Relaxation methods for parallel in line calculations of the optimum control of large systems

The optimal regulation with a sliding horizon of complex, linear or non linear, processes necessitates a device which will accomplish in real time the collection of process data, the treatment of in line information, and the action on control variables. The computing method consists of solving the Hamilton-Pontriaguine equations of the global process by : decomposition into subsystems of equations relative to subprocesses iterative coordination of corresponding subproblems by “delayed chaotic relaxation algorithms”. These family of methods generalise past works of Takahara and Wismer ; it is shown, in the linear-quadratic case, that the problem can always be coordinated by relaxation when the state matrix is the opposite of an H-matrix, with a suitable penalization of commande error. A specialized multi-microprocessor computer is under construction at Besançon. For the moment, all trials have been carried out using a hybrid system which consists of a minicomputer associated with a rapid analog integration machine constructed in the laboratory. Comparative results of global and decentralized methods are given for a thermic process example, realized by both monoprocessor systems and parallel (hybrid) system, the latter systems giving very interesting performances compatible with and in line with usage. Thusly the possibility exists of an “intermittently closed loop” command thanks to a calculation made periodically from the real state of the process, in negligeable time comparated to the horizon of the command considered. This system can be superimposed on a pre-existing classical system of regulation, whose presence does not complicate the calculations but constitutes a security (hierarchical command).