Page - 100 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign • Step4: Termination The new individuals generated from crossover and mutation will be evaluated and selected again to create another new genera- tion. Steps 2 and 3 are iterated until the number of generations is reached or a certain level of fitness value is achieved. The con- trol sequence with the highest fitness value will be selected, and the first control input vector within this sequence will be applied as thereal control inputvectorV(k). The biggest advantage of GA is that the whole process can search through the whole input space efficiently without being trapped in a local optimum [Whi94]. During the searching process, a large num- ber of predictions have to be performed, therefore the time spent on each single prediction is a key element that affects the performance of the whole algorithm. In order to have more iterations within a given control period, the time for each prediction should be as short as pos- sible. Compared with multiple layers calculations using nonlinear ac- tivation functions in the neural network estimator, the time required by the nonlinear model (equation 3.46) is much less. Therefore, the nonlinearmodel isusedfor thepredictionandGAcontrolling. Stability is always one of the most important and fundamental issues in the controller design. For the linear MPC, the general stability of DMC is proved in [GM82] in situations where the prediction horizon lengthp is significantly larger than the dimension of the input vector p>>n. It was further demonstrated in [Cut83] that DMC is stable in the case of p≥ n+nd wherend is the largest input to output delay time. So far there is no explicit proof about that under what circum- stances a finite horizon input constrained QDMC algorithm is closed- loop stable. However, as mentioned in [GM86] that in general cases QDMC is more stable and robust than DMC, because of the loss of control gain due to input constraints [Mor85]. The stability of QDMC has also been verified by a large number of successful applications in theoil industry. Compared with the QDMC algorithm, the stability conditions of non- linearMPChasnotbeenwellestablished. Totheauthor’sknowledge, currently there are no practically useful stability results established for GA. Nevertheless, a number of empirical approaches can be done to improve their stabilities and robustnesses in practical applications. 100