Def’) Cost - quadratic that penalizes the distance from desired state and control trajectories, which are only available over a finite horizon.
Hypothesis: h_{\theta} (x) = \theta_0 + \theta_1 x
Parameters: \theta_0, \theta_1
Instantaneous cost: $(h_{\theta} (x^{(i)})-y^{(i)})^2$
Cost function (additive cost): $J(\theta) = \frac {1}{2m} \displaystyle\sum_{i=1}^m ( h_{\theta}(x^{(i)}) - y^{(i)})^2$
Goal: get parameters that minimize $J(\theta)$
Def’) finite horizon - finite time
Additive cost
$\int _0^T l(x(t)),u(t)) \ dt$
where l() : instantaneous cost