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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Shooting problem: continuous problem<br />
• Let p[p0], y[p0] denote the solution <strong>of</strong> the previous ODE with initial<br />
condition (y 0 ,p0).<br />
• Shooting function: S(p0) = pT[p0]−φ ′ (yT[p0]).<br />
• Optimality system ⇔ Shooting equation: S(p0) = 0.<br />
• Assume ¯p0 well-posed solution: S(¯p0) = 0, and S ′ (¯p0) invertible.<br />
• Then locally: ¯p0 unique solution, Newton’s method converges, and<br />
sensitivity <strong>analysis</strong> thanks to IFT.<br />
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