Stochastic optimization for optimal and model-predictive control

The integrated-controlled-random-search for dynamic systems (ICRS/DS) method is improved to include a moving-grid strategy and is applied to more challenging problems including: (1) the optimal control of a fed-batch bioreactor, a plug-flow reactor exhibiting a singular are, the van der Pol oscillator; and (2) the model-predictive control (MPC) of the Czochralski (CZ) crystallization process. This technique has several advantages over the gradient-based optimization methods with respect to convergence to the global optimum and the handling of singular arcs and non-differentiable expressions. Furthermore, its implementation is very simple and avoids tedious transformations that may be required by other methods. In MPC, a nonlinear program is solved to adjust the manipulated variables so as to minimize a control objective. The major difficulty in MPC implementation is in the handling of the dynamic constraints. The ICRS/DS method is applied for the control of the CZ crystallization process and is shown to be an attractive alternative to: (1) sequential integration and optimization, (2) the use of finite element/orthogonal collocation to convert the ODEs to algebraic constraints, and (3) successive linearization of the ODEs. (C) 1998 Elsevier Science Ltd. All rights reserved.