Optimal control of fed-batch processes with particle swarm optimization

Abstract

Optimal control problems appear in several engineering fields. These problems are often described by sets of nonlinear differential and algebraic equations, usually subject to constraints in the state and control variables. Some bioprocess optimal control problems are revisited and a numerical approach to its solution is introduced. The numerical procedure used to solve the problems takes advantage of the well know modeling AMPL language, providing an external dynamic library that solve the nonlinear differential equations. The optimal control problem as generally presented belongs to the class of semi-infinite programming (SIP) problems. A transformation of the SIP problem results in a nonlinear optimization problem (NLP) that can be address by off-the-shelf optimization software. The NLP formulation results in nondifferentiable optimization problems were the global solution is mostly desirable. We apply a particle swarm optimization strategy implemented in the MLOCPSOA [13] solver. Particle swarm optimization (PSO) is a stochastic technique that mimics the social behavior of a swarm.