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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Extension to general initial-final conditions<br />
• Equality initial-final constraints Φ(y0,yT) = 0, cost φ(y0,yT) = 0.<br />
• Reduction <strong>of</strong> inequalities into equalities in case <strong>of</strong> strict complementarity<br />
with a unique multiplier<br />
• Associated multiplier Ψ ∈ R n Φ.<br />
• Costate equation<br />
−˙¯pt<br />
= ¯ptfy(ūt,¯yt), t ∈ (0,T);<br />
(−¯p0, ¯pT) = φ ′ (¯y0,¯yT)+ΨΦ ′ (¯y0,¯yT).<br />
• Shooting variables: (y0,p0,Ψ). Similar <strong>analysis</strong><br />
qualification + SOSC implies an O( ¯ h) error estimate.<br />
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