Added Stanford Benchmark

benchmarks/double_pendulum/Specifications.txt

@@ -0,0 +1,12 @@
+Initial states:
+
+x1 = [0.6, 0.7]
+x2 = [-0.7, -0.6]
+x3 = [-0.4, -0.3]
+x4 = [0.5, 0.6]
+
+t = 20 seconds
+
+Property:
+
+The system, states 1 to 3, always stays within the box x ∈ [-1,1]

benchmarks/double_pendulum/controller_double_pendulum_less_robust.nnet

@@ -0,0 +1,114 @@
+// The contents of this file are licensed under the Creative Commons
+// Attribution 4.0 International License: https://creativecommons.org/licenses/by/4.0/
+// Neural Network File Format by Kyle Julian, Stanford 2016
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benchmarks/double_pendulum/controller_double_pendulum_more_robust.nnet

@@ -0,0 +1,114 @@
+// The contents of this file are licensed under the Creative Commons
+// Attribution 4.0 International License: https://creativecommons.org/licenses/by/4.0/
+// Neural Network File Format by Kyle Julian, Stanford 2016
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+-0.50037, 0.23183, -0.81721, -0.44236, -0.29616, 0.18930, 0.19507, 0.47877, 0.83626, -0.18407, 0.12554, -0.47511, -0.10945, -0.19676, -0.28800, 0.14655, 0.18152, 0.00434, -1.84949, -0.28260, -0.23544, 0.91323, 0.45166, -1.02891, -0.17245 
+-0.28327, 0.47691, 0.07065, -0.13697, -1.62073, -2.37556, 0.08533, -2.05948, -0.13328, -0.16982, -3.06072, -0.07632, 0.20134, 0.05375, -0.27505, 0.11381, -0.03724, 0.11220, -0.70603, -0.41312, 0.16816, -0.50219, -1.26019, -0.10327, -0.04227 
+-0.41049, 0.15427, 0.00032, -0.71942, 0.25287, 0.20222, 0.01543, -0.76094, 1.03927, -0.42290, -0.21527, 0.48299, -0.34531, -1.42728, -0.37652, -0.42724, -0.00475, 0.70103, -2.08565, 0.12043, -0.10700, 0.69257, -0.18982, 0.32744, 0.06271 
+-0.24657, -0.51702, -0.27771, -0.29991, -0.07707, -0.29422, -0.08720, -0.02487, -0.22748, -0.13818, -0.40504, -0.45884, 0.11483, -0.33570, -0.22799, 0.20092, -0.05981, -0.34365, -0.16645, -0.02094, -0.11956, 0.02993, -0.16749, -0.66520, -0.25281 
+-1.62424, -0.01840, 0.59613, 0.01490, -0.80382, -0.40125, 0.91099, 0.61385, -1.20548, 0.08330, -3.05664, 0.31239, 0.36655, -1.18631, -0.32099, 0.04752, -0.62988, 0.09901, -0.73648, -0.59059, -0.55973, -0.43839, 1.32010, -4.23443, -6.35789 
+0.07545, -0.10929, 0.01518, -0.19422, 0.13895, -0.16240, 0.00401, -0.04128, -0.25825, 0.21767, -0.45609, -0.41618, 0.23268, -0.04028, -0.49908, -0.32281, -0.08444, -0.40350, -0.29310, 0.06335, -0.35127, -0.15158, -0.43069, -0.49163, -0.48867 
+0.39731, -0.54158, 0.73436, 0.77265, 1.52259, -0.79840, -0.40407, -4.12586, 0.36628, -0.42734, -0.48351, 0.53854, -0.01711, 1.01980, -0.13239, 0.22649, 0.49514, 1.09312, -1.15227, 0.26544, -0.17143, 0.23938, -1.25938, -0.06842, -0.24547 
+-1.43038, 0.76075, -0.23818, 1.01672, 0.20675, -1.18741, 0.20272, -0.52338, -0.14747, -0.10802, 0.21426, -0.27463, 0.04986, -0.52692, -1.07034, -0.09160, -2.80514, -0.55144, -1.69579, -0.94322, -0.24468, -3.21814, -0.47197, -0.20468, -0.33145 
+0.07029, -0.65586, 0.03391, 0.72134, 0.00240, 0.93639, -1.03944, 0.23261, 0.13435, -0.21882, -0.02579, -1.29813, -0.16605, -0.71788, -0.90025, 0.19813, -1.17859, -0.02102, -2.97173, 0.21008, -0.19900, 0.54103, 0.49366, -2.20122, -0.64250 
+1.52000 
+-0.30138 
+0.29734 
+0.15226 
+-0.12107 
+0.29952 
+1.25426 
+1.11472 
+1.52959 
+-0.20106 
+-0.97487 
+0.37101 
+0.49843 
+1.32355 
+1.43992 
+0.50424 
+1.15586 
+0.70909 
+1.07831 
+-0.21624 
+0.79257 
+-0.53454 
+-0.26614 
+1.45261 
+-0.46211 
+-0.48293, 0.06047, 0.02364, 0.38088, -0.32111, -0.47931, 0.31789, -0.30592, -0.11011, 0.11669, -0.09016, 2.27401, 0.04796, -0.34591, -0.25153, 0.31471, 0.47863, 0.00886, -0.18144, -0.36906, 1.22824, 0.00766, 0.22091, 0.47157, 0.76725 
+-0.15094, -0.03531, 0.01539, 0.27162, -0.27052, -0.58085, 0.28679, -0.03020, -0.52610, -0.21955, -0.34578, 1.06163, 0.24263, -0.23639, -0.68732, 0.17131, -0.17235, 0.49812, 0.37649, 0.28723, 1.14548, 0.17161, 0.32568, 0.11248, 0.14659 
+-1.05854 
+-1.33805 

