Page - 98 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign whereNg is the total number of control sequences that are initial- ized. Each control sequence is called one individual or chromo- some,andall individualsformapopulation. Intherealapplication ofHEPHAISTOS, it isassumedthat Vi(k) =Vi(k+1) = · ··=Vi(k+p−1). That is because in MPC the first input vector Vi(k) takes more credits than the rest of the sequence. It may happen that a con- trol sequence performs well referring to the cost function, but the first input vector is actually not a good choice. In order to avoid this situation, it is assumed that all following input vectors in the control sequence are identical to the first one, to fully examine the performance ofVi(k). Moreover, this arrangement also largely re- duces the search space and raises the opportunity to quickly find thebestcontrol solution. • Step2: Evaluationandselection There are two important functions in GA. One is the evaluation function and the other one is the fitness function [Whi94]. Here the cost function (equation 4.2) is used as the evaluation function. All individuals of one population are substituted into the nonlin- ear model (equation 3.46) to predict their corresponding future temperaturevectors, suchas Yi(k+1) = [A(k)]Y(k)+Ψ ( Vi(k) ) , Yi(k+2) = [A(k)]Y(k+1)+Ψ ( Vi(k+1) ) , ... Yi(k+p) = [A(k)]Y(k+p−1)+Ψ ( Vi(k+p−1) ) . Above predicted temperature vectors are further substituted into the evaluation function 4.2 to calculate individual future costsJi, suchas Ji= k+p∑ l=k+1 [( Yt(l)−Yi(l) )T [Γ(l)] ( Yt(l)−Yi(l) ) +VTi (l)[Λ(l)]Vi(l) ] , whereΓ(l)andΛ(l)aredefinedthesameas inequation 4.2. 98