Numerical analysis of time discretization of optimal control problems
Numerical analysis of time discretization of optimal control problems
Numerical analysis of time discretization of optimal control problems
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Discretize + Optimize do commute !<br />
<strong>discretization</strong><br />
(P) −−−−−−−−−−→ (DP)<br />
⏐ ⏐<br />
<strong>optimal</strong>ity ⏐ <strong>optimal</strong>ity ⏐<br />
<br />
conditions conditions<br />
(OC) <strong>discretization</strong><br />
−−−−−−−−−−→ (DOC)<br />
Error orders: notation EO(a,b), EO(a,b,â, ˆ b). By Hager (2000)<br />
2 ≤ EO(a,b,â, ˆ b) ≤ EO(a,b) iff EO(a,b) ≥ 2<br />
If EO(a,b) ≥ 3, we may have EO(a,b,â, ˆ b) < EO(a,b).<br />
Equality for the Gauss <strong>discretization</strong>, for fourth order explicit schemes...<br />
(D)<br />
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