// ~->[DNET-1]->~

// File created by Norsys using Netica 1.05a on Feb 06, 1998 at 05:01:40.

bnet Inverted_Pendulum {
numdimensions = 1;
comment = "A time delay decision network for the control problem known \
	as 'inverted pendulum', or 'pole balancing' in which the \
	bottom of a pole is moved around (in 1 dimension for this \
	network) so that the pole doesn't tip over. \n\
	Problem described in Miller, W. Thomas, Richard S. Sutton and \
	Paul J. Werbos (1990) Neural Networks for Control, MIT Press, \
	Cambridge, MA. Decision network from Brent Boerlage.";
author = "BoerlageB";
whenchanged = 783526002;

visual V1 {
	defdispform = LABELBOX;
	nodelabeling = NAMETITLE;
	nodefont = font {shape= "Arial"; size= 10;};
	linkfont = font {shape= "Arial"; size= 9;};
	commentfont = font {shape= "Arial"; size= 10;};
	windowposn = (6, 5, 551, 374);
	resolution = 72;
	drawingbounds = (1656, 730);
	showpagebreaks = FALSE;
	usegrid = TRUE;
	gridspace = (6, 6);
	};

node dd {
	kind = ASSUME;
	discrete = FALSE;
	levels = (0, INFINITY);
	parents = ();
	title = "Delay";
	comment = "Time slice interval.";
	value = 0.02;
	visual V1 {
		center = (414, 66);
		height = 12;
		};
	};

node ddc {
	kind = ASSUME;
	discrete = FALSE;
	levels = (0, INFINITY);
	parents = ();
	title = "Duration of\nDesired Position";
	comment = "Time interval between changes in desired position.";
	value = 1;
	visual V1 {
		center = (432, 102);
		height = 11;
		};
	};

node csd {
	kind = ASSUME;
	discrete = FALSE;
	parents = ();
	title = "Cost of Misposition";
	comment = "Used in calculation of the utility, V.";
	value = 1;
	visual V1 {
		center = (450, 162);
		height = 17;
		};
	};

node g {
	kind = ASSUME;
	discrete = FALSE;
	parents = ();
	title = "Gravity";
	comment = "Acceleration due to gravity";
	value = 9.81;
	visual V1 {
		center = (420, 304);
		height = 16;
		};
	};

node lp {
	kind = ASSUME;
	discrete = FALSE;
	levels = (0, INFINITY);
	parents = ();
	title = "Length Pole";
	comment = "Distance from pivot to pole's center of mass.";
	value = 0.5;
	visual V1 {
		center = (432, 274);
		height = 15;
		};
	};

node mp {
	kind = ASSUME;
	discrete = FALSE;
	levels = (0, INFINITY);
	parents = ();
	title = "Mass Pole";
	comment = "Mass of the pole.";
	value = 0.1;
	visual V1 {
		center = (430, 244);
		height = 14;
		};
	};

node mc {
	kind = ASSUME;
	discrete = FALSE;
	levels = (0, INFINITY);
	parents = ();
	title = "Mass Cart";
	comment = "Combined mass of pole and cart.";
	value = 1.1;
	visual V1 {
		center = (430, 214);
		height = 13;
		};
	};

node gx {
	kind = NATURE;
	discrete = FALSE;
	levels = (-1, 1);
	inputs = (gx1);
	parents = (gx);
	equation = "P (gx | gx1) = Triangular3Dist (gx, gx1, -1, 1)";
	delays = (
		(ddc));
	persist = (ddc);
	title = "Desired Position";
	comment = "Control input.\nDesired position (ie, x value) of pole.";
	visual V1 {
		center = (120, 306);
		height = 2;
		link 1 {
			path = ((114, 298), (102, 282), (120, 264), (138, 282), (126, 298));
			};
		};
	};

node x {
	kind = NATURE;
	discrete = FALSE;
	inputs = (x1, xd1);
	parents = (x, xd);
	equation = "x (x1, xd1) = x1 + dd * xd1";
	delays = (
		(dd),
		(dd));
	title = "Position";
	comment = "Displacement of cart.\nPositive is displacement to the \
		right.";
	visual V1 {
		center = (288, 240);
		height = 5;
		link 1 {
			path = ((282, 232), (270, 216), (288, 198), (306, 216), (294, 232));
			};
		};
	};

