Outline Review of Diagnosis and Mode Estimation Generalizing mode estimation to Optimal CSPs Model-based Programming W/o State Mode Estimation as Trajectory Tracking Mode estimation is an Optimization Problem Given System variables X with domain Dx Mode variables Y with domain Dy System model p(X,Y): DxX D> True, False Observations Obs(X,Y): DxX Dy >True, Falsel Compute Leading Arg Max P(Y I Obs st.彐X∈Dx.WQX,Y)∧OBS(X,Y) is consistent
11 Outline x Review of Diagnosis and Mode Estimation x Generalizing Mode Estimation to Optimal CSPs Model-based Programming w/o State Mode Estimation as Trajectory Tracking 12 Mode Estimation is an Optimization Problem Given: System variables X with domain DX Mode variables Y with domain DY System model Ȍ(X,Y) : DX x DYo {True, False} Observations Obs(X,Y) : DX x DYo {True, False} Compute: Leading Arg Max P(Y | Obs ) Y DY s.t. X DX . Ȍ(X,Y) OBS(X,Y) is consistent
Generalize to Optimal CsP Constraint Satisfaction Problem CSP= <X D.C> variables X with domain Dx Constraint C(×):Dx→{True, False} Find X in Dxst. C(X)is True Optimal CSP OCSP=<Y, g, CS Decision variables Y with domain Dy Utility function g():Dy→>界 CSP is over variables <XY> Find Leading arg max gY) Y∈D staXE DY s.t. C(,Y)is True Outline Review of Diagnosis and Mode Estimation Generalizing mode estimation to Optimal csPs Model-based Programming w/o State Mode Estimation as Trajectory Tracking
13 Generalize to Optimal CSP Constraint Satisfaction Problem CSP = <X, DX,C> variables X with domain DX Constraint C(X): DX o {True,False} Find X in DX s.t. C(X) is True Optimal CSP OCSP= <Y, g, CSP> Decision variables Y with domain DY Utility function g(Y): DY o CSP is over variables <X,Y> Find Leading arg max g(Y) Y Dy s.t. X DY s.t. C(X,Y) is True 14 Outline x Review of Diagnosis and Mode Estimation x Generalizing Mode Estimation to Optimal CSPs Model-based Programming w/o State Mode Estimation as Trajectory Tracking
RMPL Model-based Program Titan Model-based Executive Control Program Generates target goal states Queries(hidden) states conditioned on state estimates Asserts(hidden) state System Model State estimates Track Tracks least likel cost goal states alve plant states Open 9 001-A Stuck Open Stuck Closed Observations Commands closed inflow= outflow= Plant Example: The model-based program sets engine s thrusting, and the deductive controller Mode Oxidizer tank Fuel tank Mode reconfiguration Estimation Deduces that Plans actions thrust is off. and to open the engine is healthy six valves Deduces that a valve failed-stuck closed Determines that valves on the backup engine will achieve thrust. and plans needed actions Mode reconfiguration ode estimation
System Model Control Program RMPL Model-based Program Control Sequencer Deductive Controller Observations Commands Plant Titan Model-based Executive State estimates State goals 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 Valve Open Stuck open Stuck closed Open Close 0. 01 0. 01 0.01 0.01 inflow = outflow = 0 Generates target goal states conditioned on state estimates Example: The model-based program sets engine = thrusting, and the deductive controller . . . Determines that valves on the backup engine will achieve thrust, and plans needed actions. Deduces that a valve failed - stuck closed Plans actions to open six valves Oxidizer tank Oxidizer tank Fuel tank Fuel tank Deduces that thrust is off, and the engine is healthy Mode Estimation Mode Reconfiguration Mode Reconfiguration Mode Estimation