benchmarks/double_pendulum/double_pendulum_solver.m

@@ -0,0 +1,26 @@
+syms x1 x2 th1 th2 u1 u2 g mass l c T1 T2 'real'
+
+ex1 = 2 * x1 + x2 * cos(th2 - th1) - u2 ^ 2 * sin(th2 - th1) + ...
+          - 2 * g / l * sin(th1) + (c * u1 - T1) / (mass * l ^ 2);
+
+ex2 = x1 * cos(th2 - th1) + x2 + u1 ^ 2 * sin(th2 - th1) + ...
+      - g / l * sin(th2) + (c * u2 - T2) / (mass * l ^ 2);
+
+x1s = solve(ex1, x1);
+ex2s = subs(ex2, x1, x1s);
+x2ss = solve(ex2s, x2);
+x1ss = subs(x1s, x2, x2ss);
+
+x1ss_sub = subs(x1ss, [mass, g, l, c], [0.5, 1, 0.5, 0]);
+%x1ss_sub = subs(x1ss, [mass, g, l, c], [1, 1, 1, 0]);
+disp(x1ss_sub);
+disp(simplify(x1ss_sub))
+
+
+x2ss_sub = subs(x2ss, [mass, g, l, c], [0.5,1,0.5, 0]);
+%x2ss_sub = subs(x2ss, [mass, g, l, c], [1,1,1, 0]);
+disp(x2ss_sub);
+disp(simplify(x2ss_sub))
+
+% fprintMatPy('du1', {'th1', 'th2', 'u1', 'u2', 'g', 'mass', 'l', 'c', 'T1', 'T2'}, x1ss);
+% fprintMatPy('du2', {'th1', 'th2', 'u1', 'u2', 'g', 'mass', 'l', 'c', 'T1', 'T2'}, x2ss);

benchmarks/double_pendulum/dynamics.m

@@ -0,0 +1,20 @@
+function [dx] = dynamics(t,x,T)
+% Ex_double pendulum 
+% constants as per the documentation m=0.5, L=0.5, c= 0, g=1.0
+% description of the pararameters in these equations can be found here
+% https://github.com/amaleki2/benchmark_closedloop_verification/blob/master/AINNC_benchmark.pdf
+% Equations with different parameters of m, L, c,g, can be found in
+% double_pendulum_solver
+
+
+
+th1 = x(1);
+th2 = x(2);
+T1 = T(1);
+T2 = T(2);
+
+dx(1,1) = x(3);
+dx(2,1) = x(4);
+dx(3,1) = 4*T1 + 2*sin(th1) - (u2^2*sin(th1 - th2))/2 + (cos(th1 - th2)*(sin(th1 - th2)*u1^2 + 8*T2 + 2*sin(th2) - cos(th1 - th2)*(- (sin(th1 - th2)*u2^2)/2 + 4*T1 + 2*sin(th1))))/(2*(cos(th1 - th2)^2/2 - 1));
+dx(4,1) = -(sin(th1 - th2)*u1^2 + 8*T2 + 2*sin(th2) - cos(th1 - th2)*(- (sin(th1 - th2)*u2^2)/2 + 4*T1 + 2*sin(th1)))/(cos(th1 - th2)^2/2 - 1);
+end