node e {
	kind = NATURE;
	discrete = FALSE;
	parents = (x, gx);
	equation = "e (x, gx) = x - gx";
	persist = (dd);
	title = "Error";
	visual V1 {
		center = (240, 306);
		height = 3;
		link 1 {
			path = ((283, 249), (246, 298));
			};
		};
	};

node xd {
	kind = NATURE;
	discrete = FALSE;
	inputs = (xdd1, xd1);
	parents = (xdd, xd);
	equation = "xd (xd1, xdd1) = xd1 + dd * xdd1";
	delays = (
		(dd),
		(dd));
	title = "Velocity";
	visual V1 {
		center = (180, 240);
		height = 1;
		link 2 {
			path = ((174, 232), (162, 216), (180, 198), (198, 216), (186, 232));
			};
		};
	};

node ad {
	kind = NATURE;
	discrete = FALSE;
	inputs = (add1, ad1);
	parents = (add, ad);
	equation = "ad (ad1, add1) = ad1 + dd * add1";
	delays = (
		(dd),
		(dd));
	title = "Angular\nVelocity";
	visual V1 {
		center = (216, 72);
		height = 9;
		link 2 {
			path = ((204, 57), (192, 42), (216, 18), (240, 42), (228, 57));
			};
		};
	};

node a {
	kind = NATURE;
	discrete = FALSE;
	inputs = (ad1, a1);
	parents = (ad, a);
	equation = "a (a1, ad1) = a1 + dd * ad1";
	delays = (
		(dd),
		(dd));
	title = "Angle";
	comment = "Angle between pole and vertical.\n\
		Positive is clockwise rotation of pole.";
	visual V1 {
		center = (336, 72);
		height = 10;
		link 2 {
			path = ((330, 64), (318, 48), (336, 30), (354, 48), (342, 64));
			};
		};
	};

node F {
	kind = DECISION;
	discrete = TRUE;
	levels = (-10, 10);
	parents = (xd, e, ad, a);
	title = "Force";
	comment = "Force applied to bottom of pole.\n\
		Positive is force to the right (ie, positive x).";
	visual V1 {
		center = (240, 162);
		height = 4;
		link 1 {
			path = ((186, 232), (216, 198), (235, 171));
			};
		};
	};

node V {
	kind = UTILITY;
	discrete = FALSE;
	parents = (e, a);
	equation = "V (e, a) = - abs(a) - csd * abs(e)";
	visual V1 {
		center = (336, 306);
		height = 6;
		};
	};

node add {
	kind = NATURE;
	discrete = FALSE;
	parents = (F, ad, a);
	equation = "add (F, ad, a) = \n\
		\|  (mc * g * sin(a) - \n\
		\|              cos(a) * (F + mp * lp * ad^2 * sin(a))) /\n\
		\|  (4 * mc * lp / 3 - mp * lp * cos(a)^2)";
	title = "Angular\nAcceleration";
	visual V1 {
		center = (72, 72);
		height = 8;
		link 1 {
			path = ((223, 153), (103, 90));
			};
		link 2 {
			path = ((186, 57), (144, 36), (102, 57));
			};
		link 3 {
			path = ((312, 78), (210, 108), (108, 81));
			};
		};
	};

node xdd {
	kind = NATURE;
	discrete = FALSE;
	parents = (F, ad, a);
	equation = "xdd (a, ad, F) =  F / mc + \n\
		\|  (mp/mc) * lp * (ad^2 * sin(a) - \n\
		\|      cos(a) * ((mc * g * sin(a) - \n\
		\|          cos(a) * (F + mp * lp * ad^2 * sin(a))) /\n\
		\|         (4 * mc * lp / 3 - mp * lp * cos(a)^2)))";
	title = "Acceleration";
	visual V1 {
		center = (60, 240);
		height = 7;
		link 2 {
			path = ((196, 87), (84, 168), (62, 232));
			};
		link 3 {
			path = ((320, 81), (144, 168), (69, 232));
			};
		};
	};
};