%% Instances of the heating benchmarks, as described in: A. Fehnker %% and F. Ivancic, Benchmarks for Hybrid System Verification, 2004. %% %% For each instance we define: %% rooms number of rooms %% heaters number of heaters %% Amat matrix of exchange coefficients %% bvec vector of loss coefficients %% cvec vector of heater capacities %% u outside temperature %% xinit initial continuous state %% h initial location of heaters %% off temperature at which to switch the heater off %% on temperature at which to switch the heater back on %% get temperature at which to get a heater %% dif difference in temperature at which to get the heater %% lower lower bound on temperature for each room %% %% HEAT01 rooms = 3 heaters = 1 Amat = [0.00 0.80 0.60 0.80 0.00 0.70 0.60 0.70 0.00] bvec = [0.30; 0.20; 0.30] cvec = [12.00; 14.00; 12.00] u = 6 xinit \in [19,20]^3 h = [ 0; 1; 0] % initial value for h off = [21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00] get = [18.00; 18.00; 18.00] dif = [1.00; 1.00; 1.00] lower = [17.50; 17.50; 17.50] % lower bound on x %% HEAT02 rooms = 3 heaters = 1 Amat = [0.00 0.80 0.00 0.80 0.00 0.70 0.00 0.70 0.00] bvec = [0.30; 0.20; 0.30] cvec = [12.00; 14.00; 12.00] u \in [6,7] xinit \in [19,20]^3 h = [ 0; 1; 0] % initial value for h off = [21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00] get = [18.00; 18.00; 18.00] dif = [1.00; 1.00; 1.00] lower = [16.00; 17.50; 16.00] % lower bound on x %% HEAT03 rooms = 3 heaters = 1 Amat = [0.00 0.90 0.00 0.90 0.00 1.00 0.00 1.00 0.00] bvec = [0.20; 0.50; 0.30] cvec = [10.00; 17.00; 12.00] u \in [3,4] xinit \in [19,20]^3 h = [ 0; 0; 1] % initial value for h off = [21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00] get = [18.00; 18.00; 18.00] dif = [1.00; 1.00; 1.00] lower = [16.00; 15.50; 15.50] % lower bound on x %% HEAT04 rooms = 3 heaters = 2 Amat = [0.00 0.60 0.40 0.60 0.00 0.00 0.40 0.00 0.00] bvec = [0.40; 0.20; 0.30] cvec = [8.00; 6.00; 10.00] u \in [4,5] xinit \in [18,19]^3 h = [ 1; 0; 1] % initial value for h off = [21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00] get = [18.00; 17.00; 18.00] dif = [1.00; 1.00; 1.00] lower = [18.00; 17.00; 17.50] % lower bound on x %% HEAT05 rooms = 3 heaters = 2 Amat = [0.00 0.50 0.00 0.50 0.00 0.50 0.00 0.50 0.00] bvec = [0.40; 0.30; 0.40] cvec = [6.00; 7.00; 8.00] u \in [5,6] xinit \in [19,20]^3 h = [ 1; 0; 1] % initial value for h off = [21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00] get = [18.00; 18.00; 18.00] dif = [1.00; 1.00; 1.00] lower = [16.50; 16.50; 16.50] % lower bound on x %% HEAT06 rooms = 3 heaters = 2 Amat = [0.00 0.50 0.00 0.50 0.00 0.50 0.00 0.50 0.00] bvec = [0.38; 0.17; 0.42] cvec = [5.00; 7.00; 5.00] u \in [6,7] xinit \in [18,19]^3 h = [ 1; 0; 1] % initial value for h off = [21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00] get = [17.00; 17.00; 17.00] dif = [1.00; 1.00; 1.00] lower = [16.00; 15.50; 16.00] % lower bound on x %% HEAT07 rooms = 4 heaters = 3 Amat = [0.00 0.50 0.30 0.00 0.50 0.00 0.20 0.50 0.30 0.20 0.00 0.40 0.00 0.50 0.40 0.00] bvec = [0.56; 0.16; 0.39; 0.61] cvec = [8.00; 7.00; 6.00; 9.00] u \in [4,5] xinit \in [18.00; 19.00]^4 h = [ 1; 0; 1; 1] % initial value for h off = [20.00; 20.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00] get = [17.00; 18.00; 16.00; 17.00] dif = [1.00; 1.00; 1.00; 1.00] lower = [16.00; 16.00; 16.00; 16.00] % lower bound on x %% HEAT08 rooms = 4 heaters = 3 Amat = [0.00 0.60 0.20 0.50 0.60 0.00 0.40 0.00 0.20 0.40 0.00 0.00 0.50 0.00 0.00 0.00] bvec = [0.19; 0.39; 0.44; 0.50] cvec = [6.00; 7.00; 8.00; 9.00] u \in [2, 3] xinit \in [17.00,18.00]^4 h = [ 1; 0; 1; 1] % initial value for h off = [20.50; 20.50; 20.50; 20.50] on = [20.00; 20.00; 20.00; 20.00] get = [18.00; 17.00; 17.00; 18.00] dif = [1.00; 1.00; 1.00; 1.00] lower = [16.00; 16.50; 16.00; 16.00] % lower bound on x %% HEAT09 rooms = 4 heaters = 3 Amat = [0.00 0.40 0.00 0.30 0.40 0.00 0.50 0.40 0.00 0.50 0.00 0.30 0.30 0.40 0.30 0.00] bvec = [0.30; 0.20; 0.30; 0.50] cvec = [6.00; 8.00; 5.00; 9.00] u \in [-1.00,0] xinit \in [18.00; 19.00]^4 h = [ 1; 0; 1; 1] % initial value for h off = [20.00; 20.00; 20.00; 20.00] on = [19.00; 19.00; 19.00; 19.00] get = [18.00; 16.00; 18.00; 17.00] dif = [1.00; 1.00; 1.00; 1.00] lower = [13.50; 13.50; 14.00; 13.50] % lower bound on x %% HEAT10 rooms = 4 heaters = 2 Amat = [0.00 0.30 0.40 0.30 0.30 0.00 0.50 0.00 0.40 0.50 0.00 0.30 0.30 0.00 0.30 0.00] bvec = [0.30; 0.20; 0.50; 0.40] cvec = [9.00; 7.00; 11.00; 7.00] u \in [4.00,5.00] xinit \in [16.00, 17.00]^4 h = [ 0; 1; 1; 0] % initial value for h off = [20.00; 20.00; 20.00; 20.00] on = [19.00; 19.00; 19.00; 19.00] get = [17.00; 16.00; 16.00; 17.00] dif = [1.00; 1.00; 1.00; 1.00] lower = [15.00; 15.00; 15.00; 15.00] % lower bound on x %% HEAT11 rooms = 4 heaters = 2 Amat = [0.00 0.40 0.00 0.50 0.40 0.00 0.40 0.00 0.00 0.40 0.00 0.30 0.50 0.00 0.30 0.00] bvec = [0.30; 0.25; 0.35; 0.30] cvec = [10.00; 7.00; 11.00; 8.00] u \in [4,5] xinit \in [17.00,18.00]^4 h = [ 0; 1; 1; 0] % initial value for h off = [20.00; 20.00; 20.00; 20.00] on = [19.00; 19.00; 19.00; 19.00] get = [18.00; 17.00; 17.00; 18.00] dif = [1.00; 1.00; 1.00; 1.00] lower = [16.00; 16.50; 16.00; 16.00] % lower bound on x %% HEAT12 rooms = 4 heaters = 2 Amat = [0.00 0.60 0.80 0.60 0.60 0.00 0.70 0.00 0.80 0.70 0.00 0.50 0.60 0.00 0.50 0.00] bvec = [0.10; 0.30; 0.40; 0.35] cvec = [12.00; 7.00; 11.00; 10.00] u \in [-1.00,0] xinit \in [17.00,18.00]^4 h = [ 1; 0; 0; 1] % initial value for h off = [21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00] get = [18.00; 17.00; 15.00; 15.00] dif = [1.00; 1.00; 1.00; 1.00] lower = [14.50; 14.50; 14.00; 14.00] % lower bound on x %% HEAT13 ooms = 5 heaters = 3 Amat = [0.00 0.30 0.00 0.00 0.50 0.30 0.00 0.20 0.00 0.20 0.00 0.20 0.00 0.30 0.50 0.00 0.00 0.30 0.00 0.40 0.50 0.20 0.50 0.40 0.00] bvec = [0.25; 0.10; 0.15; 0.20; 0.40] cvec = [10.00; 12.00; 13.00; 11.00; 8.00] u \in [-2,0] xinit \in [17.00, 18.00]^5 h = [ 1; 0; 1; 0; 1] % initial value for h off = [20.00; 20.00; 20.00; 20.00; 20.00] on = [17.00; 17.00; 17.00; 17.00; 17.00] get = [18.00; 17.00; 16.00; 17.00; 18.00] dif = [1.00; 1.00; 1.00; 1.00; 1.00] lower = [15.50; 16.00; 15.50; 16.00; 16.00] % lower bound on x %% HEAT14 rooms = 5 heaters = 3 Amat = [0.00 0.30 0.00 0.50 0.60 0.30 0.00 0.20 0.00 0.20 0.00 0.20 0.00 0.30 0.50 0.50 0.00 0.30 0.00 0.00 0.60 0.20 0.50 0.00 0.00] bvec = [0.35; 0.10; 0.15; 0.30; 0.25] cvec = [9.00; 11.00; 9.00; 12.00; 6.00] u \in [-1, 1] xinit \in [17.00, 18.00]^5 h = [ 1; 0; 1; 0; 1] % initial value for h off = [20.00; 20.00; 20.00; 20.00; 20.00] on = [18.00; 18.00; 18.00; 18.00; 18.00] get = [18.00; 17.00; 18.00; 17.00; 18.00] dif = [1.00; 2.00; 1.00; 1.00; 1.00] lower = [16.50; 16.00; 16.50; 16.00; 16.50] % lower bound on x %% HEAT15 rooms = 5 heaters = 3 Amat = [0.00 0.40 0.00 0.00 0.50 0.40 0.00 0.20 0.20 0.00 0.00 0.20 0.00 0.50 0.00 0.00 0.20 0.50 0.00 0.40 0.50 0.00 0.00 0.40 0.00] bvec = [0.25; 0.35; 0.10; 0.15; 0.45] cvec = [10.00; 7.00; 10.00; 11.00; 9.00] u \in [-2,0] xinit \in [18.00, 19.00]^5 h = [ 0; 1; 1; 1; 0] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00; 19.00] get = [16.00; 17.00; 18.00; 17.00; 16.00] dif = [0.50; 0.50; 1.00; 0.50; 0.50] lower = [15.50; 16.00; 16.00; 16.00; 15.50] % lower bound on x %% HEAT16 rooms = 6 heaters = 3 Amat = [0.00 0.50 0.00 0.00 0.00 0.00 0.50 0.00 0.35 0.40 0.40 0.00 0.00 0.35 0.00 0.30 0.30 0.00 0.00 0.40 0.30 0.00 0.00 0.30 0.00 0.40 0.30 0.00 0.00 0.25 0.00 0.00 0.00 0.30 0.25 0.00] bvec = [0.30; 0.40; 0.10; 0.15; 0.20; 0.30] cvec = [10.00; 7.00; 10.00; 11.00; 9.00; 8.00] u \in [0 2.00] xinit \in [19.00, 20.00]^6 h = [ 0; 1; 0; 0; 1; 1] % initial value for h off = [20.00; 20.00; 20.00; 20.00; 20.00; 20.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [16.00; 17.00; 18.00; 17.00; 19.00; 18.00] dif = [1.00; 1.00; 2.00; 1.00; 1.00; 2.00] lower = [15.00; 16.50; 16.00; 16.00; 16.00; 15.00] % lower bound on x %% HEAT17 rooms = 6 heaters = 3 Amat = [0.00 0.60 0.15 0.00 0.00 0.45 0.60 0.00 0.50 0.25 0.00 0.20 0.15 0.50 0.00 0.45 0.00 0.00 0.00 0.25 0.45 0.00 0.55 0.00 0.00 0.00 0.00 0.55 0.00 0.20 0.45 0.20 0.00 0.00 0.20 0.00] bvec = [0.10; 0.35; 0.30; 0.15; 0.20; 0.25] cvec = [11.00; 7.00; 8.00; 10.00; 9.00; 10.00] u \in [-2 0.00] xinit \in [16, 17]^6 h = [ 1; 0; 0; 0; 1; 1] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [18.00; 17.00; 18.00; 17.00; 