l6_ocsp_conf_ast

l6_ocsp_conf_ast - 2/22/2005 copyright Brian Williams, 2002...

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Unformatted text preview: 2/22/2005 copyright Brian Williams, 2002 1 courtesy of JPL Optimal CSPs and Conflict-directed A* Brian C. Williams 16.412J/6.834J February 22 nd , 2005 Brian C. Williams, copyright 2000 2/22/2005 copyright Brian Williams, 2002 2 System Model Control Program RMPL Model-based Program Control Sequencer Deductive Controller Commands Observations Plant Titan Model-based Executive State goals State estimates Mode Estimation Mode Reconfiguration Tracks likely plant states Tracks least cost goal states z Executes concurrently z Preempts z Queries (hidden) states z Asserts (hidden) state Closed Closed Valve Valve Open Open Stuck Stuck open open Stuck Stuck closed closed Open Open Close Close 0. 01 0. 01 0. 01 0. 01 0.01 0.01 0.01 0.01 inflow = outflow = 0 Generates target goal states conditioned on state estimates Mode Reconfiguration: Select a least cost set of commandable component modes that entail the current goal, and are consistent Mode Estimation: Select a most likely set of component modes that are consistent with the model and observations arg min P t (Y| Obs) s.t. (X,Y) O(m) is consistent arg max R t (Y) s.t. (X,Y) entails G(X,Y) s.t. (X,Y) is consistent 2/22/2005 copyright Brian Williams, 2002 3 Outline Optimal CSPs Application to Model-based Execution Review of A* Conflict-directed A* Generating the Best Kernel Intelligent Tree Expansion Extending to Multiple Solutions Performance Comparison 2/22/2005 copyright Brian Williams, 2002 4 Constraint Satisfaction Problem CSP = <X, D X ,C> variables X with domain D X Constraint C(X): D X {True,False} Find X in D X s.t. C(X) is True R , G, B G R , G Different-color constraint V 1 V 2 V 3 2/22/2005 copyright Brian Williams, 2002 5 Optimal CSP OCSP= <Y, g , CSP> Decision variables Y with domain D Y Utility function g(Y): D Y CSP is over variables <X,Y> Find Leading arg max g (Y) Y D y s.t. X D X s.t. C(X,Y) is True Frequently we encode C in propositional state logic g() is a multi-attribute utility function that is preferentially independent . 2/22/2005 copyright Brian Williams, 2002 6 CSP Frequently in Propositional Logic (mode(E1) = ok implies (thrust(E1) = on if and only if flow(V1) = on and flow(V2) = on)) and (mode(E1) = ok or mode(E1) = unknown) and not (mode(E1) = ok and mode(E1) = unknown) V1 V2 E1 2/22/2005 copyright Brian Williams, 2002 7 Multi Attribute Utility Functions g(Y) = G(g 1 (y 1 ), g 2 (y 2 ), . . .) where G(u 1 , u 2 u n ) = G(u 1 ,G(u 2 u n )) G(u 1 ) = G(u 1 , I G ) Example: Diagnosis g i (y i =mode ij ) = P(y i = mode ij ) G(u 1 ,u 2 ) = u 1 x u 2 I G = 1 2/22/2005 copyright Brian Williams, 2002 8 Mutual Preferential Independence Assignment 1 is preferred over 2 if g( 1 ) < g( 2 ) For any set of decision variables W Y , our preference between two assignments to W is independent of the assignment to the remaining variables W Y . 2/22/2005 copyright Brian Williams, 2002...
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l6_ocsp_conf_ast - 2/22/2005 copyright Brian Williams, 2002...

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