Optimal Control of a Batch Reactor Using the Linearized Hamilton-Jacobi-Bellman Equation
Conference contribution, 2012
AbstractIn this work we present an efficient method for solving an optimal control problem for a batch reactor, where a temperature dependent exothermic reaction takes place within a preset duration and within specified temperature bounds. The Hamilton-Jacobi-Bellman (HJB) equation corresponding to the optimal control problem is nonlinear and has infinite boundary conditions due to the state constraints (bounds on temperature and concentration),
which makes it troublesome to solve. However, using a logarithmic transformation, the HJB-equation is transformed into a linear partial differential equation with zero boundary conditions.
Furthermore, the problem can then be solved using variable separation such that the time-
dependent part has an analytical solution and the state dependent part becomes a linear
eigenvalue problem which can readily be solved using standard software.