19.00; 18.00] dif = [2.00; 1.00; 1.00; 1.00; 2.00; 1.00] lower = [15.00; 15.00; 14.50; 15.00; 14.50; 14.50] % lower bound on x %% HEAT18 rooms = 6 heaters = 3 Amat = [0.00 0.30 0.00 0.00 0.05 0.20 0.30 0.00 0.25 0.00 0.05 0.00 0.00 0.25 0.00 0.20 0.40 0.00 0.00 0.00 0.20 0.00 0.25 0.00 0.05 0.05 0.40 0.25 0.00 0.40 0.20 0.00 0.00 0.00 0.40 0.00] bvec = [0.10; 0.20; 0.25; 0.20; 0.05; 0.15] cvec = [10.00; 7.00; 6.00; 7.00; 10.00; 7.00] u \in [-3.00, -1.00] xinit \in [17, 18]^6 h = [ 1; 1; 1; 0; 0; 0] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [20.00; 20.00; 20.00; 20.00; 20.00; 20.00] get = [16.00; 17.00; 18.00; 17.00; 18.00; 17.00] dif = [2.00; 1.00; 1.00; 2.00; 1.00; 1.00] lower = [15.50; 16.00; 16.00; 15.00; 16.50; 15.00] % lower bound on x %% HEAT19 rooms = 7 heaters = 4 Amat = [0.00 0.10 0.00 0.10 0.00 0.00 0.00 0.10 0.00 0.10 0.10 0.20 0.00 0.00 0.00 0.10 0.00 0.00 0.10 0.00 0.00 0.10 0.10 0.00 0.00 0.10 0.10 0.00 0.00 0.20 0.10 0.10 0.00 0.05 0.00 0.00 0.00 0.00 0.10 0.05 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.10 0.00] bvec = [0.15; 0.10; 0.15; 0.13; 0.13; 0.15; 0.15] cvec = [7.00; 4.00; 6.00; 5.00; 4.00; 5.00; 6.00] u \in [0, 2] xinit \in [17, 18]^7 h = [ 1; 1; 0; 0; 1; 0; 1] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [17.00; 18.00; 17.00; 16.00; 18.00; 17.00; 17.00] dif = [1.00; 2.00; 1.00; 2.00; 2.00; 1.00; 1.00] lower = [14.50; 16.00; 15.00; 15.50; 16.00; 15.50; 14.50] % lower bound on x %% HEAT20 rooms = 7 heaters = 4 Amat = [0.00 0.10 0.12 0.00 0.00 0.00 0.00 0.10 0.00 0.15 0.00 0.10 0.00 0.00 0.12 0.15 0.00 0.05 0.10 0.00 0.00 0.00 0.00 0.05 0.00 0.05 0.05 0.05 0.00 0.10 0.10 0.05 0.00 0.15 0.00 0.00 0.00 0.00 0.05 0.15 0.00 0.15 0.00 0.00 0.00 0.05 0.00 0.15 0.00] bvec = [0.16; 0.26; 0.24; 0.22; 0.20; 0.20; 0.20] cvec = [7.00; 5.00; 6.00; 7.00; 7.00; 7.00; 7.00] u \in [-1,1] xinit \in [16, 17]^7 h = [ 0; 0; 1; 0; 1; 1; 1] % initial value for h off = [22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00] on = [20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00] get = [16.00; 17.00; 15.00; 14.00; 16.00; 16.00; 16.00] dif = [2.00; 1.00; 1.00; 2.00; 2.00; 1.00; 2.00] lower = [13.00; 14.50; 14.00; 13.00; 14.00; 14.00; 13.00] % lower bound on x %% HEAT21 rooms = 7 heaters = 3 Amat = [0.00 0.40 0.00 0.00 0.32 0.00 0.00 0.40 0.00 0.40 0.00 0.00 0.32 0.00 0.00 0.40 0.00 0.12 0.00 0.00 0.32 0.00 0.00 0.12 0.00 0.00 0.00 0.12 0.32 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.32 0.00 0.00 0.40 0.00 0.40 0.00 0.00 0.32 0.12 0.00 0.40 0.00] bvec = [0.14; 0.10; 0.12; 0.15; 0.14; 0.10; 0.12] cvec = [4.00; 5.00; 5.00; 4.00; 5.00; 5.00; 4.00] u \in [0,2] xinit \in [17,18]^7 h = [ 0; 0; 0; 1; 1; 0; 1] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [18.00; 18.00; 18.00; 18.00; 18.00; 18.00; 18.00] get = [17.00; 17.00; 17.00; 17.00; 17.00; 17.00; 17.00] dif = [1.00; 2.00; 2.00; 1.00; 2.00; 2.00; 1.00] lower = [13.00; 13.50; 13.00; 13.50; 13.00; 13.50; 13.50] % lower bound on x %% HEAT22 rooms = 8 heaters = 3 Amat = [0.00 0.18 0.13 0.13 0.08 0.08 0.13 0.13 0.18 0.00 0.08 0.00 0.00 0.00 0.00 0.08 0.13 0.08 0.00 0.08 0.00 0.00 0.00 0.00 0.13 0.00 0.08 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.00 0.08 0.00 0.08 0.00 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.08 0.00 0.13 0.00 0.00 0.00 0.00 0.08 0.00 0.08 0.13 0.08 0.00 0.00 0.00 0.00 0.08 0.00] bvec = [0.04; 0.14; 0.14; 0.10; 0.12; 0.10; 0.14; 0.14] cvec = [2.00; 6.00; 6.00; 7.00; 6.00; 8.00; 6.00; 6.00] u \in [-2 0] xinit \in [17, 18]^8 h = [ 0; 0; 1; 0; 1; 0; 0; 1] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [17.00; 16.00; 16.00; 16.00; 17.00; 16.00; 16.00; 17.00] dif = [3.00; 1.00; 1.00; 2.00; 1.00; 1.00; 1.00; 2.00] lower = [16.00; 14.00; 13.50; 14.00; 14.00; 14.50; 14.00; 14.50] % lower bound on x %% HEAT23 rooms = 8 heaters = 3 Amat = [0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.16 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.16 0.00 0.00 0.00 0.16 0.16 0.16 0.00 0.30 0.00 0.00 0.00 0.00 0.00 0.16 0.30 0.00] bvec = [0.20; 0.12; 0.20; 0.12; 0.02; 0.20; 0.12; 0.30] cvec = [9.00; 9.00; 9.00; 9.00; 9.00; 8.00; 8.00; 7.00] u \in [-3,-1] xinit \in [16.00,17.00]^8 h = [ 1; 0; 0; 0; 1; 1; 0; 0] % initial value for h off = [22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [16.00; 16.00; 16.00; 16.00; 17.00; 17.00; 17.00; 18.00] dif = [1.00; 1.00; 1.00; 1.00; 2.00; 2.00; 2.00; 2.00] lower = [12.50; 14.50; 14.00; 14.50; 15.00; 14.00; 14.00; 13.50] % lower bound on x %% HEAT24 rooms = 8 heaters = 3 Amat = [0.00 0.10 0.10 0.10 0.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.10 0.10 0.00 0.00 0.10 0.00 0.00 0.20 0.00 0.00 0.10 0.00 0.10 0.00 0.20 0.00 0.20 0.00 0.10 0.00 0.00 0.10 0.00 0.20 0.00 0.20 0.00 0.10 0.00 0.10 0.00 0.00 0.20 0.00 0.00 0.10 0.00 0.00 0.10 0.10 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.10 0.10 0.10 0.00] bvec = [0.24; 0.24; 0.16; 0.02; 0.02; 0.16; 0.24; 0.24] cvec = [7.00; 7.00; 6.00; 6.00; 6.00; 6.00; 7.00; 7.00] u \in [0,1] xinit \in [16.00, 17.00]^8 h = [ 1; 1; 0; 0; 0; 0; 0; 1] % initial value for h off = [22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00] on = [20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00] get = [16.00; 17.00; 16.00; 16.00; 17.00; 17.00; 16.00; 17.00] dif = [1.00; 1.00; 2.00; 2.00; 2.00; 2.00; 1.00; 1.00] lower = [13.50; 13.50; 13.00; 14.00; 14.00; 13.00; 13.50; 13.50] % lower bound on x %% HEAT25 rooms = 9 heaters = 4 Amat = [0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.16 0.00] bvec = [0.24; 0.16; 0.24; 0.16; 0.01; 0.16; 0.24; 0.16; 0.24] cvec = [7.00; 6.00; 7.00; 