Model Predictive Control - Stanford University

Model Predictive Control linear convex optimal Control finite horizon approximation Model Predictive Control fast MPC implementations supply chain managementProf. S. Boyd, EE364b, Stanford UniversityLinear time-invariant convex optimal controlminimizeJ= t=0 (x(t), u(t))subject tou(t) U, x(t) X, t= 0,1, ..x(t+ 1) =Ax(t) +Bu(t), t= 0,1, ..x(0) =z. variables: state and input trajectoriesx(0), x(1), .. Rn,u(0), u(1), .. Rm problem data: dynamics and input matricesA Rn n,B Rn m convex stage cost function :Rn Rm R, (0,0) = 0 convex state and input constraint setsX,U, with0 X,0 U initial statez XProf. S. Boyd, EE364b, Stanford University1 Greedy Control useu(t) = argminw{ (x(t), w)|w U, Ax(t) +Bw X} minimizes current stage cost only, ignoring effect ofu(t)on future,except forx(t+ 1) X typically works very poorly; can lead toJ= (when optimalugivesfiniteJ)Prof.

Model Predictive Control • linear convex optimal control • finite horizon approximation • model predictive control • fast MPC implementations • supply chain management Prof. S. Boyd, EE364b, Stanford University. Linear time-invariant convex optimal control

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