58 lines
2.1 KiB
Plaintext
58 lines
2.1 KiB
Plaintext
// ----------------------------------------------------------
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// Hybrid System Example: Bouncing Ball
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// ----------------------------------------------------------
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// ----------------------------------------------------------
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// Constants
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// ----------------------------------------------------------
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g:=1; // constant for gravity
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// ----------------------------------------------------------
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// System Description
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// ----------------------------------------------------------
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automaton bouncing_ball
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contr_var: v, x;
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synclabs: jump;
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loc state: while x>=0 & x<=10 & v<=10 & v>=-10 wait {x'==v & v'==-g}
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when x==0 & v<0 sync jump do {v'==-v*0.5 & x'==x} goto state;
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initially: state & x==2 & v==0;
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end
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// ----------------------------------------------------------
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// Define Partitioning
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// ----------------------------------------------------------
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// Add a new label for the transitions that are introduced
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// between partitions
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bouncing_ball.add_label(tau);
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// Define the directions of the partitions
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// here: in both axes with a min. threshold of partition size 0.2
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bouncing_ball.set_refine_constraints((x, 0.2),(v,0.2),tau);
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// With this partitioning we can use convex hull overapproximations,
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// resulting in fewer polyhedra (one per partition)
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//REACH_USE_CONVEX_HULL=true;
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// ----------------------------------------------------------
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// Define Partitioning (alternative)
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// ----------------------------------------------------------
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// We can also just partition in the v-direction, but then we must turn off
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// the convex hull (try it...)
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// bouncing_ball.set_refine_constraints((v,0.2),tau);
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// REACH_USE_CONVEX_HULL=false;
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// ----------------------------------------------------------
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// Analysis Commands
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// ----------------------------------------------------------
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reg=bouncing_ball.reachable;
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// ----------------------------------------------------------
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// Saving Data for Graphical Output
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// ----------------------------------------------------------
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reg.print("out_reach",2); // output as a list of vertices
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// for display with graph use, e.g.:
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// graph -T X -C -B -q0.5 out_reach
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// for display with matlab use, e.g.:
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// plot_2d_vertices('out_m_reach')
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