6.00; 5.00; 6.00; 7.00; 6.00; 7.00] u \in [0 2.00] xinit \in [17,18.00]^9 h = [ 0; 0; 0; 0; 1; 1; 0; 1; 1] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [17.00; 16.00; 17.00; 16.00; 17.00; 17.00; 17.00; 16.00; 17.00] dif = [1.00; 1.00; 2.00; 2.00; 1.00; 2.00; 2.00; 1.00; 1.00] lower = [14.00; 14.00; 13.00; 14.00; 15.50; 14.00; 13.00; 14.00; 13.50] % lower bound on x %% HEAT26 rooms = 9 heaters = 4 Amat = [0.00 0.08 0.00 0.08 0.02 0.00 0.00 0.00 0.00 0.08 0.00 0.08 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.08 0.00 0.00 0.02 0.08 0.00 0.00 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.08 0.00 0.00 0.02 0.08 0.02 0.08 0.00 0.08 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.00 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.08 0.00 0.08 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.08 0.00 0.08 0.00] bvec = [0.24; 0.12; 0.24; 0.18; 0.06; 0.18; 0.24; 0.12; 0.24] cvec = [8.00; 6.00; 7.00; 6.00; 4.00; 6.00; 7.00; 6.00; 8.00] u \in [0,1] xinit \in [16,17]^9 h = [ 1; 0; 1; 0; 0; 0; 1; 1; 0] % initial value for h off = [22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [16.00; 17.00; 15.00; 17.00; 16.00; 16.00; 15.00; 17.00; 16.00] dif = [1.00; 1.00; 1.00; 2.00; 1.00; 1.00; 2.00; 2.00; 1.00] lower = [13.50; 14.50; 12.50; 13.50; 15.00; 14.00; 12.50; 13.50; 13.00] % lower bound on x %% HEAT27 rooms = 9 heaters = 4 Amat = [0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.16 0.02 0.16 0.02 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.02 0.00 0.00 0.16 0.00 0.16 0.02 0.00 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.16 0.00 0.00 0.02 0.16 0.00 0.16 0.00 0.00 0.02 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.02 0.16 0.02 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.16 0.00] bvec = [0.24; 0.12; 0.24; 0.16; 0.06; 0.16; 0.24; 0.12; 0.24] cvec = [7.00; 5.00; 8.00; 5.00; 3.00; 6.00; 8.00; 5.00; 7.00] u \in [1,2] xinit \in [16.00,17.00]^9 h = [ 1; 1; 0; 1; 0; 0; 1; 0; 0] % initial value for h off = [21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00; 21.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [15.00; 17.00; 15.00; 17.00; 16.00; 16.00; 15.00; 16.00; 17.00] dif = [2.00; 1.00; 2.00; 1.00; 1.00; 1.00; 2.00; 1.00; 2.00] lower = [13.50; 15.50; 13.50; 15.00; 15.50; 15.00; 13.50; 15.00; 13.50] % lower bound on x %% HEAT28 rooms = 10 heaters = 4 Amat = [0.00 0.12 0.06 0.00 0.12 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.12 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.12 0.00 0.06 0.12 0.12 0.00 0.00 0.00 0.00 0.00 0.12 0.06 0.00 0.00 0.12 0.00 0.00 0.00 0.00 0.12 0.00 0.12 0.00 0.00 0.16 0.12 0.12 0.00 0.00 0.00 0.00 0.12 0.12 0.16 0.00 0.00 0.00 0.12 0.12 0.00 0.00 0.00 0.00 0.12 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.16 