Development of methods for parallel computation of the solution of the problem for optimal control

Abstract

Optimal control of fermentation processes is necessary for better behaviour of the process in order to achieve maximum production of product and biomass. The problem for optimal control is a very complex nonlinear, dynamic problem requiring long time for calculation Application of decomposition-coordinating methods for the solution of this type of problems simplifies the solution if it is implemented in a parallel way in a cluster of computers. Parallel computing can reduce tremendously the time of calculation through process of distribution and parallelization of the computation algorithm. These processes can be achieved in different ways using the characteristics of the problem for optimal control.

Problem for optimal control of a fed-batch, batch and continuous fermentation processes for production of biomass and product are formulated. The problems are based on a criterion for maximum production of biomass at the end of the fermentation process for the fed-batch process, maximum production of metabolite at the end of the fermentation for the batch fermentation process and minimum time for achieving steady state fermentor behavior for the continuous process and on unstructured mass balance biological models incorporating in the kinetic coefficients, the physiochemical variables considered as control inputs. An augmented functional of Lagrange is applied and its decomposition in time domain is used with a new coordinating vector. Parallel computing in a Matlab cluster is used to solve the above optimal control problems. The calculations and tasks allocation to the cluster workers are based on a shared memory architecture. Real-time control implementation of calculation algorithms using a cluster of computers allows quick and simpler solutions to the optimal control problems.