Optimal control of non-linear chemical reactors via an initial-value Hamiltonian problem

The problem of designing strategies for optimal feedback control of non-linear processes, specially for regulation and set-point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary-value situation for the coupled state–costate system is transformed into an initial-value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on-line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical non-linear chemical reactor model, and compared against suboptimal bilinear–quadratic strategies based on power series expansions. Since state variables calculated from Hamiltonian equations may differ from the values of physical states; the proposed control strategy is suboptimal with respect to the original plant.