Page - 93 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4.1. AdaptiveControl [Fd(k)] =          [Cd(k)][Ad(k)] [Cd(k)][Ad(k)] 2 [Cd(k)][Ad(k)] 3 ... [Cd(k)][Ad(k)] p          , Yd(k) =          Y(k+1|k) Y(k+2|k) Y(k+3|k) ... Y(k+p|k)          , ∆Ud(k) =          ∆U(k) ∆U(k+1) ∆U(k+2) ... ∆U(k+p−1)          , (4.13) where [ON×M] is thezeromatrixwith thedimensionN×M. With the modified state-space system model 4.12, the original cost function 4.2 isalsomodifiedinto [Wan09] JLM(k) = [( Yd,t(k)−Yd(k) )T [Γ] ( Yd,t(k)−Yd(k) ) (4.14) + ∆Ud(k) T [Λ]∆Ud(k) ] = [( Yd,t(k)− [Fd(k)]Xd(k) )T Γ ( Yd,t(k)− [Fd(k)]Xd(k) ) −2∆UTd(k)[Ξd(k)]T [Γ] ( Yd,t(k)− [Fd(k)]Xd(k) ) +∆UTd(k) ( [Ξd(k)] T [Γ] [Ξd(k)]+[Λ] ) ∆Ud(k) ] , (4.15) with [Γ] :=       [Γ(1)] [ON] · ·· [ON] [ON] [Γ(2)] · ·· [ON] ... ... ... ... [ON] [ON] · ·· [Γ(p)]       , 93