1. 1 University of Pennsylvania Demonstrations Alur, Kumar, Lee, Pappas Rafael Fierro Yerang Hur Franjo Ivancic PK Mishra

2. 2 CHARON Toolset Analysis Tools Abstraction  Exploit hierarchy, modularity  Simplified model for controller design or analysis Reachability computations  Toolboxes for reachability computations  Accurate event detection for hybrid systems Symbolic toolbox for reachability analysis of nilpotent systemsAccurate event detection for power train and V2V controller Abstractions and approximations for the power train Hierarchy for the power train and V2V controller

3. 3 Powertrain and V 2 V OEPs V2V Abstraction  The input variable u(t) is the desired acceleration sent by the V 2 V controller  The actual throttle position and brake commands are computed using backstepping from u(t) Powertrain Approximation Engine has physical limitation and the vehicle cannot change its state (velocity and acceleration) instantaneously.  Acceleration mode  The engine, transmission and throttle systems are approximated by a linear system in series with a saturation element  Deceleration mode  The engine, transmission and braking systems are approximated by a saturation element in series with a first-order system

4. 4 Approximate Hybrid Model PP' Approximate model for Engine and Transmission  

5. 5 mode Acceleration mode Brake  = 90   = 10   = 0  = 10   = 40  = 20  = 10 Comparison: Approximate Model and OEP Model

6. 6 CHARON Visual Editor

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10. 10 CHARON Text Editor

11. 11 Two Keys to Analysis Modularity  Efficient and accurate  Integration of sub modes, agents at different time scales Detection of Events  Accurate detection of constraint violations or transitions Applications  Reachability Analysis  Simulation

12. 12 Event Detection dynamicsoutput input Given: We re-parameterize time by controlling the integration step size: output dynamics Using feedback linearization we select our “speed” (step-size) along the integral curves to converge to the event surface Event ! x(t) g(x)

13. 13 Requiem Reachability of the system  A is nilpotent  g(x, u) can be any nonlinear function Functions  Forward and Backward reachable sets for continuous and discrete systems.  Forward and Backward reachable sets for timed continuous systems.  Forward and Backward reachable sets continuous systems under invariants.  Forward and Backward reachable sets for discrete systems with guards.  Parametric forward and backward reachable set for continuous systems. http://www.seas.upenn.edu/hybrid/requiem.html