Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

A suboptimal solution to the bilinear quadratic regulator problem with infinite final time is studied. The proposed control law is based on the steady-state solution of the state-dependent Riccati equation. A power-series approach of the Riccati equation is presented which results in offline calculations of one Riccati equation and a sequence of Lyapunov equations. Special emphasize is devoted to illustrate the performance of the derived control law applied to the activated sludge process.