Page - 97 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4.1. AdaptiveControl switches between only two states [MTA+06]. When the bang-bang control scheme is used in the nonlinear model of HEPHAISTOS, it is defined that the control input variables switch between 0 and 1, which indicate the feeding source is turned off or turned on with full power respectively. Compared with normal control where the control variable can take any value between 0 and 1, it seems that the bang- bangcontrolschemeslosesa largepartof theoverallcontroldiversity. But when the dimension of control inputs is large enough such as in HEPHAISTOS, the remained control diversity of such a binary con- trol scheme is considerably large. For instance, in the new HEPHAIS- TOS Cavity 3, the number of feeding sources is 18 (the old HEPHAIS- TOS Cavity 3 had 36 sources), the total number of different heating combinations is 218. It means in theory the system could provide 218 different heating patterns, which is still sufficient to provide a rather uniformheating. To derive the control solution in the bang-bang control schemes, a binary programming algorithm [Sch98] has to be used. But due to the special nonlinear form of 3.46, normal binary programming al- gorithms are difficult to be implemented (most binary programming algorithms can only deal with linear optimization problems [Sch98]). Under this circumstance, the genetic algorithm(GA) is used here. GA is a powerful global optimization and search algorithm inspired by the natural evolution process [DAJ02]. Although many parts of GA arestillnotwellunderstoodsuchas itsconvergingandstabilityprop- erties, it can achieve surprisingly good performance for many prac- tical problems where traditional algorithms could not work [HJK95]. Nowadays it has been one of the most successful optimization algo- rithms that are widely used in computer science, engineering, eco- nomicsandotherfields. Explicit introductionsaboutGAcanbefound in[Whi94]. ThebinaryGAbasednonlinearMPCsystemofHEPHAIS- TOScontains the followingfourprocedures. • Step1: Initialization At each time k, a number of possible control sequences are ran- domlygenerated, suchas Vci = [ Vi(k) T Vi(k+1) T . .. Vi(k+p−1)T ]T , 1≤ i≤Ng, 97