Algorithm 12: Functional Flow of Hildreth’s Quadratic Programming solution for MPC, constrained solution

For iterations 1 to 40 1. Save λcurrent → λprevious 2.  LOOP1 to build λ, i = 0 to # elements in M or Msize a.  w = 0; b.  LOOP2 to build λ, j starts at 0 i.  w = w + P[i][j]∙λ[j] ii.  If j<Msize, repeat LOOP2 else GOTO 2.c c.  w = w + K[i]-P[i][i]∙λ[i] d.  λtest = -w/P[i][i] e.  if λtest< 0 then λ[i] = 0, else λ[i] = λtest f.  i<Msize repeat LOOP1 else GOTO 3 3.  Check convergence a.  calculate the Euclidean length of previous λ b.  calculate the Euclidean length of current λ c.  Compare ratio to reference value d.  if converged is false GOTO 1, else GOTO 4. 4.  Calculate new Δu a.  Start loop, j = 0 to j = Msize i.  Δuc = Δuc +∙λ[j] ME−1[j] b.  GOTO 4.a if j<Msize else GOTO 4.c c.  DU = Δu°-Δuc 5. End