Page - 105 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4.1. AdaptiveControl smaller than 1. Another simpler method is to randomly choose ∆i(k) to be either 1 or -1. Different methods of determining ∆i(k) canbeappliedaccordingly. • In the standard SPSA control system, one complete weight update of w(k) takes three control periods. In the beginning time k, the NN controller generates ∆(k),w(±)(k) and U(±)(k). and imple- ments the new control action U(+)(k). At timek+1, it measures correspondingsystemoutputY(+)(k) (whichisalsoY(k+1)), cal- culates the first evaluation valueJ(+)(k) using Y(+)(k), and then implements U(−)(k). The same procedures are repeated at time k+2 to calculateJ(−)(k). After that the weight w(k) will be up- dated using equation 4.25. The resulted new weight is not strictly w(k+1), butw(k+3)whichwillbeusedtocalculatenewcontrol action for the periodk+3. In principle, the output sequence can beexpressedas (seefigure 4.5) O= {. .. ,Y(k),Y(+)(k),Y(−)(k), Y(k+3),Y(+)(k+3),Y(−)(k+3), .. .}. (4.28) k k+1 k+5k+2 Time U(k) k+3 k+4 Y(k) Y+(k) Y-(k) Y+(k+3) Y-(k+3)Y(k+3) U+(k) U-(k) U(k+3) U +(k+3) U-(k+3) update of weights update of weights Figure4.5. Weightsupdate in thestandardSPSAalgorithm. The standard SPSA algorithm (equation 4.26) has a critical limita- tion that makes it difficult to be realized in practice. It is defined 105