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 arc, 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 nondifferentiable 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.