Control of goods production, storage and delivery based onprediction model systems output

The object is modeled using the following state space systems:qt+1 = qt + ϕt + Ґоt , zt+1 = zt + Ґшt − ϕt + Ґжt ,where zt - vector of amounts of goods in a storehouse , qt - vector of amounts of consumersgoods, Ґшt - production volume vector, ϕt − deliveries volume vector. Constraints on some stateand control components are:zmin ≤ zt ≤ zmax, 0 ≤ ƒt ≤ ƒmax, 0 ≤ ƒt ≤ zt.The system transformed to:xt+1 = Axt + But + wt .Equations for output vector yt and an observation vector ƒt become accordingly:yt = Gxt , Ґчt = Hxt + vt .The problem is to determine a control strategy providing consumers with as much product asgiven vector q . The task is accomplished by using output prediction system:xˆt+i+1|t = A xˆt+i|t + But+i|t , yˆt+i|t = Gxˆt+i|t ,where xˆi| j and yˆi| j represent estimates of the state and output formed by optimal Kalman predictor.The criterion function is:J(t) = _t+k|t-)C(_t+k|t-)+(u _t+k|t-u _t+k-1|t)D(u _t+k|t-u _t+k-1|t)}where С > 0, D > 0 - weighting matrices, N − prediction horizon. For optimization of the criterionthe Matlab quadprog procedure has been used.

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