## Classification

# of variables | # of modes | # of jumps |
---|---|---|

2 | 4 | 7 |

Type | Continuous dynamics | Guards & Invariants | Resets |
---|---|---|---|

hybrid | linear polynomial | hyperplane & half-space | identity |

## Download

Flow* | flow*_files |

SpaceEx | spaceEx_files |

## Model description

The considered benchmark presented in Fig.1(a) consists of two tanks. The liquid in the first tank comes from two outside sources: a constant inflow source and a second source equipped with a controlled valve *valve1*, with flows and respectively. A drain placed at the bottom of tank 1 allows the liquid to flow into tank 2 with flow .

Tank 2 is itself equipped with two drains. In the first one a pump is placed to assure a constant liquid outflow whereas the flow in the second one is controlled by an electro-valve *valve2*.Both valves can take the states On/Off. This results consequently in four possible discrete modes for the hybrid automaton. The liquid levels in tank i is given by .

The dynamics of the above system is defined by the following differential equations:

## Reachability settings

We consider an initial set of

and the starting location , a time horizon , and a time step . The set of bad states are all states, where .

## Results

Fig.2 shows the flowpipes computed for the above-mentioned parameters using a) HyReach and b) SpaceEx. The results given in Fig. 2 show tightness difference between the two obtained flowpipes, although both proposed tools are based on the same reachability analysis technique using support functions.

Figure 2: Flowpipe of the two-tank system

## References

[1] J. Lygeros. *Lecture notes on hybrid systems.* Technical Report, 2004.

[2] I. A. Hiskens. *Stability of limit cycles in hybrid systems.* In Proceedings of the 34th Hawaii International Conference on System Sciences (HICSS’01), pages 163-328, IEEE, 2001.

[3] A. Girard. *Reachability of Uncertain Linear Systems Using Zonotopes. *In Proceedings of the 8th International Workshop on Hybrid Systems: Computation and Control (HSCC’05), Volume 3414 of LNCS, pp 291-305, Springer, 2005.