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

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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 + ( t,x,u )] , x R n , u R p Nominal Model: x = f ( x ) + G ( x ) u Stabilizing Control: u = ( x ) V x [ f ( x ) + G ( x ) ( x )] W ( x ) , x D, W is p.d. u = ( x ) + v bardbl ( t,x, ( x ) + v ) bardbl ( x ) + bardbl v bardbl , < 1 x = f ( x ) + G ( x ) ( x ) + G ( x )[ v + ( t,x, ( x ) + v )] V = V x ( f + G ) + V x G ( v + ) p. 2/ ? ? w T = V x G V W ( x ) + w T v + w T w T v + w T w T v + bardbl w bardbl bardbl bardbl w T v + bardbl w bardbl [ ( x )+ bardbl v bardbl ] v = ( x ) w bardbl w bardbl parenleftbigg w bardbl w bardbl = sgn( w ) for p = 1 parenrightbigg w T v + w T bardbl w bardbl + bardbl w bardbl + bardbl w bardbl = (1 ) bardbl w bardbl + bardbl w bardbl ( x ) ( x ) (1 ) w T v + w T V W ( x ) p. 3/ ? ? v = ( x ) w bardbl w bardbl , if ( x ) bardbl w bardbl 2 ( x ) w , if ( x ) bardbl w bardbl < ( x ) bardbl w bardbl V W ( x ) For ( x ) bardbl w bardbl < V W ( x ) + w T bracketleftbigg...
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This note was uploaded on 07/25/2008 for the course ME 859 taught by Professor Choi during the Spring '08 term at Michigan State University.

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

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