential equation for the LTI system x(t) = ax(t) + bu(t) with cost function $J = \frac{1}{2} \int_0^\infty \{\alpha [x(t)]^2 + \beta [u(t)]^2\} dt$ $\alpha, \beta > 0$ (a) 5 pts. What is the Hamiltonian for this system? (b) 5 pts. What are the 3 equations that must be satisfied for the optimal state trajectory $x^(t)$, optimal costate $p^(t)$ and optimal control $u^*(t)$?

          Problem 5: (10 points extra credit)
Given the state space differential equation for the LTI system
x(t) = ax(t) + bu(t)
with cost function
$J = \frac{1}{2} \int_0^\infty \{\alpha [x(t)]^2 + \beta [u(t)]^2\} dt$
$\alpha, \beta > 0$
(a) 5 pts. What is the Hamiltonian for this system?
(b) 5 pts. What are the 3 equations that must be satisfied for the optimal state trajectory $x^*(t)$, optimal costate $p^*(t)$ and optimal control $u^*(t)$?

$Problem 5: (10 points extra credit) Given the state space differential equation for the LTI system x(t) = ax(t) + bu(t) with cost function J = (1)/(2)∫0^∞{α [x(t)]^2 + β [u(t)]^2} dt α, β > 0 (a) 5 pts. What is the Hamiltonian for this system? (b) 5 pts. What are the 3 equations that must be satisfied for the optimal state trajectory x^*(t), optimal costate p^*(t) and optimal control u^*(t)?$

Added by Emilio C.

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