1 | yalmip('clear') |
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2 | clear all |
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3 | |
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4 | % Prediction horizon |
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5 | N = 5; |
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6 | |
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7 | opt_sincos |
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8 | |
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9 | probStruct.N=N-1; |
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10 | |
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11 | ctrl=mpt_control(sysStruct,probStruct) |
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12 | |
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13 | nx = 2; |
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14 | nu = 1; |
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15 | |
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16 | % States x(k), ..., x(k+N) |
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17 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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18 | |
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19 | % Inputs u(k), ..., u(k+N) (last one not used) |
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20 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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21 | |
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22 | % Binary for PWA selection |
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23 | d = binvar(2,1); |
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24 | |
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25 | % Value functions |
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26 | J = cell(1,N); |
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27 | |
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28 | % Initialize value function at stage N |
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29 | J{N} = 0; |
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30 | |
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31 | for k = N-1:-1:1 |
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32 | % Feasible region |
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33 | t = sdpvar(2,1); |
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34 | bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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35 | bounds(u{k},sysStruct.umin,sysStruct.umax); |
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36 | bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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37 | bounds(t,0,60); |
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38 | |
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39 | F = set(sysStruct.umin < u{k} < sysStruct.umax); |
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40 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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41 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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42 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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43 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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44 | |
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45 | F = F + set(-t(1) < x{k} < t(1)) ; |
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46 | F = F + set(-t(2) < u{k} < t(2)) ; |
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47 | |
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48 | % PWA Dynamics |
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49 | for i = 1:length(sysStruct.A) |
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50 | F = F + set(implies(d(i),x{k+1} == sysStruct.A{i}*x{k}+sysStruct.B{i}*u{k}+sysStruct.f{i})); |
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51 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} < sysStruct.guardC{i})); |
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52 | end |
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53 | F = F + set(sum(d) == 1); |
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54 | |
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55 | % Compute value function for one step backwards |
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56 | [mpsol{k},sol{k},Uz{k},J{k},U{k}] = solvemp(F,sum(t) + J{k+1},[],x{k},u{k}); |
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57 | |
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58 | end |
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59 | |
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60 | mpsol{1} = rmovlps(mpsol{1}) |
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61 | |
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62 | mpt_isPWAbigger(mpsol{1},ctrl) |
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63 | |
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64 | %mpt_plotpwA(mpsol{k}.Pn,mpsol{k}.Bi,mpsol{k}.Ci);hold on |
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65 | %mpt_plotpwA(ctrl.Pn,ctrl.Bi,ctrl.Ci) |
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66 | |
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