controller structure & nonsmooth programming - Pierre Apkarian - Free
controller structure & nonsmooth programming - Pierre Apkarian - Free
controller structure & nonsmooth programming - Pierre Apkarian - Free
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
challenges <strong>nonsmooth</strong> opt. MATLAB tools The End<br />
<strong>controller</strong> design as <strong>nonsmooth</strong> program<br />
• optimization problems are <strong>nonsmooth</strong> and/or nonconvex<br />
• but gentle special composite <strong>structure</strong> with cast<br />
minimize<br />
x<br />
max λ 1 ◦ T (x, ω)<br />
ω∈Ω<br />
Ω index set freq. or times<br />
where max Ω∈Ω λ 1 is convex but <strong>nonsmooth</strong><br />
T (x, Ω) differentiable but nonconvex wrt. x, ∀ω<br />
• Clarke subdifferential<br />
Clarke calculus is closed (chain rules, etc)<br />
Clarke regularity ⇒ specialized and efficient techniques<br />
• directly formulated in <strong>controller</strong> tunable space (no dummies !)<br />
• efficient: can handle large models<br />
<strong>controller</strong> <strong>structure</strong> & <strong>nonsmooth</strong> <strong>programming</strong> - http://pierre.apkarian.free.fr<br />
<br />
17 / 28