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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The simplest <strong>optimal</strong> <strong>time</strong> problem II<br />
• Solution: Bang-bang <strong>optimal</strong> <strong>control</strong>, at most one switching <strong>time</strong><br />
• Discretized solution <strong>of</strong> same nature (costate affine function <strong>of</strong> <strong>time</strong>)<br />
• Exact integrators <strong>control</strong> constant over a <strong>time</strong>: mid point rule<br />
• In that case, error only due to the switching <strong>time</strong> step<br />
• Expected error: at most O( ˜ h), with ˜ h = <strong>time</strong> step a switching <strong>time</strong>.<br />
Ref. for LQ bang-bang <strong>problems</strong> Alt, Baier, Gerdts, Lempio, Error<br />
bounds for Euler approximation <strong>of</strong> linear-quadratic <strong>control</strong> <strong>problems</strong> with<br />
bang-bang solutions. Preprint, 2010.<br />
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