{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lect_34 - Nonlinear Systems and Control Lecture 34 Robust...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Nonlinear Systems and Control Lecture # 34 Robust Stabilization Lyapunov Redesign & Backstepping – p. 1/ ? ? Lyapunov Redesign (Min-max control) ˙ x = f ( x ) + G ( x )[ u + δ ( t,x,u )] , x ∈ R n , u ∈ R p Nominal Model: ˙ x = f ( x ) + G ( x ) u Stabilizing Control: u = ψ ( x ) ∂V ∂x [ f ( x ) + G ( x ) ψ ( x )] ≤ − W ( x ) , ∀ x ∈ D, W is p.d. u = ψ ( x ) + v bardbl δ ( t,x,ψ ( x ) + v ) bardbl ≤ ρ ( x ) + κ bardbl v bardbl , ≤ κ < 1 ˙ x = f ( x ) + G ( x ) ψ ( x ) + G ( x )[ v + δ ( t,x,ψ ( x ) + v )] ˙ V = ∂V ∂x ( f + Gψ ) + ∂V ∂x G ( v + δ ) – p. 2/ ? ? w T = ∂V ∂x G ˙ V ≤ − W ( x ) + w T v + w T δ w T v + w T δ ≤ w T v + bardbl w bardbl bardbl δ bardbl ≤ w T v + bardbl w bardbl [ ρ ( x )+ κ bardbl v bardbl ] v = − η ( x ) w bardbl w bardbl parenleftbigg w bardbl w bardbl = sgn( w ) for p = 1 parenrightbigg w T v + w T δ ≤ − η bardbl w bardbl + ρ bardbl w bardbl + κ η bardbl w bardbl = − η (1 − κ ) bardbl w bardbl + ρ bardbl w bardbl η ( x ) ≥ ρ ( x ) (1 − κ ) ⇒ w T v + w T δ ≤ ⇒ ˙ V ≤ − W ( x ) – p. 3/ ? ? v = − η ( x ) w bardbl w bardbl , if η ( x ) bardbl w bardbl ≥ ε − η 2 ( x ) w ε , if η ( x ) bardbl w bardbl < ε η ( x ) bardbl w bardbl ≥ ε ⇒ ˙ V ≤ − W ( x ) For η ( x ) bardbl w bardbl < ε ˙ V ≤ − W ( x ) + w T bracketleftbigg −...
View Full Document

{[ snackBarMessage ]}

Page1 / 14

Lect_34 - Nonlinear Systems and Control Lecture 34 Robust...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online