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.00 0.16 0.00] bvec = [0.24; 0.12; 0.05; 0.24; 0.16; 0.16; 0.24; 0.12; 0.12; 0.24] cvec = [7.00; 5.00; 5.00; 7.00; 6.00; 6.00; 8.00; 7.00; 7.00; 8.00] u \in [1,2] xinit \in [16,17]^10 h = [ 0; 1; 0; 1; 0; 0; 0; 1; 0; 1] % initial value for h off = [22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00; 22.00] on = [19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00; 19.00] get = [15.00; 17.00; 16.00; 15.00; 16.00; 16.00; 16.00; 15.00; 16.00; 17.00] dif = [1.00; 1.00; 1.00; 1.00; 2.00; 2.00; 1.00; 2.00; 2.00; 1.00] lower = [13.00; 14.00; 15.00; 13.00; 14.00; 14.00; 13.00; 13.50; 13.50; 13.00] % lower bound on x %% HEAT29 rooms = 10 heaters = 4 Amat = [0.00 0.12 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.04 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.04 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.16 0.00 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.16 0.00 0.04 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.08 0.00 0.12 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.08 0.00] bvec = [0.10; 0.14; 0.18; 0.14; 0.14; 0.18; 0.14; 0.18; 0.18; 0.10] cvec = [7.00; 6.00; 5.00; 6.00; 6.00; 5.00; 7.00; 6.00; 6.00; 8.00] u \in [1,2] xinit \in [17.00, 18.00]^10 h = [ 1; 1; 0; 0; 0; 0; 0; 0; 1; 1] % initial value for h off = [24.00; 24.00; 24.00; 24.00; 24.00; 24.00; 24.00; 24.00; 24.00; 24.00] on = [20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00] get = [17.00; 16.00; 17.00; 16.00; 16.00; 15.00; 17.00; 16.00; 17.00; 16.00] dif = [1.00; 1.00; 0.50; 0.50; 1.00; 1.00; 0.50; 0.50; 1.00; 1.00] lower = [11.00; 11.00; 10.50; 11.50; 12.50; 13.00; 12.50; 12.50; 12.00; 12.50] % lower bound on x %% HEAT30 rooms = 10 heaters = 4 Amat = [0.00 0.12 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.12 0.00 0.04 0.08 0.00 0.00 0.00 0.00 0.08 0.00 0.08 0.04 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.16 0.00 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.16 0.00 0.04 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.08 0.00 0.12 0.08 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.08 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.08 0.00] bvec = [0.08; 0.10; 0.18; 0.14; 0.14; 0.18; 0.14; 0.18; 0.14; 0.08] cvec = [7.00; 6.00; 5.00; 6.00; 6.00; 5.00; 7.00; 6.00; 6.00; 8.00] u \in [1,2] xinit \in [17,18]^10 h = [ 0; 0; 1; 1; 1; 0; 0; 1; 0; 0] % initial value for h off = [23.00; 23.00; 23.00; 23.00; 23.00; 23.00; 23.00; 23.00; 23.00; 23.00] on = [20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00; 20.00] get = [16.00; 17.00; 17.00; 16.00; 15.00; 16.00; 17.00; 16.00; 16.00; 17.00] dif = [1.50; 1.50; 0.50; 0.50; 1.50; 1.50; 0.50; 0.50; 1.50; 1.50] lower = [14.50; 14.50; 13.50; 14.00; 13.00; 14.00; 14.00; 13.00; 13.50; 14.00] % lower bound on x